the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 8.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?

Explanation: "i tried using time / rate approach : - initial price difference = 8.80 - 3.20 = 5.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 5.6 = t ( 5.4 x ) - > t = ( 5.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 5.6 / 5.4 = 8.4 answer a ."

add(3.20, multiply(divide(subtract(8.80, 3.20), add(5, subtract(sqrt(2), 1))), 5))

<gadget id="calculator">8.8 - 3.2</gadget>
<output>5.6</output>
<gadget id="calculator">2 ** (1/2)</gadget>
<output>sqrt(2) = around 1.414214</output>
<gadget id="calculator">(sqrt(2)) - 1</gadget>
<output>-1 + sqrt(2) = around 0.414214</output>
<gadget id="calculator">5 + (-1 + sqrt(2))</gadget>
<output>sqrt(2) + 4 = around 5.414214</output>
<gadget id="calculator">5.6 / (sqrt(2) + 4)</gadget>
<output>5.6/(sqrt(2) + 4) = around 1.034315</output>
<gadget id="calculator">(5.6/(sqrt(2) + 4)) * 5</gadget>
<output>28.0/(sqrt(2) + 4) = around 5.171573</output>
<gadget id="calculator">3.2 + (28.0/(sqrt(2) + 4))</gadget>
<output>3.2 + 28.0/(sqrt(2) + 4) = around 8.371573</output>
<result>3.2 + 28.0/(sqrt(2) + 4) = around 8.371573</result>


find the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 9 cm and 6 cm ?

Explanation: "1 / 2 * 28 ( 9 + 6 ) = 210 cm 2 answer : a"

multiply(multiply(divide(const_1, const_2), add(6, 9)), 28)

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">6 + 9</gadget>
<output>15</output>
<gadget id="calculator">(1/2) * 15</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">(15/2) * 28</gadget>
<output>210</output>
<result>210</result>


when the price of a product was decreased by 20 % , the number sold increased by 60 % . what was the effect on the total revenue ?

Explanation: let the price of the product be $ 100 and let original sale be 100 pieces then , total revenue = 100 * 100 = $ 10000 new revenue = 80 * 160 = $ 12800 increase in revenue = 2800 * 100 / 10000 = 28 % answer is a

multiply(subtract(multiply(add(const_1, divide(60, const_100)), divide(subtract(const_100, 20), const_100)), const_1), const_100)

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 + (3/5)</gadget>
<output>8/5 = around 1.6</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">(8/5) * (4/5)</gadget>
<output>32/25 = around 1.28</output>
<gadget id="calculator">(32/25) - 1</gadget>
<output>7/25 = around 0.28</output>
<gadget id="calculator">(7/25) * 100</gadget>
<output>28</output>
<result>28</result>


in a rare coin collection , all coins are either pure gold or pure silver , and there is initially one gold coin for every 3 silver coins . with the addition of 15 more gold coins to the collection , the ratio of gold coins to silver coins is 1 to 2 . based on this information , how many total coins are there now in this collection ( after the acquisition ) ?

Explanation: initially the number of gold coins and silver coins is 2 k and 6 k . after adding gold coins , the number of coins is 3 k and 6 k . thus k = 15 and the total number of coins is 9 k = 135 . the answer is b .

add(add(multiply(multiply(2, 15), 3), multiply(2, 15)), 15)

<gadget id="calculator">2 * 15</gadget>
<output>30</output>
<gadget id="calculator">30 * 3</gadget>
<output>90</output>
<gadget id="calculator">90 + 30</gadget>
<output>120</output>
<gadget id="calculator">120 + 15</gadget>
<output>135</output>
<result>135</result>


a student has to obtain 35 % of the total marks to pass . he got 100 marks and failed by 40 marks . the maximum marks are ?

Explanation: "let the maximum marks be x then , 35 % of x = 100 + 40 35 x / 100 = 140 35 x = 140 * 100 = 14000 x = 400 answer is b"

divide(add(100, 40), divide(35, const_100))

<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">140 / (7/20)</gadget>
<output>400</output>
<result>400</result>


Explanation: "a / d = ( 3 / 4 ) * ( 7 / 9 ) * ( 5 / 7 ) = > 5 / 12 answer : a"

divide(multiply(multiply(3, 7), 5), multiply(multiply(4, 9), 7))

<gadget id="calculator">3 * 7</gadget>
<output>21</output>
<gadget id="calculator">21 * 5</gadget>
<output>105</output>
<gadget id="calculator">4 * 9</gadget>
<output>36</output>
<gadget id="calculator">36 * 7</gadget>
<output>252</output>
<gadget id="calculator">105 / 252</gadget>
<output>5/12 = around 0.416667</output>
<result>5/12 = around 0.416667</result>


the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?

