sand is poured into a box so that the box is being filled at the rate of 4 cubic feet per hour . if the empty rectangular box is 7 feet long , 6 feet wide , and 2 feet deep , approximately how many hours does it take to fill the box ?

Explanation: the volume the box is : length * width * depth = 7 * 6 * 2 = 84 cubic feet . 84 cubic feet / 4 cubic feet per hour = 21 hours . it will take 21 hours to fill the box . the answer is b .

<gadget id="calculator">7 * 6</gadget>
<output>42</output>
<gadget id="calculator">42 * 2</gadget>
<output>84</output>
<gadget id="calculator">84 / 4</gadget>
<output>21</output>
<result>21</result>


two trains 111 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 40 km and the other at the rate of 50 kmph . in what time will they be completely clear of each other from the moment they meet ?

Explanation: "t = ( 111 + 165 ) / ( 40 + 50 ) * 18 / 5 t = 11.04 answer : a"

<gadget id="calculator">111 + 165</gadget>
<output>276</output>
<gadget id="calculator">40 + 50</gadget>
<output>90</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">90 * (5/18)</gadget>
<output>25</output>
<gadget id="calculator">276 / 25</gadget>
<output>276/25 = around 11.04</output>
<result>276/25 = around 11.04</result>


a and b walk around a circular track . they start at 8 a . m from the same point in the opposite directions . a and b walk at a speed of 2 rounds per hour and 3 rounds per hour respectively . how many times shall they cross each other before 9 a . m

Explanation: explanation : relative speed = ( 2 + 3 ) = 5 rounds per hour so , they cross each other 5 times in an hour hence , they cross 5 times before 9 a . m answer : option a

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<result>5</result>


10 men and 15 women together can complete a work in 6 days . it takes 100 days for one man alone to complete the same work . how many days will be required for one woman alone to complete the same work ?

Explanation: 1 man ' s 1 day work = 1 / 100 ( 10 men + 15 women ) ' s 1 day work = 1 / 6 15 women ' s 1 day work = ( 1 / 6 - 10 / 100 ) = 1 / 15 1 woman ' s 1 day work = 1 / 225 1 woman alone can complete the work in 225 days . answer : e

multiply(divide(multiply(const_1, 100), subtract(multiply(const_1, 100), multiply(10, 6))), multiply(15, 6))

<gadget id="calculator">1 * 100</gadget>
<output>100</output>
<gadget id="calculator">10 * 6</gadget>
<output>60</output>
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">100 / 40</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">15 * 6</gadget>
<output>90</output>
<gadget id="calculator">(5/2) * 90</gadget>
<output>225</output>
<result>225</result>


in a basket of apples , 12 % of them are rotten and 66 are in good condition . find the total number of apples in the basket .

Explanation: let the total number of apples in the basket be m 12 % of the apples are rotten , and apples in good condition are 66 therefore , according to the question , 88 % of m = 66 88 / 100 × m = 66 m = ( 66 × 100 ) / 88 m = 3 × 25 m = 75 therefore , total number of apples in the basket is 75 . answer : b

divide(66, subtract(const_1, divide(12, const_100)))

<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">1 - (3/25)</gadget>
<output>22/25 = around 0.88</output>
<gadget id="calculator">66 / (22/25)</gadget>
<output>75</output>
<result>75</result>


a piece of cloth cost rs 35 . if the length of the piece would have been 4 m longer and each meter cost re 1 less , the cost would have remained unchanged . how long is the piece ?

Explanation: if length of piece is x and cost per mtr is c , then x * c = 35 or c = 35 / x ( x + 4 ) * ( c - 1 ) = 35 or x * c + 4 c - x - 4 = 35 or 35 + 4 c - x - 4 = 35 4 c - x = 4 4 * ( 35 / x ) - x = 4 x = 10 mtrs answer : b

divide(35, divide(add(4, sqrt(add(multiply(multiply(4, 4), 35), multiply(4, 4)))), multiply(const_2, 4)))

<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 * 35</gadget>
<output>560</output>
<gadget id="calculator">560 + 16</gadget>
<output>576</output>
<gadget id="calculator">576 ** (1/2)</gadget>
<output>24</output>
<gadget id="calculator">4 + 24</gadget>
<output>28</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">28 / 8</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">35 / (7/2)</gadget>
<output>10</output>
<result>10</result>


what is the average of 4 tenths and 5 thousandths ?

Explanation: four tenths = 0.4 five thousandths = 0.005 the average is ( 0.4 + 0.005 ) / 2 = 0.2025 answer : c

divide(add(divide(4, const_10), divide(5, multiply(const_10, const_100))), const_2)

<gadget id="calculator">4 / 10</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">10 * 100</gadget>
<output>1_000</output>
<gadget id="calculator">5 / 1_000</gadget>
<output>1/200 = around 0.005</output>
<gadget id="calculator">(2/5) + (1/200)</gadget>
<output>81/200 = around 0.405</output>
<gadget id="calculator">(81/200) / 2</gadget>
<output>81/400 = around 0.2025</output>
<result>81/400 = around 0.2025</result>


the average weight of a , b and c is 43 kg . if the average weight of a and b be 48 kg and that of b and c be 42 kg , then the weight of b is :

Explanation: "explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 43 x 3 ) = 129 â € ¦ . ( i ) a + b = ( 48 x 2 ) = 96 â € ¦ . ( ii ) b + c = ( 42 x 2 ) = 84 â € ¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 180 â € ¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 51 . b â € ™ s weight = 51 kg . answer e"

subtract(add(multiply(48, const_2), multiply(42, const_2)), multiply(43, const_3))

<gadget id="calculator">48 * 2</gadget>
<output>96</output>
<gadget id="calculator">42 * 2</gadget>
<output>84</output>
<gadget id="calculator">96 + 84</gadget>
<output>180</output>
<gadget id="calculator">43 * 3</gadget>
<output>129</output>
<gadget id="calculator">180 - 129</gadget>
<output>51</output>
<result>51</result>


pipe p can fill a tank in 3 hours , pipe q in 9 hours and pipe r in 18 hours . if all the pipes are open , in how many hours will the tank be filled ?

Explanation: "explanation : part filled by ( p + q + r ) in 1 hour = ( 1 / 3 + 1 / 9 + 1 / 18 ) = 1 / 2 all the three pipes together will fill the tank = 2 / 1 = 2 hours answer a"

inverse(add(divide(const_1, 18), add(divide(const_1, 3), divide(const_1, 9))))

<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 9</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">(1/3) + (1/9)</gadget>
<output>4/9 = around 0.444444</output>
<gadget id="calculator">(1/18) + (4/9)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / (1/2)</gadget>
<output>2</output>
<result>2</result>


if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 25 minutes ?

Explanation: "since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 25 minutes the population increases by 25 x 4 = 100 people . answer . b ."

<gadget id="calculator">60 / 15</gadget>
<output>4</output>
<gadget id="calculator">4 * 25</gadget>
<output>100</output>
<result>100</result>


a monkey ascends a greased pole 10 meters high . he ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute . if this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?

Explanation: the money is climbing 1 meter in 2 min . this pattern will go on till he reaches 10 meters . i mean this will continue for first 8 * 2 = 16 mins . he would have reached 8 meters . after that he will climb 2 meters and he will reach the pole . so total time taken = 16 + 1 = 17 mins . so , asnwer will be c

add(multiply(multiply(const_4, const_2), 2), 1)

<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">16 + 1</gadget>
<output>17</output>
<result>17</result>


the number 35 is equal to the sum of the cubes of two integers . what is the product of those integers ?

Explanation: "2 ^ 3 + 3 ^ 3 = 35 therefore product is 2 * 3 = 6 a"

multiply(floor(power(divide(35, const_2), divide(const_1, const_3))), power(subtract(35, power(floor(power(divide(35, const_2), divide(const_1, const_3))), const_3)), divide(const_1, const_3)))

<gadget id="calculator">35 / 2</gadget>
<output>35/2 = around 17.5</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(35/2) ** (1/3)</gadget>
<output>2**(2/3)*35**(1/3)/2 = around 2.596247</output>
<gadget id="calculator">floor(2**(2/3)*35**(1/3)/2)</gadget>
<output>2</output>
<gadget id="calculator">2 ** 3</gadget>
<output>8</output>
<gadget id="calculator">35 - 8</gadget>
<output>27</output>
<gadget id="calculator">27 ** (1/3)</gadget>
<output>3</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<result>6</result>


fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 22 percent , what is the discount rate on pony jeans ?

Explanation: "let x be the percentage decrease in fox jeans pony jeans = 22 - x ( 15 * x / 100 ) * 3 + ( 18 ( 22 - x ) / 100 ) * 2 = 9 . . . . . . . . . . . given 45 x / 100 + 792 - 36 x / 100 = 9 9 x + 792 / 100 = 9 9 x + 792 = 900 9 x = 108 x = 12 = fox jeans hence pony jeans = 22 - 12 = 10 answer : b"

multiply(subtract(divide(22, const_100), divide(subtract(9, multiply(divide(22, const_100), multiply(18, 2))), subtract(multiply(15, 3), multiply(18, 2)))), const_100)

<gadget id="calculator">22 / 100</gadget>
<output>11/50 = around 0.22</output>
<gadget id="calculator">18 * 2</gadget>
<output>36</output>
<gadget id="calculator">(11/50) * 36</gadget>
<output>198/25 = around 7.92</output>
<gadget id="calculator">9 - (198/25)</gadget>
<output>27/25 = around 1.08</output>
<gadget id="calculator">15 * 3</gadget>
<output>45</output>
<gadget id="calculator">45 - 36</gadget>
<output>9</output>
<gadget id="calculator">(27/25) / 9</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(11/50) - (3/25)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 100</gadget>
<output>10</output>
<result>10</result>


if i walk at 4 km / h , i miss the bus by 10 minutes . if i walk at 5 km / h , i reach 5 minutes before the arrival of the bus . how far i walk to reach the bus stand ?

Explanation: "d = product of speed difference of time / difference of speed d = 4 × 5 / 60 [ 10 − ( − 5 ) / 5 − 4 ] [ here , – ve sign indicates before the schedule time ] ⇒ d = 5 km answer a"

multiply(divide(multiply(4, 5), subtract(5, 4)), divide(add(10, 5), const_60))

<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">5 - 4</gadget>
<output>1</output>
<gadget id="calculator">20 / 1</gadget>
<output>20</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">15 / 60</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">20 * (1/4)</gadget>
<output>5</output>
<result>5</result>


a jogger running at 9 kmph along side a railway track is 260 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?

Explanation: "speed of train relative to jogger = ( 45 – 9 ) km / h = 36 km / h = ( 36 × 5 ⁄ 18 ) m / sec = 10 m / sec distance to be covered = ( 260 + 120 ) m = 380 m . ∴ time taken = ( 380 ⁄ 10 ) sec = 38 sec . answer b"

multiply(multiply(divide(divide(add(260, 120), const_1000), subtract(45, 9)), const_60), const_60)

<gadget id="calculator">260 + 120</gadget>
<output>380</output>
<gadget id="calculator">380 / 1_000</gadget>
<output>19/50 = around 0.38</output>
<gadget id="calculator">45 - 9</gadget>
<output>36</output>
<gadget id="calculator">(19/50) / 36</gadget>
<output>19/1_800 = around 0.010556</output>
<gadget id="calculator">(19/1_800) * 60</gadget>
<output>19/30 = around 0.633333</output>
<gadget id="calculator">(19/30) * 60</gadget>
<output>38</output>
<result>38</result>


mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 2 children and 6 grandchildren , then approximately what percentage of mr . evans estate will each grandchild receive ?

Explanation: 33.33 / 6 = 5.5 answer : c

multiply(divide(divide(divide(const_100, const_3), 6), const_100), const_100)

<gadget id="calculator">100 / 3</gadget>
<output>100/3 = around 33.333333</output>
<gadget id="calculator">(100/3) / 6</gadget>
<output>50/9 = around 5.555556</output>
<gadget id="calculator">(50/9) / 100</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">(1/18) * 100</gadget>
<output>50/9 = around 5.555556</output>
<result>50/9 = around 5.555556</result>


find the quotient when total no . of divisors of 16 ! is divided by right most non - zero digit of 15 !

Explanation: first find the factors of 16 ! and then divide with non zero digit of 15 ! factors of 16 ! prime no below 16 are 2 3 5 7 11 13 now highest power of 2 in 16 ! is 15 3 is 65 is 37 is 211 , is 113 is 1 so no of factors is 16 * 7 * 4 * 3 * 2 * 2 = 5376 now last digit in 15 ! it can be written as 2 ^ 11 * 3 ^ 6 * 5 ^ 3 * 7 ^ 2 * 11 ^ 1 * 13 * 1 5 ^ 3 * 2 ^ 3 gives 0 so remaining is 2 ^ 3 = 8 therefore 5376 / 8 = 672 answer : a

add(subtract(multiply(multiply(16, 15), const_3), const_100), multiply(const_10, const_4))

<gadget id="calculator">16 * 15</gadget>
<output>240</output>
<gadget id="calculator">240 * 3</gadget>
<output>720</output>
<gadget id="calculator">720 - 100</gadget>
<output>620</output>
<gadget id="calculator">10 * 4</gadget>
<output>40</output>
<gadget id="calculator">620 + 40</gadget>
<output>660</output>
<result>660</result>


if the wheel is 14 cm then the number of revolutions to cover a distance of 1408 cm is ?

Explanation: "2 * 22 / 7 * 14 * x = 1408 = > x = 16 answer : a"

divide(1408, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 14))

<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">1 * 10</gadget>
<output>10</output>
<gadget id="calculator">300 + 10</gadget>
<output>310</output>
<gadget id="calculator">310 + 4</gadget>
<output>314</output>
<gadget id="calculator">314 / 100</gadget>
<output>157/50 = around 3.14</output>
<gadget id="calculator">2 * (157/50)</gadget>
<output>157/25 = around 6.28</output>
<gadget id="calculator">(157/25) * 14</gadget>
<output>2_198/25 = around 87.92</output>
<gadget id="calculator">1_408 / (2_198/25)</gadget>
<output>17_600/1_099 = around 16.014559</output>
<result>17_600/1_099 = around 16.014559</result>


calculate the area of a triangle , if the sides of are 65 cm , 60 cm and 25 cm , what is its area ?

Explanation: "the triangle with sides 65 cm , 60 cm and 25 cm is right angled , where the hypotenuse is 65 cm . area of the triangle = 1 / 2 * 60 * 25 = 750 cm 2 answer : b"

<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<gadget id="calculator">30 * 25</gadget>
<output>750</output>
<result>750</result>


the admission charge in a water park is $ 1 by adult and $ 0.75 by child accompanying an adult . how much was there of child with an adult who paid in quite $ 3.25 to have access to the water park ?

Explanation: a = # of adults price for on adult = $ 1.00 e = # of kids price for on kid ( accompanying an adult ) = $ 0.75 t = total ( $ ) $ 3.25 t = price for an adult * a + price for on kid * e 3.25 = $ 1 * a + $ 0.75 * e 3.25 = a + $ 0.75 * e because the kids have to be accompanying by an adult , a = 1 $ 3.25 = 1 + $ 0.75 * e $ 3.25 - 1 = 1 - 1 + $ 0.75 * e $ 2.25 = $ 0.75 * e $ 2.25 / $ 0.75 = ( $ 0.75 * e ) / $ 0.75 3 = e = number of kids accompanying an adult . correct option : c ) 3 kids

subtract(add(subtract(subtract(multiply(multiply(3.25, 1), const_2), const_0_25), const_0_25), 1), const_4)

<gadget id="calculator">3.25 * 1</gadget>
<output>3.25</output>
<gadget id="calculator">3.25 * 2</gadget>
<output>6.5</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">6.5 - (1/4)</gadget>
<output>6.25</output>
<gadget id="calculator">6.25 - (1/4)</gadget>
<output>6</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">7 - 4</gadget>
<output>3</output>
<result>3</result>


the area of a square is 4225 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .

Explanation: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4225 a = 65 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 41 : 130 answer : e"

divide(subtract(sqrt(4225), 24), multiply(sqrt(4225), const_2))

<gadget id="calculator">4_225 ** (1/2)</gadget>
<output>65</output>
<gadget id="calculator">65 - 24</gadget>
<output>41</output>
<gadget id="calculator">65 * 2</gadget>
<output>130</output>
<gadget id="calculator">41 / 130</gadget>
<output>41/130 = around 0.315385</output>
<result>41/130 = around 0.315385</result>


jisha walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked the same number of hours as on the first day , but at the same speed as on the second day . how many miles in total did she walk ?

Explanation: jisha walked 18 miles on the first day , walking 3 miles per hour i . e . total time of walk on day - 1 = 18 / 3 = 6 hours second day time of walk = 6 - 1 = 5 hours and speed = 3 + 1 = 4 miles per hour i . e . distance walked on second day = 5 * 4 = 20 miles third day time of walk = 6 hours and speed = 4 miles per hour i . e . distance walked on second day = 6 * 4 = 24 miles total distance travelled on three days = 18 + 20 + 24 = 62 answer : option e

add(multiply(speed(18, 3), add(const_1, 3)), add(18, multiply(subtract(speed(18, 3), const_1), add(const_1, 3))))

<gadget id="calculator">18 / 3</gadget>
<output>6</output>
<gadget id="calculator">1 + 3</gadget>
<output>4</output>
<gadget id="calculator">6 * 4</gadget>
<output>24</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">18 + 20</gadget>
<output>38</output>
<gadget id="calculator">24 + 38</gadget>
<output>62</output>
<result>62</result>


the spherical ball of lead 3 cm in diameter is melted and recast into 3 spherical balls . the diameters of two of these are 1 1 / 2 cm and 2 cm respectively . the diameter of third ball is ?

Explanation: "4 / 3 π * 3 * 3 * 3 = 4 / 3 π [ ( 3 / 2 ) 3 + 23 + r 3 ] r = 1.25 d = 2.5 answer : b"

multiply(power(subtract(subtract(power(divide(3, 1), 3), power(divide(add(1, divide(1, 1)), 1), 3)), 1), inverse(3)), 1)

<gadget id="calculator">3 / 1</gadget>
<output>3</output>
<gadget id="calculator">3 ** 3</gadget>
<output>27</output>
<gadget id="calculator">1 / 1</gadget>
<output>1</output>
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 / 1</gadget>
<output>2</output>
<gadget id="calculator">2 ** 3</gadget>
<output>8</output>
<gadget id="calculator">27 - 8</gadget>
<output>19</output>
<gadget id="calculator">19 - 1</gadget>
<output>18</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">18 ** (1/3)</gadget>
<output>18**(1/3) = around 2.620741</output>
<gadget id="calculator">(18**(1/3)) * 1</gadget>
<output>18**(1/3) = around 2.620741</output>
<result>18**(1/3) = around 2.620741</result>


ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 2 percent and the mobile phone at a profit of 10 percent . overall he make a .

Explanation: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 2 / 100 ) = 15000 - 300 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 300 + 800 = rs . 500 as this is positive , an overall profit of rs . 500 was made . answer : c"

subtract(add(multiply(15000, subtract(const_1, divide(2, const_100))), multiply(8000, add(const_1, divide(10, const_100)))), add(15000, 8000))

<gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">1 - (1/50)</gadget>
<output>49/50 = around 0.98</output>
<gadget id="calculator">15_000 * (49/50)</gadget>
<output>14_700</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">8_000 * (11/10)</gadget>
<output>8_800</output>
<gadget id="calculator">14_700 + 8_800</gadget>
<output>23_500</output>
<gadget id="calculator">15_000 + 8_000</gadget>
<output>23_000</output>
<gadget id="calculator">23_500 - 23_000</gadget>
<output>500</output>
<result>500</result>


on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 28 inch from the base of the mountain . how many km is he from the base of the mountain ?

Explanation: "explanation : since 312 inch = 136 km so 1 inch = 136 / 312 km so 28 inch = ( 136 ã — 28 ) / 312 = 12.2 km answer : b"

<gadget id="calculator">28 * 136</gadget>
<output>3_808</output>
<gadget id="calculator">3_808 / 312</gadget>
<output>476/39 = around 12.205128</output>
<result>476/39 = around 12.205128</result>


positive integer y is 50 percent of 25 percent of positive integer x , and y percent of x equals 100 . what is the value of y ?