Explanation: "let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 ⇒ 40 y + 384 = 36 y + 432 ⇒ 4 y = 48 ∴ y = 12 b"

divide(subtract(multiply(12, subtract(40, 4)), multiply(12, 32)), 4)

<gadget id="calculator">40 - 4</gadget>
<output>36</output>
<gadget id="calculator">12 * 36</gadget>
<output>432</output>
<gadget id="calculator">12 * 32</gadget>
<output>384</output>
<gadget id="calculator">432 - 384</gadget>
<output>48</output>
<gadget id="calculator">48 / 4</gadget>
<output>12</output>
<result>12</result>


a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 12 days before the completion of the work . in how many days was the work completed ?

Explanation: "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 12 days = 12 * ( 1 / 24 + 1 / 30 ) = 9 / 10 remaining work = 1 / 10 the number of days required for this initial work = 1 days . the total number of days required = 12 + 1 = 13 days . answer : a"

add(divide(subtract(const_1, multiply(add(divide(const_1, 24), divide(const_1, 30)), 12)), add(divide(const_1, multiply(add(const_2, const_3), multiply(const_2, 12))), add(divide(const_1, 24), divide(const_1, 30)))), 12)

<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(1/24) + (1/30)</gadget>
<output>3/40 = around 0.075</output>
<gadget id="calculator">(3/40) * 12</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">1 - (9/10)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">2 * 12</gadget>
<output>24</output>
<gadget id="calculator">5 * 24</gadget>
<output>120</output>
<gadget id="calculator">1 / 120</gadget>
<output>1/120 = around 0.008333</output>
<gadget id="calculator">(1/120) + (3/40)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/10) / (1/12)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) + 12</gadget>
<output>66/5 = around 13.2</output>
<result>66/5 = around 13.2</result>


the total marks obtained by a student in mathematics and physics is 30 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .

Explanation: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 30 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 30 + 20 ) / 2 = 25 . answer : c"

<gadget id="calculator">30 + 20</gadget>
<output>50</output>
<gadget id="calculator">50 / 2</gadget>
<output>25</output>
<result>25</result>


a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 1540 in all from both of them as interest . the rate of interest per annum is ?

Explanation: "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 1540 100 r + 120 r = 1540 r = 7 % answer : a"

multiply(divide(1540, add(multiply(5000, 2), multiply(3000, 4))), const_100)

<gadget id="calculator">5_000 * 2</gadget>
<output>10_000</output>
<gadget id="calculator">3_000 * 4</gadget>
<output>12_000</output>
<gadget id="calculator">10_000 + 12_000</gadget>
<output>22_000</output>
<gadget id="calculator">1_540 / 22_000</gadget>
<output>7/100 = around 0.07</output>
<gadget id="calculator">(7/100) * 100</gadget>
<output>7</output>
<result>7</result>


Explanation: "solution : dividing each side by 25 , we obtain ( 25 x / 675 ) = ( 675 / 25 ) therefore : x = 27 check : 25 x = 675 ( 25 * 27 ) = 675 675 = 675 answer : a"

<gadget id="calculator">675 / 25</gadget>
<output>27</output>
<gadget id="calculator">25 * 27</gadget>
<output>675</output>
<result>675</result>


given that x and y are events such that z ( x ) = 0.02 z ( y ) = 0.10 z ( xny ) = 0.10 z ( x | y ) = find z ( x | y ) and z ( x | y )

Explanation: here , x and y are events z ( x | y ) = z ( xny ) / z ( y ) = 0.10 / 0.10 = 1 q ( g | h ) = z ( xny ) / z ( x ) = 0.4 / 0.02 = 1 / 5 answer is a

<gadget id="calculator">0.1 / 0.02</gadget>
<output>5</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<result>1/5 = around 0.2</result>


a jar contains a mixture of ab in the ratio 4 : 1 . when 40 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .

Explanation: 40 litres of mixture that is replaced will contain 32 litres of a and 8 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 32 ] / [ k - 8 + 40 ] = 2 / 3 = > 12 k - 96 = 2 k - 16 + 80 = > 10 k = 160 solve for k which is k = 16 so initial volume of liquid a = 4 k = 64 litres answer : d

multiply(divide(multiply(add(multiply(3, const_2), multiply(2, const_2)), divide(40, subtract(multiply(3, const_2), 1))), add(4, 1)), 4)

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">40 / 5</gadget>
<output>8</output>
<gadget id="calculator">10 * 8</gadget>
<output>80</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">80 / 5</gadget>
<output>16</output>
<gadget id="calculator">16 * 4</gadget>
<output>64</output>
<result>64</result>


the length of a rectangle is 3 times its width . if the width of the rectangle is 6 inches , what is the rectangle ' s area , in square inches ?

Explanation: "if the width is 6 in and the length is 3 times the width , then the length is 3 * 6 = 18 in the area is given by 6 * 18 = 108 square inches correct answer b"

<gadget id="calculator">3 * 6</gadget>
<output>18</output>
<gadget id="calculator">6 * 18</gadget>
<output>108</output>
<result>108</result>


a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 2500 . the difference between the profit shares of a and c is ?

Explanation: "explanation : ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 2500 = > 5 parts out of 15 parts is rs . 2500 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 2500 ) = rs . 1000 answer : d"

<gadget id="calculator">12_000 / 10_000</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">8_000 / 10_000</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(6/5) - (4/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 2_500</gadget>
<output>1_000</output>
<result>1_000</result>


a truck drives 80 miles on local roads at 30 mph , and 50 miles on the highway at 60 mph , the truck also take a hour lunch break . what is the average speed of the entire trip ?

Explanation: so the answer is plainly a . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 80 miles , and v = 30 mph so we can obtain time : 30 * t = 80 or t = 80 / 30 = 2.6 hours the needed time to cover 80 miles in the same way we should divide 50 to 60 to find the needed time to cover 50 miles , so t = 0.8 hours so the total time for covering total distance would be 2.6 + 0.8 + 1 ( lunch time ) = 4.4 hours and total distance is 80 + 50 = 130 miles final stage : average speed is total distance divide to total time : 130 / 4.4 = 29.5 miles per hour rounding up to 30 . . . .

divide(add(80, 60), add(add(divide(50, 60), divide(80, 30)), const_1))

<gadget id="calculator">80 + 60</gadget>
<output>140</output>
<gadget id="calculator">50 / 60</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">80 / 30</gadget>
<output>8/3 = around 2.666667</output>
<gadget id="calculator">(5/6) + (8/3)</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">(7/2) + 1</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">140 / (9/2)</gadget>
<output>280/9 = around 31.111111</output>
<result>280/9 = around 31.111111</result>


carrey rented a car for rs . 20 plus rs . 0.25 per kilometer driven . samuel rented a car for rs . 24 plus rs . 0.16 per kilometer driven . if each drove d km . and each was charged exactly the same amount for the rental , then d equals ?

Explanation: explanation : 20 + 0.25 × d = 24 + 0.16 d solving we get d = 44.4 answer : a

divide(subtract(24, 20), subtract(0.25, 0.16))

<gadget id="calculator">24 - 20</gadget>
<output>4</output>
<gadget id="calculator">0.25 - 0.16</gadget>
<output>0.09</output>
<gadget id="calculator">4 / 0.09</gadget>
<output>44.444444</output>
<result>44.444444</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 $ 24 ?

Explanation: $ 24 = 4 * $ 6 the number of doughnuts is 4 * 12 = 48 the answer is c .

<gadget id="calculator">24 / 6</gadget>
<output>4</output>
<gadget id="calculator">4 * 12</gadget>
<output>48</output>
<result>48</result>


the speed of the boat in still water in 12 kmph . it can travel downstream through 48 kms in 3 hrs . in what time would it cover the same distance upstream ?

Explanation: "still water = 12 km / hr downstream = 48 / 3 = 16 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 16 / 2 = 8 km / hr so time taken in upstream = 48 / 8 = 6 hrs answer : e"

divide(48, subtract(12, subtract(divide(48, 3), 12)))

<gadget id="calculator">48 / 3</gadget>
<output>16</output>
<gadget id="calculator">16 - 12</gadget>
<output>4</output>
<gadget id="calculator">12 - 4</gadget>
<output>8</output>
<gadget id="calculator">48 / 8</gadget>
<output>6</output>
<result>6</result>


on a sum of money , the simple interest for 2 years is rs . 326 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is

Explanation: "explanation : the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r ã — si ) / ( 2 ã — 100 ) difference between the compound interest and simple interest = 340 - 326 = 14 ( r ã — si ) / ( 2 ã — 100 ) = 14 ( r ã — 326 ) / ( 2 ã — 100 ) = 14 r = 8.58 % answer : option c"

divide(multiply(const_100, subtract(subtract(340, divide(326, 2)), divide(326, 2))), divide(326, 2))