Explanation: y = 50 % of 25 % 0 f x = x / 8 and y / 100 of x = 100 y / 100 * 8 y = 100 y = 125 answer - b

multiply(multiply(divide(50, 100), divide(25, const_100)), const_1000)

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/2) * (1/4)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 1_000</gadget>
<output>125</output>
<result>125</result>


in simple interest what sum amounts of rs . 1120 / - in 4 years and rs . 1200 / - in 5 years ?

Explanation: for 1 year interest = 1200 - 1120 = 80 for 4 year 320 then sum = 1120 - 320 = 800 answer : c

subtract(1120, multiply(4, subtract(1200, 1120)))

<gadget id="calculator">1_200 - 1_120</gadget>
<output>80</output>
<gadget id="calculator">4 * 80</gadget>
<output>320</output>
<gadget id="calculator">1_120 - 320</gadget>
<output>800</output>
<result>800</result>


the current of a stream runs at the rate of 4 kmph . a boat goes 6 km and back to the starting point in 2 hours , then find the speed of the boat in still water ?

Explanation: s = 4 m = x ds = x + 4 us = x - 4 6 / ( x + 4 ) + 6 / ( x - 4 ) = 2 x = 8 answer : c

<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<result>8</result>


cathy and jim begin running at the same time and they start at the same place on a straight path . cathy runs at 10 miles per hour , and jim runs at 6 miles per hour . after 18 minutes , cathy stops to stretch . if it takes cathy 27 minutes to stretch and jim continues to run during this time , how many minutes will it take cathy to catch up to jim ?

Explanation: in 18 minutes , cathy runs 3 miles . in 45 minutes , jim runs 4.5 miles . cathy can catch jim at a rate of 4 miles per hour . since jim is ahead by 1.5 miles , it will take cathy 1.5 / 4 hours = 22.5 minutes to catch jim . the answer is c .

divide(subtract(multiply(6, divide(add(18, 27), const_60)), multiply(10, divide(18, const_60))), divide(subtract(10, 6), const_60))

<gadget id="calculator">18 + 27</gadget>
<output>45</output>
<gadget id="calculator">45 / 60</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">6 * (3/4)</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">18 / 60</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">10 * (3/10)</gadget>
<output>3</output>
<gadget id="calculator">(9/2) - 3</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">10 - 6</gadget>
<output>4</output>
<gadget id="calculator">4 / 60</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(3/2) / (1/15)</gadget>
<output>45/2 = around 22.5</output>
<result>45/2 = around 22.5</result>


the speed of a car is 65 km in the first hour and 45 km in the second hour . what is the average speed of the car ?

Explanation: "s = ( 65 + 45 ) / 2 = 55 kmph answer : b"

<gadget id="calculator">65 + 45</gadget>
<output>110</output>
<gadget id="calculator">110 / 2</gadget>
<output>55</output>
<result>55</result>


set x consists of all two - digit primes and set y consists of all positive multiples of 4 less than 100 . if the two sets are combined into one , what will be the range of the new set ?

Explanation: "set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 4 , 8 , 12 , . . . . . . . . . . . . . . . , 88 , 92 , 96 } combining two sets , say set z set z = { 4,8 , 11 , 12,13 , 17 , . . . . . . . . . . . . . . . . . . . , 83 , 88 , 89 , 92 , 96 , 97 } range = max value - min value range ( z ) = 97 - 4 = 93 oa b is the answer ."

<gadget id="calculator">100 - 3</gadget>
<output>97</output>
<gadget id="calculator">97 - 4</gadget>
<output>93</output>
<result>93</result>


car z travels 50 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?

Explanation: "the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 50 miles / hour , the car will run 40 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 40 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 40 miles / gallon * 10 gallons = 400 miles . answer c ."

multiply(multiply(subtract(const_1, divide(20, const_100)), 50), 10)

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 50</gadget>
<output>40</output>
<gadget id="calculator">40 * 10</gadget>
<output>400</output>
<result>400</result>


30 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?

Explanation: "i came up with ( e ) 75 think of 100 people total : from the first fact , 30 of these are women with fair hair . from the second fact , these 20 women make up 40 % of the total fair haired population . we can then make a ratio of 60 : 40 fair haired men to fair haired women . this means that ( 60 / 40 ) * 30 equals the number of fair haired men , which is 45 men with fair hair . add this 45 to the 30 women and get 75 fair haired men and women out of 100 total men and women . 75 % e"

<gadget id="calculator">30 / 40</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 100</gadget>
<output>75</output>
<result>75</result>


the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 255 , then the mean profit for the last 15 days would be

Explanation: "average would be : 350 = ( 255 + x ) / 2 on solving , x = 445 . answer : b"

divide(subtract(multiply(30, 350), multiply(15, 255)), 15)

<gadget id="calculator">30 * 350</gadget>
<output>10_500</output>
<gadget id="calculator">15 * 255</gadget>
<output>3_825</output>
<gadget id="calculator">10_500 - 3_825</gadget>
<output>6_675</output>
<gadget id="calculator">6_675 / 15</gadget>
<output>445</output>
<result>445</result>


a rectangle the length of which is 8 inches and the width of which is 6 inches is made up 48 1 inch by 1 inch squares . through how many of the squares does a diagonal of the rectangle pass ?

Explanation: 1 ) if the two sides are co - prime , sum of sides - 1 . . 2 ) and if not co - prime , sum of sides - hcf of sides . . the difference is related to the diagonal passing through a vertex of squares at some place . . here 6 and 8 are not co - primes , so ans = 6 + 8 − hcf ( 6,8 ) = 14 − 2 = 12 answer : d

<gadget id="calculator">8 + 6</gadget>
<output>14</output>
<gadget id="calculator">14 - 2</gadget>
<output>12</output>
<result>12</result>


if x + y = 3 and x 2 y 3 + y 2 x 3 = 27 , what is the value of xy ?

Explanation: "xy = 3 as x + y = 3 x 2 y 3 + y 2 x 3 = 27 x 2 y 2 ( y + x ) = 27 substituting x + y x 2 y 2 = 9 xy = 3 answer : c"

<gadget id="calculator">27 / 3</gadget>
<output>9</output>
<gadget id="calculator">9 ** (1/2)</gadget>
<output>3</output>
<result>3</result>


a 600 meter long train crosses a signal post in 40 seconds . how long will it take to cross a 7.2 kilometer long bridge , at the same speed ?

Explanation: "s = 600 / 40 = 15 mps s = 7200 / 15 = 480 sec = 8 min . answer : c"

divide(divide(multiply(7.2, const_1000), speed(600, 40)), const_60)

<gadget id="calculator">7.2 * 1_000</gadget>
<output>7_200</output>
<gadget id="calculator">600 / 40</gadget>
<output>15</output>
<gadget id="calculator">7_200 / 15</gadget>
<output>480</output>
<gadget id="calculator">480 / 60</gadget>
<output>8</output>
<result>8</result>


a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 100 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?

Explanation: "many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 100 kilometers per hour is 1 / 100 hours = 3,600 / 100 seconds = 36 seconds ; time to cover this distance at regular speed is 36 + 2 = 38 seconds = 38 / 3,600 hours = 4 / 379 hours ; so , we get that to cover 1 kilometer 1 / ( 4 / 379 ) hours is needed - - > regular speed 94.7 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : e ."

divide(1, divide(add(multiply(const_3600, divide(1, 100)), 2), const_3600))

<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">3_600 * (1/100)</gadget>
<output>36</output>
<gadget id="calculator">36 + 2</gadget>
<output>38</output>
<gadget id="calculator">38 / 3_600</gadget>
<output>19/1_800 = around 0.010556</output>
<gadget id="calculator">1 / (19/1_800)</gadget>
<output>1_800/19 = around 94.736842</output>
<result>1_800/19 = around 94.736842</result>


a can do a piece of work in 5 hours ; b and c together can do it in 3 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ?

Explanation: "a ' s 1 hour ' s work = 1 / 5 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( a + c ) ' s 1 hour ' s work = 1 / 2 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 5 + 1 / 3 ) = 8 / 15 . b ' s 1 hour ' s work = ( 8 / 15 - 1 / 2 ) = 1 / 30 . therefore a alone will take 30 hours to do the work . a"

divide(const_1, subtract(divide(const_1, 3), subtract(divide(const_1, 2), divide(const_1, 5))))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/2) - (1/5)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(1/3) - (3/10)</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">1 / (1/30)</gadget>
<output>30</output>
<result>30</result>


lally ' s internet provider offers unlimited traffic which costs $ 0.5 per day charged off at 12 a . m . the service is discontinued when client ' s debt exceeds $ 5 . if today in the morning lally makes a payment of $ 7 , for how many days , including today , will she be connected to the internet without any additional payments , given her initial balance was $ 0 ?

Explanation: day 0 - payment of $ 7 is made in the morning ( after 12 am midnight ) day 1 onwards ( after 12 am midnight ) internet service will begin and will run for 7 * 2 = 14 days i . e . at the end of day 15 balance will be zero . now lally can still use the internet till her debt reaches $ 5 which means total of 5 * 2 = 10 days . now the question states for how many days , including today , will she be connected to the internet without any additional payments i . e . we will have to include day 0 also in our final answer . therefore total no . of days = 1 + 14 + 10 = 25 = c

subtract(multiply(12, 5), multiply(multiply(7, 0.5), const_10))

<gadget id="calculator">12 * 5</gadget>
<output>60</output>
<gadget id="calculator">7 * 0.5</gadget>
<output>3.5</output>
<gadget id="calculator">3.5 * 10</gadget>
<output>35</output>
<gadget id="calculator">60 - 35</gadget>
<output>25</output>
<result>25</result>


a retailer bought a machine at a wholesale price of $ 108 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?

Explanation: "my solution : wholesale price = 108 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 108 + 1 / 5 ( 108 ) x = 144 ; answer : e"

divide(multiply(add(108, divide(multiply(108, 20), const_100)), const_100), multiply(multiply(const_3, const_3), 10))

<gadget id="calculator">108 * 20</gadget>
<output>2_160</output>
<gadget id="calculator">2_160 / 100</gadget>
<output>108/5 = around 21.6</output>
<gadget id="calculator">108 + (108/5)</gadget>
<output>648/5 = around 129.6</output>
<gadget id="calculator">(648/5) * 100</gadget>
<output>12_960</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">12_960 / 90</gadget>
<output>144</output>
<result>144</result>


in one day , juan sends keith 8 times as many messages as he sends laurence , and laurence sends missy 4.5 times as many messages as he receives from juan . if missy received 18 messages from laurence , how many messages does keith receive from juan ?