<gadget id="calculator">326 / 2</gadget>
<output>163</output>
<gadget id="calculator">340 - 163</gadget>
<output>177</output>
<gadget id="calculator">177 - 163</gadget>
<output>14</output>
<gadget id="calculator">100 * 14</gadget>
<output>1_400</output>
<gadget id="calculator">1_400 / 163</gadget>
<output>1_400/163 = around 8.588957</output>
<result>1_400/163 = around 8.588957</result>


in a certain supermarket , a triangular display of cans is arranged in 9 rows , numbered 1 through 9 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 120 cans in the entire display , how many cans are in the seventh row ?

Explanation: "let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 24 ) = 9 x + 3 ( 1 + 2 + . . . + 8 ) = 9 x + 3 ( 8 ) ( 9 ) / 2 = 9 x + 108 since the total is less than 120 , x must equal 1 . the number of cans in the 7 th row is 1 + 3 ( 6 ) = 19 the answer is d ."

add(multiply(add(3, 3), 3), floor(divide(subtract(120, multiply(divide(multiply(3, subtract(9, 1)), const_2), 9)), 9)))

<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">3 * 8</gadget>
<output>24</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<gadget id="calculator">12 * 9</gadget>
<output>108</output>
<gadget id="calculator">120 - 108</gadget>
<output>12</output>
<gadget id="calculator">12 / 9</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">floor(4/3)</gadget>
<output>1</output>
<gadget id="calculator">18 + 1</gadget>
<output>19</output>
<result>19</result>


the length of a rectangle is 3 times its width . if the width of the rectangle is 4 inches , what is the rectangle ' s area , in square inches ?

Explanation: "if the width is 4 in and the length is 3 times the width , then the length is 3 * 4 = 12 in the area is given by 4 * 12 = 48 square inches correct answer d"

<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">4 * 12</gadget>
<output>48</output>
<result>48</result>


the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.7 years . the ration of the number of boys to the number of girls in the class is ?

Explanation: "let the ratio be k : 1 . then , k * 16.4 + 1 * 15.7 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.7 ) = k = 0.1 / 0.6 = 1 / 6 required ratio = 1 / 6 : 1 = 1 : 6 . answer : a"

<gadget id="calculator">15.8 - 15.7</gadget>
<output>0.1</output>
<gadget id="calculator">16.4 - 15.8</gadget>
<output>0.6</output>
<gadget id="calculator">0.1 / 0.6</gadget>
<output>0.166667</output>
<result>0.166667</result>


a man walking at a rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge is ?

Explanation: "speed = 5 * 5 / 18 = 25 / 18 m / sec distance covered in 15 minutes = 25 / 18 * 15 * 60 = 1250 m answer is a"

multiply(divide(multiply(5, const_1000), const_60), 15)

<gadget id="calculator">5 * 1_000</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 / 60</gadget>
<output>250/3 = around 83.333333</output>
<gadget id="calculator">(250/3) * 15</gadget>
<output>1_250</output>
<result>1_250</result>


the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 11 . if p invested the money for 5 months , find for how much time did q invest the money ?

Explanation: "7 * 5 : 5 * x = 7 : 11 x = 11 answer : d"

multiply(multiply(divide(7, 5), divide(11, 7)), 5)

<gadget id="calculator">7 / 5</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">11 / 7</gadget>
<output>11/7 = around 1.571429</output>
<gadget id="calculator">(7/5) * (11/7)</gadget>
<output>11/5 = around 2.2</output>
<gadget id="calculator">(11/5) * 5</gadget>
<output>11</output>
<result>11</result>


a fair price shopkeeper takes 10 % profit on his goods . he lost 30 % goods during theft . his loss percent is :

Explanation: "explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 70 . s . p . of each item = rs . 1.10 total sale = 1.10 * 70 = rs . 77 hence , loss % = 23 / 100 * 100 = 23 % answer : a"

subtract(const_100, subtract(add(const_100, 10), divide(multiply(add(const_100, 10), 30), const_100)))

<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">110 * 30</gadget>
<output>3_300</output>
<gadget id="calculator">3_300 / 100</gadget>
<output>33</output>
<gadget id="calculator">110 - 33</gadget>
<output>77</output>
<gadget id="calculator">100 - 77</gadget>
<output>23</output>
<result>23</result>


how many seconds will a 500 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?