Explanation: juan - - > laurence = x messages ; juan - - > keith = 8 x messages ( juan sends keith eight times as many messages as he sends laurence ) ; laurence - - > missy = 4.5 x = 18 ( laurence sends missy 4.5 times as many messages as he receives from juan ) . 4.5 x = 18 - - > x = 4 - - > 8 x = 32 . answer : c .

<gadget id="calculator">18 / 4.5</gadget>
<output>4</output>
<gadget id="calculator">4 * 8</gadget>
<output>32</output>
<result>32</result>


edward earns $ 7.00 per hour for the first 40 hours he works per week , and twice this rate for overtime . if michael earned $ 210 last week , how many hours did he work ?

Explanation: $ 7 * 40 + $ 12 * x = $ 210 - - > x = 5 hours . total working hours = 40 + 5 = 45 answer : c .

add(divide(subtract(multiply(7, 40), 210), multiply(7, const_2)), 40)

<gadget id="calculator">7 * 40</gadget>
<output>280</output>
<gadget id="calculator">280 - 210</gadget>
<output>70</output>
<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">70 / 14</gadget>
<output>5</output>
<gadget id="calculator">5 + 40</gadget>
<output>45</output>
<result>45</result>


i bought two books ; for rs . 470 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?

Explanation: "x * ( 85 / 100 ) = ( 470 - x ) 119 / 100 x = 274.17 answer : a"

divide(multiply(470, add(const_100, 19)), add(subtract(const_100, 15), add(const_100, 19)))

<gadget id="calculator">100 + 19</gadget>
<output>119</output>
<gadget id="calculator">470 * 119</gadget>
<output>55_930</output>
<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">85 + 119</gadget>
<output>204</output>
<gadget id="calculator">55_930 / 204</gadget>
<output>1_645/6 = around 274.166667</output>
<result>1_645/6 = around 274.166667</result>


18 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?

Explanation: "1 women ' s 1 day work = 1 / 126 1 child ' s 1 day work = 1 / 140 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 126 + 10 / 140 ) = 1 / 9 5 women and 10 children will complete the work in 9 days . answer : d"

inverse(add(divide(5, multiply(18, 7)), divide(18, multiply(18, 14))))

<gadget id="calculator">18 * 7</gadget>
<output>126</output>
<gadget id="calculator">5 / 126</gadget>
<output>5/126 = around 0.039683</output>
<gadget id="calculator">18 * 14</gadget>
<output>252</output>
<gadget id="calculator">18 / 252</gadget>
<output>1/14 = around 0.071429</output>
<gadget id="calculator">(5/126) + (1/14)</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">1 / (1/9)</gadget>
<output>9</output>
<result>9</result>


when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.45 , what is the value of y ?

Explanation: "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.45 and remainder is 9 so . 45 x y = 9 hence y = 20 ans d"

<gadget id="calculator">floor(96.45)</gadget>
<output>96</output>
<gadget id="calculator">96.45 - 96</gadget>
<output>0.45</output>
<gadget id="calculator">9 / 0.45</gadget>
<output>20</output>
<result>20</result>


an employee ’ s annual salary was increased $ 5000 . if her new annual salary now equals $ 25000 what was the percent increase ?

Explanation: new annual salary = $ 25000 salary increase = $ 5000 . original salary = $ 25000 - $ 5000 . = $ 20000 % increase = ( $ 15000 / $ 75000 ) * 100 = 80 % hence b .

multiply(divide(subtract(25000, 5000), 25000), const_100)

<gadget id="calculator">25_000 - 5_000</gadget>
<output>20_000</output>
<gadget id="calculator">20_000 / 25_000</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 100</gadget>
<output>80</output>
<result>80</result>


of the 200 employees in a certain company , 30 percent will be relocated to city x and the remaining 70 percent will be relocated to city y . however , 40 percent of the employees prefer city y and 60 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ?

Explanation: 120 prefer x ( group 1 ) ; 80 prefer y ( group 2 ) . city y needs 140 people : letall 80 who prefer y ( entire group 2 ) be relocated there , the rest 60 will be those who prefer x from group 1 ; city x needs 60 people : 120 - 60 = 60 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 80 + 60 = 140 . answer : c .

<gadget id="calculator">40 * 2</gadget>
<output>80</output>
<gadget id="calculator">80 + 60</gadget>
<output>140</output>
<result>140</result>


the arithmetic mean and standard deviation of a certain normal distribution are 14.5 and 1.7 , respectively . what value is exactly 2 standard deviations less than the mean ?

Explanation: "mean = 14.5 two standard deviations is 1.7 + 1.7 = 3.4 there could be two calues for this . mean + two standard deviations = 17.9 mean - two standard deviations = 11.1 answer choice has 11.1 and so c is the answer ."

<gadget id="calculator">2 * 1.7</gadget>
<output>3.4</output>
<gadget id="calculator">14.5 - 3.4</gadget>
<output>11.1</output>
<result>11.1</result>


what is the x - intercept of a line that passes through the point ( 3 , 4 ) and has a slope of 2 ?

Explanation: first , plot the point ( 3 , 4 ) on a graph . a slope of 2 means “ up 2 , over 1 , ” so plot this point on a graph , too . here ’ s the resulting graph : y over 1 up 2 ( 1 , 0 ) ( 2 , 2 ) ( 3 , 4 ) ( 4 , 6 ) x the line passes through the x - axis at 1 , making the correct answer d ) 1

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 - 4</gadget>
<output>2</output>
<gadget id="calculator">2 / 2</gadget>
<output>1</output>
<result>1</result>


raja spends 35 % of his monthly income on household items , 20 % of his monthly income on buying cloths , 5 % of his monthly income on medicines and saves the remaining amount which is rs . 15000 . find his monthly income .

Explanation: savings 40 % - 15000 expenditure 60 % - 22500 total - 37500 answer : c

divide(15000, subtract(const_1, add(add(divide(35, const_100), divide(20, const_100)), divide(5, const_100))))

<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(7/20) + (1/5)</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(11/20) + (1/20)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">15_000 / (2/5)</gadget>
<output>37_500</output>
<result>37_500</result>


what least number should be subtracted from 13600 such that the remainder is divisible by 87 ?

Explanation: "13600 ÷ 87 = 156 , remainder = 28 hence 28 is the least number which can be subtracted from 13600 such that the remainder is divisible by 87 answer is c"

<gadget id="calculator">13_600 % 87</gadget>
<output>28</output>
<result>28</result>


list k consists of 12 consecutive integers . if - 5 is the least integer in list k , what is the range of the positive integers in list k ?

Explanation: "answer = a = 5 if least = - 5 , then largest = 6 range = 6 - 1 = 5"

subtract(subtract(subtract(12, 5), const_1), const_1)

<gadget id="calculator">12 - 5</gadget>
<output>7</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<result>5</result>


a dishonest dealer professes to sell goods at the cost price but uses a weight of 920 grams per kg , what is his percent ?

Explanation: "920 - - - 80 100 - - - ? = > 8.7 % answer : e"

subtract(multiply(divide(const_100, 920), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100)

<gadget id="calculator">100 / 920</gadget>
<output>5/46 = around 0.108696</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">(5/46) * 1_000</gadget>
<output>2_500/23 = around 108.695652</output>
<gadget id="calculator">(2_500/23) - 100</gadget>
<output>200/23 = around 8.695652</output>
<result>200/23 = around 8.695652</result>


a case contains c cartons . each carton contains b boxes , and each box contains 600 paper clips . how many paper clips are contained in 2 cases ?

Explanation: 2 cases * c cartons / case * b boxes / carton * 600 clips / box = 1200 bc paper clips the answer is c .

<gadget id="calculator">2 * 600</gadget>
<output>1_200</output>
<result>1_200</result>


an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 10000 people who applied for the army and 350 were finally selected , what was the value of n ?

Explanation: "fastly i reduce 60 % till it gets closer to our required 2000 candidates step ( 1 ) 40000 accepted . step ( 2 ) another 40 % of 40000 = 16000 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 16000 = 8000 step ( 4 ) 50 % of 8000 = 4000 step ( 5 ) 50 % of 4000 = 2000 step ( 6 ) 50 % of 2000 = 1000 step ( 7 ) 50 % of 1000 = 500 last step of accepting 70 % of 500 = 350 ( our target ) total 8 steps required . ans d"

add(add(const_2, add(const_1, const_4)), const_2)

<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">2 + 5</gadget>
<output>7</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<result>9</result>


a ladder 30 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 10 feet from the base of the wall . if the top of the ladder slips down 5 feet , how many feet will the bottom of the ladder slip ?

Explanation: 30 ^ 2 - 10 ^ 2 = 800 it means that the height is equal to 28.28 . since the top of the ladder slips down 5 feet , then the height of the wall = 28.28 - 5 = 23.28 the bottom = sqrt ( 30 ^ 2 - 23.28 ^ 2 ) = sqrt ( 900 - 541.95 ) = 18.92 ans is c

sqrt(subtract(power(30, const_2), power(subtract(sqrt(subtract(power(30, const_2), power(10, const_2))), 5), const_2)))

<gadget id="calculator">30 ** 2</gadget>
<output>900</output>
<gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">900 - 100</gadget>
<output>800</output>
<gadget id="calculator">800 ** (1/2)</gadget>
<output>20*sqrt(2) = around 28.284271</output>
<gadget id="calculator">(20*sqrt(2)) - 5</gadget>
<output>-5 + 20*sqrt(2) = around 23.284271</output>
<gadget id="calculator">(-5 + 20*sqrt(2)) ** 2</gadget>
<output>(-5 + 20*sqrt(2))**2 = around 542.157288</output>
<gadget id="calculator">900 - ((-5 + 20*sqrt(2))**2)</gadget>
<output>900 - (-5 + 20*sqrt(2))**2 = around 357.842712</output>
<gadget id="calculator">(900 - (-5 + 20*sqrt(2))**2) ** (1/2)</gadget>
<output>sqrt(900 - (-5 + 20*sqrt(2))**2) = around 18.916731</output>
<result>sqrt(900 - (-5 + 20*sqrt(2))**2) = around 18.916731</result>


if 3 workers collect 48 kg of cotton in 4 days , how many kg of cotton will 9 workers collect in 2 days ?

Explanation: ( 3 * 4 ) / 48 = ( 9 * 2 ) / x x = 72 kg answer : c

multiply(multiply(divide(divide(48, 3), 4), 9), 2)

<gadget id="calculator">48 / 3</gadget>
<output>16</output>
<gadget id="calculator">16 / 4</gadget>
<output>4</output>
<gadget id="calculator">4 * 9</gadget>
<output>36</output>
<gadget id="calculator">36 * 2</gadget>
<output>72</output>
<result>72</result>


Explanation: "according to order of operations , inner brackets first . hence | 8 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 8 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 8 + 72 | - | 5 - 11 | = | 80 | - | - 6 | = 80 - 6 = 74 correct answer b ) 74"

subtract(subtract(8, multiply(8, subtract(3, 12))), negate(subtract(5, 11)))

<gadget id="calculator">3 - 12</gadget>
<output>-9</output>
<gadget id="calculator">8 * (-9)</gadget>
<output>-72</output>
<gadget id="calculator">8 - (-72)</gadget>
<output>80</output>
<gadget id="calculator">5 - 11</gadget>
<output>-6</output>
<gadget id="calculator">-(-6)</gadget>
<output>6</output>
<gadget id="calculator">80 - 6</gadget>
<output>74</output>
<result>74</result>


heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 25 litres of tomato juice ?

Explanation: answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . â ‡ ’ â ‡ ’ 10 % ( 25 ) = 80 % ( x ) â ‡ ’ â ‡ ’ x = 3.125 liters . answer : b

divide(multiply(divide(subtract(const_100, 90), const_100), 25), divide(subtract(const_100, 20), const_100))

<gadget id="calculator">100 - 90</gadget>
<output>10</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 25</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(5/2) / (4/5)</gadget>
<output>25/8 = around 3.125</output>
<result>25/8 = around 3.125</result>


triathlete dan runs along a 4 - mile stretch of river and then swims back along the same route . if dan runs at a rate of 10 miles per hour and swims at a rate of 6 miles per hour , what is his average rate for the entire trip in miles per minute ?

Explanation: "dan travels 8 miles round trip . running part : ( 4 / 10 * 60 = 24 minutes ) swimming part : ( 4 / 6 * 60 = 40 minutes ) 8 miles in ( 24 + 40 ) minutes 8 / 64 = 1 / 8 mile per minute answer : 1 / 8 mile per minute"

divide(add(4, 4), add(multiply(divide(4, 6), const_60), multiply(divide(4, 10), const_60)))

<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">4 / 6</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 60</gadget>
<output>40</output>
<gadget id="calculator">4 / 10</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 60</gadget>
<output>24</output>
<gadget id="calculator">40 + 24</gadget>
<output>64</output>
<gadget id="calculator">8 / 64</gadget>
<output>1/8 = around 0.125</output>
<result>1/8 = around 0.125</result>


at a small company , 58 percent of the employees are women , and 60 percent of the employees are married . if 2 / 3 of the men are single , what fraction of the women are married ?

Explanation: lets take total employees are 100 . given that , total women = 58 and total married = 60 . total men = 100 - 58 = 42 and single men = 2 / 3 * 42 = 28 . married men = total men - single men = 42 - 28 = 14 . married women = total married - married men = 60 - 14 = 46 . fraction of women are married = married women / total women = 46 / 58 = 23 / 29 . ans c

divide(subtract(divide(60, const_100), multiply(subtract(const_1, divide(58, const_100)), subtract(const_1, divide(2, 3)))), divide(58, const_100))

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">58 / 100</gadget>
<output>29/50 = around 0.58</output>
<gadget id="calculator">1 - (29/50)</gadget>
<output>21/50 = around 0.42</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(21/50) * (1/3)</gadget>
<output>7/50 = around 0.14</output>
<gadget id="calculator">(3/5) - (7/50)</gadget>
<output>23/50 = around 0.46</output>
<gadget id="calculator">(23/50) / (29/50)</gadget>
<output>23/29 = around 0.793103</output>
<result>23/29 = around 0.793103</result>


if 10 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?

Explanation: "explanation : let the required no of hectares be x . then men - - - hectares - - - days 10 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 10 * 30 / 24 * 80 x = 360 answer : c"

divide(multiply(36, 30), divide(multiply(10, 24), 80))

<gadget id="calculator">36 * 30</gadget>
<output>1_080</output>
<gadget id="calculator">10 * 24</gadget>
<output>240</output>
<gadget id="calculator">240 / 80</gadget>
<output>3</output>
<gadget id="calculator">1_080 / 3</gadget>
<output>360</output>
<result>360</result>


a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 20 km in 10 hours . how much time he would have saved if the direction of tide has not changed ?

Explanation: "explanation : he covered 5 km in 1 hour , so he might cover 20 km in 4 hours . but he took 10 hours . he would have saved 10 – 4 = 6 hours . answer : d"

<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">10 - 4</gadget>
<output>6</output>
<result>6</result>


a couple who own an appliance store discover that if they advertise a sales discount of 10 % on every item in the store , at the end of one month the number of total items sold increases 15 % . their gross income from sales for one month increases by what percent ?

Explanation: "let p be the original price and let x be the number of items sold originally . the original income is p * x . after the changes , the income is 0.9 p * 1.15 x = 1.035 * ( p * x ) , an increase of 3.5 % . the answer is c ."

subtract(subtract(15, 10), divide(15, 10))

<gadget id="calculator">15 - 10</gadget>
<output>5</output>
<gadget id="calculator">15 / 10</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">5 - (3/2)</gadget>
<output>7/2 = around 3.5</output>
<result>7/2 = around 3.5</result>


if a man lost 8 % by selling oranges at the rate of 25 a rupee at how many a rupee must he sell them to gain 25 % ?

Explanation: "92 % - - - - 25 125 % - - - - ? 92 / 125 * 25 = 18.4 answer : c"

divide(multiply(subtract(const_100, 8), 25), add(const_100, 25))

<gadget id="calculator">100 - 8</gadget>
<output>92</output>
<gadget id="calculator">92 * 25</gadget>
<output>2_300</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">2_300 / 125</gadget>
<output>92/5 = around 18.4</output>
<result>92/5 = around 18.4</result>


express a speed of 90 kmph in meters per second ?

Explanation: "90 * 5 / 18 = 25 mps answer : e"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(5/18) * 90</gadget>
<output>25</output>
<result>25</result>


together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many w hours would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ?

Explanation: "say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the job w in 44 hours . answer : c ."

it can not be determined from the information above .

divide(const_1, divide(add(divide(const_1, 4), divide(const_1, 11)), 15))

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 11</gadget>
<output>1/11 = around 0.090909</output>
<gadget id="calculator">(1/4) + (1/11)</gadget>
<output>15/44 = around 0.340909</output>
<gadget id="calculator">(15/44) / 15</gadget>
<output>1/44 = around 0.022727</output>
<gadget id="calculator">1 / (1/44)</gadget>
<output>44</output>
<result>44</result>


a man traveled from the village to the post - office at the rate of 25 kmph and walked back at the rate of 4 kmph . if the whole journey took 5 hours 48 minutes , find the distance of the post - office from the village ?

Explanation: explanation : average speed = , here a = 25 b = 4 = 2 x 25 x 4 / ( 25 + 4 ) = 200 / 29 km / hr . distance covered in 5 hours 48 minutes = speed x time = ( 200 / 29 ) x ( 29 / 5 ) distance covered in 5 hours 48 minutes = 40 kms . distance of the post office from the village = ( 40 / 2 ) = 20 km . answer : c

divide(multiply(divide(multiply(multiply(const_2, 25), 4), add(25, 4)), divide(add(25, 4), 5)), const_2)

<gadget id="calculator">2 * 25</gadget>
<output>50</output>
<gadget id="calculator">50 * 4</gadget>
<output>200</output>
<gadget id="calculator">25 + 4</gadget>
<output>29</output>
<gadget id="calculator">200 / 29</gadget>
<output>200/29 = around 6.896552</output>
<gadget id="calculator">29 / 5</gadget>
<output>29/5 = around 5.8</output>
<gadget id="calculator">(200/29) * (29/5)</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>20</result>


a bag contains 21 toys numbered 1 to 21 . a toy is drawn and then another toy is drawn without replacement . find the probability that both toys will show even numbers .

Explanation: since there are 10 even numbers in the given range , the probability that the first toy shows an even number = 10 / 21 since the toy is not replaced , there are now 9 even numbered toys and total 20 toys left . hence , probability that the second toy shows an even number = 9 / 20 . required probability = 10 / 21 x 9 / 20 = 9 / 42 . answer : b

multiply(divide(subtract(floor(divide(21, const_2)), const_1), subtract(21, const_1)), divide(floor(divide(21, const_2)), 21))

<gadget id="calculator">21 / 2</gadget>
<output>21/2 = around 10.5</output>
<gadget id="calculator">floor(21/2)</gadget>
<output>10</output>
<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">21 - 1</gadget>
<output>20</output>
<gadget id="calculator">9 / 20</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">10 / 21</gadget>
<output>10/21 = around 0.47619</output>
<gadget id="calculator">(9/20) * (10/21)</gadget>
<output>3/14 = around 0.214286</output>
<result>3/14 = around 0.214286</result>


trapezoid jklm in the x - y plane has coordinates j = ( – 2 , – 4 ) , k = ( – 2 , 1 ) , l = ( 6 , 7 ) , and m = ( 6 , – 4 ) . what is its perimeter ?

Explanation: "this one may look challenging initially , but all kinds of simplifying tricks . first of all , j & k have the same x - coordinate , so that ’ s a vertical segment , and the length is jk = 1 – ( – 4 ) = 5 . l & m also have the same x - coordinate , so that ’ s also a vertical segment , and the length is lm = 7 – ( – 4 ) = 11 . j & m have the same y - coordinate , so that ’ s also a horizontal segment , and the length is jm = 6 – ( – 2 ) = 8 . right there , we have the lengths of three of the four sides . the last side to find is kl . from k = ( – 2 , 1 ) , we have to go over 8 and up 6 to get to l = ( 6 , 7 ) , so 6 and 8 the legs of the right triangle , and kl is the hypotenuse . we recognize another common pythagorean triplet — ( 6 , 8 , 10 ) , which is a multiple of the ( 3 , 4 , 5 ) triplet . thus , without further calculations , we immediately know kl = 10 . perimeter = jk + kl + lm + jm = 5 + 10 + 11 + 8 = 34 answer = a"

<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">2 + 6</gadget>
<output>8</output>
<gadget id="calculator">15 + 8</gadget>
<output>23</output>
<gadget id="calculator">7 + 4</gadget>
<output>11</output>
<gadget id="calculator">23 + 11</gadget>
<output>34</output>
<result>34</result>


a tradesman by means of his false balance defrauds to the extent of 20 % ? in buying goods as well as by selling the goods . what percent does he gain on his outlay ? a . 20 % b . 45 %

Explanation: g % = 20 + 20 + ( 20 * 20 ) / 100 = 44 % answer : c

add(add(20, 20), divide(multiply(20, 20), const_100))

<gadget id="calculator">20 + 20</gadget>
<output>40</output>
<gadget id="calculator">20 * 20</gadget>
<output>400</output>
<gadget id="calculator">400 / 100</gadget>
<output>4</output>
<gadget id="calculator">40 + 4</gadget>
<output>44</output>
<result>44</result>


a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability e that all 3 jellybeans removed from the bag are blue ?

Explanation: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability e = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 2 / 19 answer : option b"

divide(choose(10, 3), choose(add(10, 10), 3))

<gadget id="calculator">binomial(10, 3)</gadget>
<output>120</output>
<gadget id="calculator">10 + 10</gadget>
<output>20</output>
<gadget id="calculator">binomial(20, 3)</gadget>
<output>1_140</output>
<gadget id="calculator">120 / 1_140</gadget>
<output>2/19 = around 0.105263</output>
<result>2/19 = around 0.105263</result>


a train 50 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?

Explanation: "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 50 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 900 x = 25 kmph answer is b"

subtract(divide(divide(50, 6), const_0_2778), 5)

<gadget id="calculator">50 / 6</gadget>
<output>25/3 = around 8.333333</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(25/3) / (5/18)</gadget>
<output>30</output>
<gadget id="calculator">30 - 5</gadget>
<output>25</output>
<result>25</result>


on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with 5 times the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.80 per glass on the first day , what was the price per glass on the second day ?

Explanation: on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 5 units of water was used to make 6 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 6 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 6 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 6 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.8 = 6 * x - - > x = $ 0.27 . answer : b .

<gadget id="calculator">0.8 / 3</gadget>
<output>0.266667</output>
<result>0.266667</result>


the average of 11 10 prime numbers which are odd is ?

Explanation: explanation : sum of first 11 prime no . which are odd = 195 average = 195 / 11 = 17.72 answer : a

add(divide(divide(11, const_0_33), const_2), const_1)

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">11 / (1/3)</gadget>
<output>33</output>
<gadget id="calculator">33 / 2</gadget>
<output>33/2 = around 16.5</output>
<gadget id="calculator">(33/2) + 1</gadget>
<output>35/2 = around 17.5</output>
<result>35/2 = around 17.5</result>


the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 25 ?

Explanation: "$ 25 = 4 * $ 6 + $ 1 the number of doughnuts is 4 * 12 + 1 = 49 the answer is b ."

<gadget id="calculator">25 / 6</gadget>
<output>25/6 = around 4.166667</output>
<gadget id="calculator">(25/6) * 12</gadget>
<output>50</output>
<result>50</result>


during the first two weeks of january , the total rainfall in springdale was 25 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?

Explanation: "total rainfall in 2 weeks = 25 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 25 inches x = 10 and 1.5 x = 15 rainfall during second week = 9 inches option e"

multiply(25, divide(1.5, add(const_1, 1.5)))

<gadget id="calculator">1 + 1.5</gadget>
<output>2.5</output>
<gadget id="calculator">1.5 / 2.5</gadget>
<output>0.6</output>
<gadget id="calculator">25 * 0.6</gadget>
<output>15</output>
<result>15</result>


a train crosses a bridge of length 200 m in 10 seconds and a lamp post on the bridge in 5 seconds . what is the length of the train in metres ?

Explanation: "let length of train = l case - 1 : distance = 200 + l ( while crossing the bridge ) time = 10 seconds i . e . speed = distance / time = ( 200 + l ) / 10 case - 2 : distance = l ( while passing the lamp post ) time = 5 seconds i . e . speed = distance / time = ( l ) / 5 but since speed has to be same in both cases so ( 200 + l ) / 10 = ( l ) / 5 i . e . 2 l = l + 200 i . e . l = 200 answer : option c"

multiply(divide(200, subtract(10, 5)), 5)

<gadget id="calculator">10 - 5</gadget>
<output>5</output>
<gadget id="calculator">200 / 5</gadget>
<output>40</output>
<gadget id="calculator">40 * 5</gadget>
<output>200</output>
<result>200</result>


the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 385 the other is

Explanation: the other number = l . c . m * h . c . f / given number = 2310 * 30 / 385 = 180 answer is a .

<gadget id="calculator">30 * 2_310</gadget>
<output>69_300</output>
<gadget id="calculator">69_300 / 385</gadget>
<output>180</output>
<result>180</result>


mary and mike enter into a partnership by investing $ 550 and $ 450 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if mary received $ 1000 more than mike did , what was the profit made by their business in that year ?

Explanation: "explanatory answer let the profit made during the year be $ 3 x therefore , $ x would have been shared equally and the remaining $ 2 x would have been shared in the ratio 5.5 : 4.5 i . e . , 55 % of 2 x would go to mary and 45 % of 2 x would go to mike . hence , mary would get ( 55 - 45 ) % of 2 x more than mike or 10 % of 2 x = $ 1000 i . e . , ( 60 / 100 ) * 2 x = 1000 or 2 x = 10000 . hence , the profit made by the company during the year $ 3 x = $ 15000 . answer : c"

divide(1000, multiply(subtract(divide(550, const_1000), divide(450, const_1000)), subtract(const_1, divide(const_1, const_3))))

<gadget id="calculator">550 / 1_000</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">450 / 1_000</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(11/20) - (9/20)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(1/10) * (2/3)</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">1_000 / (1/15)</gadget>
<output>15_000</output>
<result>15_000</result>


a goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 24 seconds . what is the length of the goods train ?

Explanation: "explanation : speed = [ 72 x ( 5 / 18 ) ] m / sec = 20 m / sec . time = 24 sec . let the length of the train be x metres . then , [ ( x + 250 ) / 24 ] = 20 = > x + 250 = 480 = > x = 230 . answer : a"

multiply(subtract(24, divide(250, multiply(const_0_2778, 72))), multiply(const_0_2778, 72))

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(5/18) * 72</gadget>
<output>20</output>
<gadget id="calculator">250 / 20</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">24 - (25/2)</gadget>
<output>23/2 = around 11.5</output>
<gadget id="calculator">(23/2) * 20</gadget>
<output>230</output>
<result>230</result>


20 men can dig a tunnel in 30 days . if after 10 days , 20 more men are deployed to dig the tunnel , how many more days it will take to dig the whole tunnel ?

Explanation: a remaining work can be completed by 20 men in 30 - 10 = 20 days . if 20 men can do x work in 20 days , and let us say 40 men take n days to do the same work . now , more men , less number of days ( inversely proportion ) 20 : 40 : : n : 20 n = 20 x 20 / 40 = 10 days .

divide(subtract(const_1, multiply(divide(const_1, 30), 10)), multiply(divide(const_1, 30), const_2))

<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(1/30) * 10</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(1/30) * 2</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(2/3) / (1/15)</gadget>
<output>10</output>
<result>10</result>


if the product of 10 integers is negative , at most how many of the integers can be negative ?

Explanation: "the product of 10 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 9 correct option : d"

<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<result>9</result>


the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 72 . find the principal ?

Explanation: "p = 72 ( 100 / 5 ) ^ 2 = > p = 1800 answer : e"

divide(72, subtract(power(add(divide(20, const_100), const_1), 2), add(multiply(divide(20, const_100), 2), const_1)))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) + 1</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) ** 2</gadget>
<output>36/25 = around 1.44</output>
<gadget id="calculator">(1/5) * 2</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) + 1</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">(36/25) - (7/5)</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">72 / (1/25)</gadget>
<output>1_800</output>
<result>1_800</result>


in a division , a student took 63 as divisor instead of 36 . his answer was 24 . the correct answer is -

Explanation: "x / 63 = 24 . x = 24 * 63 . so correct answer would be , ( 24 * 63 ) / 36 = 42 . answer : a"

<gadget id="calculator">63 * 24</gadget>
<output>1_512</output>
<gadget id="calculator">1_512 / 36</gadget>
<output>42</output>
<result>42</result>


the sum of the numbers is 550 . if the first number be twice the second and third number be one - third of the first , then the second number is :

Explanation: "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 550 11 x / 3 = 550 x = 150 answer : b"

divide(multiply(550, const_3), add(const_10, const_1))

<gadget id="calculator">550 * 3</gadget>
<output>1_650</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">1_650 / 11</gadget>
<output>150</output>
<result>150</result>


Explanation: "( 1 – 1.25 ) n = 4 simplify to get : - 0.25 n = 4 rewrite as ( - 1 / 4 ) n = 4 multiply both sides by - 4 to get : n = - 16 answer : b"

<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">-16</gadget>
<output>-16</output>
<result>-16</result>


a team p of 20 engineers can complete work or task in 32 days . another team q of 16 engineers can complete same task in 30 days . then the ratio of working capacity of 1 member of p to the 1 member of q is a . 3 : 2

Explanation: explanation : let the capacity of an engineer in p = x units , and in q = y units . working capacity of p = x × 32 × 20 working capacity of q = y × 16 × 30 as the total work is same , we equate the above equations . ⇒ x × 32 × 20 = y × 16 × 30 ⇒ xy = 16 × 3032 × 20 = 34 answer : b

<gadget id="calculator">3 * 10</gadget>
<output>30</output>
<gadget id="calculator">30 + 4</gadget>
<output>34</output>
<result>34</result>


a certain kind of necklace is made from 9 green , 6 white , and 3 orange beads . what is the maximum number of these necklaces that can be made from 45 beads of each color ?

Explanation: atleast 9 green breads are needed to make a necklace , so irrespective of the combinations of white and orange beads , the number of necklaces that can be formed will be 45 / 9 = 5 answer : - c

<gadget id="calculator">45 / 9</gadget>
<output>5</output>
<result>5</result>


the average of 45 results is 25 and the average of other 25 results is 45 . what is the average of all the results ?

Explanation: "answer sum of 70 result = sum of 45 result + sum of 25 result . = 45 x 25 + 25 x 45 = 2250 / 70 correct option : b"

divide(add(multiply(45, 25), multiply(25, 45)), add(45, 25))

<gadget id="calculator">45 * 25</gadget>
<output>1_125</output>
<gadget id="calculator">25 * 45</gadget>
<output>1_125</output>
<gadget id="calculator">1_125 + 1_125</gadget>
<output>2_250</output>
<gadget id="calculator">45 + 25</gadget>
<output>70</output>
<gadget id="calculator">2_250 / 70</gadget>
<output>225/7 = around 32.142857</output>
<result>225/7 = around 32.142857</result>


10 friends meet for movie 20 for picnic and 5 for games 4 for movie & picnic 2 for movie & games , 0 for picnic & games , 2 for all , how many are students are there in all ?

Explanation: n ( a u b u c ) = n ( a ) + n ( b ) + n ( c ) - n ( a intersection b ) - n ( a intersection c ) - n ( c intersection b ) + n ( a intersection b - intersection c ) hence , total no . of students = 10 + 20 + 5 - 4 - 0 - 2 + 2 = 31 . answer : b

add(subtract(add(subtract(add(10, 20), 4), 5), 2), 2)

<gadget id="calculator">10 + 20</gadget>
<output>30</output>
<gadget id="calculator">30 - 4</gadget>
<output>26</output>
<gadget id="calculator">26 + 5</gadget>
<output>31</output>
<gadget id="calculator">31 - 2</gadget>
<output>29</output>
<gadget id="calculator">29 + 2</gadget>
<output>31</output>
<result>31</result>


a can give b 100 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?

Explanation: "explanation : a runs 1000 m while b runs 900 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 900 = 8000 / 9 = 888.88 m . b can give c = 1000 - 888.88 = 111.12 m . answer : a"

subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 200)), subtract(multiply(const_100, const_10), 100)))

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 200</gadget>
<output>800</output>
<gadget id="calculator">1_000 * 800</gadget>
<output>800_000</output>
<gadget id="calculator">1_000 - 100</gadget>
<output>900</output>
<gadget id="calculator">800_000 / 900</gadget>
<output>8_000/9 = around 888.888889</output>
<gadget id="calculator">1_000 - (8_000/9)</gadget>
<output>1_000/9 = around 111.111111</output>
<result>1_000/9 = around 111.111111</result>


alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 961 . find the cost of each ice - cream cup ?

Explanation: "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 961 96 + 225 + 490 + 6 x = 961 6 x = 150 = > x = 25 . answer : a"

divide(subtract(subtract(subtract(961, multiply(16, 6)), multiply(5, 45)), multiply(7, 70)), 6)

<gadget id="calculator">16 * 6</gadget>
<output>96</output>
<gadget id="calculator">961 - 96</gadget>
<output>865</output>
<gadget id="calculator">5 * 45</gadget>
<output>225</output>
<gadget id="calculator">865 - 225</gadget>
<output>640</output>
<gadget id="calculator">7 * 70</gadget>
<output>490</output>
<gadget id="calculator">640 - 490</gadget>
<output>150</output>
<gadget id="calculator">150 / 6</gadget>
<output>25</output>
<result>25</result>


a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 20 - sided polygon have ?

Explanation: there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 20 . plugging it in , we get 170 diagonals ! answer ( b ) .

divide(multiply(subtract(20, const_3), 20), const_2)

<gadget id="calculator">20 - 3</gadget>
<output>17</output>
<gadget id="calculator">17 * 20</gadget>
<output>340</output>
<gadget id="calculator">340 / 2</gadget>
<output>170</output>
<result>170</result>


a number is said to be prime saturated if the product of all the different positive prime factors of z is less than the square root of z . what is the greatest two digit prime saturated integer ?

Explanation: "clearly d a number is said to be prime saturated if the product of all the different positive prime factors of z is less than the square root of z . 96 has more number of smaller prime factor thats the clue ! ! = d"

add(multiply(const_2, const_3), subtract(const_100, const_10))

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">6 + 90</gadget>
<output>96</output>
<result>96</result>


find large number from below question the difference of two numbers is 1311 . on dividing the larger number by the smaller , we get 11 as quotient and the 11 as remainder

Explanation: "let the smaller number be x . then larger number = ( x + 1311 ) . x + 1311 = 11 x + 11 10 x = 1300 x = 130 large number = 130 + 1311 = 1441 answer : c"

multiply(divide(subtract(1311, 11), subtract(11, const_1)), 11)

<gadget id="calculator">1_311 - 11</gadget>
<output>1_300</output>
<gadget id="calculator">11 - 1</gadget>
<output>10</output>
<gadget id="calculator">1_300 / 10</gadget>
<output>130</output>
<gadget id="calculator">130 * 11</gadget>
<output>1_430</output>
<result>1_430</result>


1 blue dice and 2 red dice are thrown . . . . what is the probability that the no . appeared on blue dice is always greater than both the no . appeared on the 2 red dice . .

Explanation: if the no . on blue dice is 2 then 2 red dice can take ( 1,1 ) value = 1 ^ 2 if the no . on blue dice is 3 then 2 red dice can take ( 1,1 ) ( 1,2 ) ( 2,1 ) ( 2,2 ) = 2 ^ 2 if the no . on blue dice is 4 then 2 red dice can take ( 1,1 ) ( 1,2 ) ( 2,1 ) ( 2,2 ) ( 1,3 ) ( 2,3 ) ( 3,2 ) ( 3,1 ) ( 3,3 ) = 3 ^ 2 similarly , if the no . on blue dice is 5 then 2 red dice can take = 4 ^ 2 and if the no . on blue dice is 6 then 2 red dice can take = 5 ^ 2 therefor , probability = total no . of favourable outcome / total no . of possible outcome = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 + 5 ^ 2 / 216 = 55 / 216 answer : a

divide(add(add(add(add(power(1, const_2), power(2, const_2)), power(const_3, const_2)), power(const_4, const_2)), power(add(const_3, const_2), const_2)), add(power(multiply(multiply(const_3, const_2), const_2), const_2), add(multiply(multiply(multiply(const_3, const_2), const_2), add(power(1, const_2), power(2, const_2))), multiply(multiply(const_3, const_2), const_2))))

<gadget id="calculator">1 ** 2</gadget>
<output>1</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">5 + 9</gadget>
<output>14</output>
<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">14 + 16</gadget>
<output>30</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">30 + 25</gadget>
<output>55</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">12 ** 2</gadget>
<output>144</output>
<gadget id="calculator">12 * 5</gadget>
<output>60</output>
<gadget id="calculator">60 + 12</gadget>
<output>72</output>
<gadget id="calculator">144 + 72</gadget>
<output>216</output>
<gadget id="calculator">55 / 216</gadget>
<output>55/216 = around 0.25463</output>
<result>55/216 = around 0.25463</result>


excluding stoppages , the speed of the bus is 54 kmph and including stoppages , it is 36 kmph . for how many minutes does the bus stop per hr

Explanation: due to stoppages , it covers 18 km less . time taken to cover 18 km is [ 18 / 54 * 60 ] min = 20 min answer is e .

multiply(subtract(const_1, divide(36, 54)), const_60)

<gadget id="calculator">36 / 54</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 60</gadget>
<output>20</output>
<result>20</result>


a 150 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?

Explanation: "speed = 150 / 18 = 25 / 3 m / sec . let the length of the platform be x meters . then , ( x + 150 ) / 39 = 25 / 3 = > x = 325 m . l = 325 - 150 = 175 m answer : option b"

subtract(multiply(speed(150, 18), 39), 150)

<gadget id="calculator">150 / 18</gadget>
<output>25/3 = around 8.333333</output>
<gadget id="calculator">(25/3) * 39</gadget>
<output>325</output>
<gadget id="calculator">325 - 150</gadget>
<output>175</output>
<result>175</result>


a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 35 , how many coins of each type are there ?

Explanation: "let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 35 ⇒ 1.75 x = 35 ⇒ x = 20 coins answer a"

divide(35, add(add(inverse(const_4), inverse(const_2)), const_1))

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/4) + (1/2)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) + 1</gadget>
<output>7/4 = around 1.75</output>
<gadget id="calculator">35 / (7/4)</gadget>
<output>20</output>
<result>20</result>


a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 588.25 . how many boxes of plain cookies did she sell ?

Explanation: "let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1588.25 = > x = 786 first get the difference of the revenue to the number of boxes . 1588.25 - 1585 = 3.25 now you know that the difference between plain cookies boxes and chocolate cookies boxes is small . we now divide the revenue by two . 1588.25 / 2 = ~ 794 because the difference between the possible answers is big , this leaves us with choice e ."

<gadget id="calculator">1_000 + 588.25</gadget>
<output>1_588.25</output>
<gadget id="calculator">1_588.25 / 2</gadget>
<output>794.125</output>
<result>794.125</result>


how many positive even integers less than 100 contain digits 5 or 7 ?

Explanation: "two digit numbers : 5 at tens place : 50 , 52,54 , 56,58 7 at tens place : 70 , 72,74 , 76,78 if 5 and 7 is at units place , the number cant be even total : 5 + 5 = 10 answer a"

<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<result>10</result>


a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 10 km ?

Explanation: "m = 4 s = 2 us = 4 - 2 = 2 d = 10 t = 10 / 2 = 5 answer : b"

<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<result>5</result>


the price of a certain painting increased by 25 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?

Explanation: "easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 25 = 125 price at the end of year 2 = 125 - 125 * 0.15 = 125 * 0.85 = 106.25 hence required answer = ( 106.25 / 100 ) * 100 % = 106.25 % answer is b ."

add(subtract(subtract(25, 15), divide(multiply(15, 25), const_100)), const_100)

<gadget id="calculator">25 - 15</gadget>
<output>10</output>
<gadget id="calculator">15 * 25</gadget>
<output>375</output>
<gadget id="calculator">375 / 100</gadget>
<output>15/4 = around 3.75</output>
<gadget id="calculator">10 - (15/4)</gadget>
<output>25/4 = around 6.25</output>
<gadget id="calculator">(25/4) + 100</gadget>
<output>425/4 = around 106.25</output>
<result>425/4 = around 106.25</result>


rs . 1010 / - distributed among a , b and c such that on decreasing their shares by rs . 25 , rs . 10 and rs . 15 respectively , the balance money would be divided among them in the ratio 3 : 2 : 5 . then , c ’ s share is : ?

Explanation: a : b : c = 3 : 2 : 5 total parts = 10 c ' s share is = 5 parts 10 - - - - - > rs . 960 / - 3 - - - - - > rs . 480 / - a ' s total = 480 + 15 = rs . 495 / - b )

<gadget id="calculator">25 + 10</gadget>
<output>35</output>
<gadget id="calculator">35 + 15</gadget>
<output>50</output>
<gadget id="calculator">1_010 - 50</gadget>
<output>960</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 + 5</gadget>
<output>10</output>
<gadget id="calculator">960 / 10</gadget>
<output>96</output>
<gadget id="calculator">5 * 96</gadget>
<output>480</output>
<gadget id="calculator">480 + 15</gadget>
<output>495</output>
<result>495</result>


a is twice as good a work man as b and together they finish a piece of work in 36 days . the number of days taken by b alone to finish the work is :

Explanation: solution ( a ’ s 1 day ’ s work ) : ( b ’ s 1 day ’ s work ) = 2 : 1 . ( a + b ) ' s 1 day ’ s work = 1 / 36 divide 1 / 36 in the ratio 2 : 1 . ∴ b ’ s 1 day ’ s work = ( 1 / 36 x 1 / 3 ) = 1 / 108 hence , b alone can finish the work in 108 days . answer b

<gadget id="calculator">1 / 36</gadget>
<output>1/36 = around 0.027778</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">(1/36) / 3</gadget>
<output>1/108 = around 0.009259</output>
<gadget id="calculator">1 / (1/108)</gadget>
<output>108</output>
<result>108</result>


Explanation: 5 % of ( 25 % of $ 1600 ) = 5 / 100 ( 25 / 100 * 1600 ) = $ 20 answer is a

divide(multiply(divide(multiply(1600, 25), const_100), 5), const_100)

<gadget id="calculator">1_600 * 25</gadget>
<output>40_000</output>
<gadget id="calculator">40_000 / 100</gadget>
<output>400</output>
<gadget id="calculator">400 * 5</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>
<result>20</result>


how many diagonals does a 60 - sided convex polygon have ?

Explanation: "a 60 - sided convex polygon has 60 vertices . if we examine a single vertex , we can see that we can connect it with 57 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 60 vertices can be connected with 57 vertices to create a diagonal then the total number of diagonals would be ( 60 ) ( 57 ) = 3420 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3420 by 2 to get 1710 . the answer is c ."

divide(factorial(60), multiply(factorial(subtract(60, const_2)), factorial(const_2)))


rs . 1210 were divided among 3 person p , q , r so that p : q = 5 : 4 and q : r = 9 : 10 . then r gets the amount ?

Explanation: p : q = 5 : 4 , q : r = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9 . so , p : q : r = 5 : 4 : 40 / 9 = 45 : 36 : 40 sum of ratio terms is = ( 45 + 36 + 40 ) = 121 . r share of amount is rs ( 1210 x 40 / 121 ) = rs . 400 . b

multiply(divide(1210, add(add(divide(5, 4), divide(10, 9)), const_1)), divide(10, 9))

<gadget id="calculator">5 / 4</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">10 / 9</gadget>
<output>10/9 = around 1.111111</output>
<gadget id="calculator">(5/4) + (10/9)</gadget>
<output>85/36 = around 2.361111</output>
<gadget id="calculator">(85/36) + 1</gadget>
<output>121/36 = around 3.361111</output>
<gadget id="calculator">1_210 / (121/36)</gadget>
<output>360</output>
<gadget id="calculator">360 * (10/9)</gadget>
<output>400</output>
<result>400</result>


a fruit drink is made of orange , watermelon , and grape juice , where 35 percent of the drink is orange juice and 35 percent is watermelon juice . if the drink is made with 45 ounces of grape juice , how many ounces is the drink total ?

Explanation: "let the total number of ounces in the drink be x . % of orange = 35 % % of watermelon = 35 % % of grape = 100 % - 70 % = 30 % 0.30 x = 45 x = 150 therefore there are a total of 150 ounces in the drink . the answer is c ."

add(add(45, divide(multiply(45, 35), subtract(const_100, add(35, 35)))), divide(multiply(45, 35), subtract(const_100, add(35, 35))))

<gadget id="calculator">45 * 35</gadget>
<output>1_575</output>
<gadget id="calculator">35 + 35</gadget>
<output>70</output>
<gadget id="calculator">100 - 70</gadget>
<output>30</output>
<gadget id="calculator">1_575 / 30</gadget>
<output>105/2 = around 52.5</output>
<gadget id="calculator">45 + (105/2)</gadget>
<output>195/2 = around 97.5</output>
<gadget id="calculator">(195/2) + (105/2)</gadget>
<output>150</output>
<result>150</result>


for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 24 , then v =

Explanation: "( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 24 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 54 the answer is d ."

divide(divide(24, subtract(const_1, divide(const_1, 3))), subtract(const_1, divide(const_1, 3)))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">24 / (2/3)</gadget>
<output>36</output>
<gadget id="calculator">36 / (2/3)</gadget>
<output>54</output>
<result>54</result>


the least perfect square , which is divisible by each of 21,36 and 66 is

Explanation: l . c . m . of 21 , 36 , 66 = 2772 . now , 2772 = 2 x 2 x 3 x 3 x 7 x 11 to make it a perfect square , it must be multiplied by 7 x 11 . so , required number = 22 x 32 x 72 x 112 = 213444 answer a

multiply(multiply(multiply(power(add(const_3, const_4), const_2), power(divide(divide(66, const_3), const_2), const_2)), power(const_2, const_2)), power(const_3, const_2))

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 ** 2</gadget>
<output>49</output>
<gadget id="calculator">66 / 3</gadget>
<output>22</output>
<gadget id="calculator">22 / 2</gadget>
<output>11</output>
<gadget id="calculator">11 ** 2</gadget>
<output>121</output>
<gadget id="calculator">49 * 121</gadget>
<output>5_929</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">5_929 * 4</gadget>
<output>23_716</output>
<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">23_716 * 9</gadget>
<output>213_444</output>
<result>213_444</result>


Explanation: w / x = 2 / 3 = > x = 3 / 2 w and w / y = 6 / 15 = > y = 15 / 6 w ( x + y ) / y = ( 3 / 2 w + 15 / 6 w ) / 15 / 6 w = 4 w / ( 15 / 6 w ) = 8 / 5 correct option : d

add(divide(divide(6, 2), divide(15, 3)), const_1)

<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">15 / 3</gadget>
<output>5</output>
<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) + 1</gadget>
<output>8/5 = around 1.6</output>
<result>8/5 = around 1.6</result>


a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 500,000 ?

Explanation: the first digit and last digit are the same so the 2 possibilities are 6 or 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 2 * 10 * 10 = 200 the answer is b .

multiply(multiply(subtract(6, const_4), const_10), const_10)

<gadget id="calculator">6 - 4</gadget>
<output>2</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<result>200</result>


a trader sold an article on a certain price with 40 % profit . if he sold double of previous selling price then find its profit %

Explanation: "let cost price = 100 % selling price = 140 % new s . p . = 280 % p % = 280 - 100 = 180 % answer is b"

subtract(multiply(const_2, add(const_100, 40)), const_100)

<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">2 * 140</gadget>
<output>280</output>
<gadget id="calculator">280 - 100</gadget>
<output>180</output>
<result>180</result>


the average price of an decoration piece increases over the years . if from 1990 to 1996 , the price of the decoration piece increased by 13 % and from 1996 to 2001 it increased by 20 % , what is the price of the decoration piece in 2001 if the price in 1990 was $ 11500 ?

Explanation: whenever you have a question in which a value is increased by x % and then increased by y % then the overall effective increase = ( x + y + xy / 100 ) % the effective increase = 13 + 20 + ( 13 × 20 / 100 ) = 35.6 % this is a little more 33 % or 1 / 3 the original value . the quickest way to solve this question is to use approximation . 11500 + 1 / 3 ( 12000 ) = 15500 therefore option a is the answer . i selected 12000 because it ' s value is a little more 11500 and it ' s easier to divide by 3 ( ie to calculate 1 / 3 or 33 % ) .

multiply(add(const_1, divide(20, const_100)), multiply(add(const_1, divide(13, const_100)), 11500))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">13 / 100</gadget>
<output>13/100 = around 0.13</output>
<gadget id="calculator">1 + (13/100)</gadget>
<output>113/100 = around 1.13</output>
<gadget id="calculator">(113/100) * 11_500</gadget>
<output>12_995</output>
<gadget id="calculator">(6/5) * 12_995</gadget>
<output>15_594</output>
<result>15_594</result>


a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many h cubes are painted on only 2 faces ?

Explanation: "1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . h = 4 + 4 + 4 = 12 . answer a"

multiply(const_4, power(27, divide(const_1, const_3)))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">27 ** (1/3)</gadget>
<output>3</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<result>12</result>


the length of a rectangle is increased by 15 % and its breadth is decreased by 20 % . what is the effect on its area ?

Explanation: "100 * 100 = 10000 115 * 80 = 9200 answer : e"

multiply(add(15, const_100), subtract(const_100, 20))

<gadget id="calculator">15 + 100</gadget>
<output>115</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">115 * 80</gadget>
<output>9_200</output>
<result>9_200</result>


how many seconds will a train 150 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?

Explanation: "d d = 150 + 150 = 300 s = 36 * 5 / 18 = 10 mps t = 300 / 10 = 30 sec"

<gadget id="calculator">150 + 150</gadget>
<output>300</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">300 / 10</gadget>
<output>30</output>
<result>30</result>