Explanation: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 500 * 3 / 50 = 30 sec . answer : b"

divide(500, multiply(subtract(63, 3), const_0_2778))

<gadget id="calculator">63 - 3</gadget>
<output>60</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">500 / (50/3)</gadget>
<output>30</output>
<result>30</result>


the average age of 10 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is

Explanation: "total age increased = ( 10 * 2 ) years = 20 years . sum of ages of two new men = ( 21 + 23 + 20 ) years = 64 years average age of two new men = ( 64 / 2 ) years = 32 years . answer : e"

add(divide(add(21, 23), const_2), multiply(const_1, 10))

<gadget id="calculator">21 + 23</gadget>
<output>44</output>
<gadget id="calculator">44 / 2</gadget>
<output>22</output>
<gadget id="calculator">1 * 10</gadget>
<output>10</output>
<gadget id="calculator">22 + 10</gadget>
<output>32</output>
<result>32</result>


Explanation: "8 ^ x = 1 / 64 8 ^ x = 1 / 8 ^ 2 8 ^ x = 8 ^ - 2 x = - 2 e"

<gadget id="calculator">1 / 64</gadget>
<output>1/64 = around 0.015625</output>
<gadget id="calculator">log(1/64)</gadget>
<output>-log(64) = around -4.158883</output>
<gadget id="calculator">log(8)</gadget>
<output>log(8) = around 2.079442</output>
<gadget id="calculator">(-log(64)) / log(8)</gadget>
<output>-log(64)/log(8) = around -2</output>
<result>-log(64)/log(8) = around -2</result>


the base and height of a parallelogram are 12 m and 6 m respectively . then its area is = = = = = = ?

Explanation: a = b * h = > a = 12 * 6 = 72 sq . m . answer : ( e )

<gadget id="calculator">12 * 6</gadget>
<output>72</output>
<result>72</result>


pipe a can fill a tank in 6 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?

Explanation: "let the pipe b be closed after x minutes . 30 / 6 - x / 24 = 1 = > x / 24 = 30 / 6 - 1 = 4 = > x = 4 * 24 = 96 . answer : c"

multiply(subtract(divide(30, 6), const_1), 24)

<gadget id="calculator">30 / 6</gadget>
<output>5</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">4 * 24</gadget>
<output>96</output>
<result>96</result>


the number of diagonals of a polygon of n sides is given by the formula q = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?

Explanation: "q = n ( n - 3 ) q = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b"

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


a fair price shopkeeper takes 10 % profit on his goods . he lost 70 % goods during theft . his loss percent is :

Explanation: "explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 30 . s . p . of each item = rs . 1.10 total sale = 1.10 * 30 = rs . 33 hence , loss % = 67 / 100 * 100 = 67 % answer : d"

subtract(const_100, subtract(add(const_100, 10), divide(multiply(add(const_100, 10), 70), const_100)))

<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">110 * 70</gadget>
<output>7_700</output>
<gadget id="calculator">7_700 / 100</gadget>
<output>77</output>
<gadget id="calculator">110 - 77</gadget>
<output>33</output>
<gadget id="calculator">100 - 33</gadget>
<output>67</output>
<result>67</result>


the age of somu is one - third his father ' s . 8 years back he was one - fifth of his father ' s age . what is his persent age ?

Explanation: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 8 = 3 x - 8 / 5 = x = 16 answer : option d"

divide(subtract(multiply(add(const_4, const_1), 8), 8), subtract(add(const_4, const_1), const_3))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 8</gadget>
<output>40</output>
<gadget id="calculator">40 - 8</gadget>
<output>32</output>
<gadget id="calculator">5 - 3</gadget>
<output>2</output>
<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<result>16</result>


13 buckets of water fill a tank when the capacity of each bucket is 42 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 6 litres ?

Explanation: "capacity of the tank = ( 13 ã — 42 ) litre number of buckets required of capacity of each bucket is 17 litre = 13 ã — 42 / 6 = 13 ã — 7 = 91 answer is a"

<gadget id="calculator">42 * 13</gadget>
<output>546</output>
<gadget id="calculator">546 / 6</gadget>
<output>91</output>
<result>91</result>


two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 22 seconds . the ratio of their speeds is ?

Explanation: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 22 = = > 27 x + 17 y = 22 x + 22 y = = > 5 x = 5 y = = > x / y = 1 / 1 . answer : c"

divide(subtract(27, 22), subtract(22, 17))

<gadget id="calculator">27 - 22</gadget>
<output>5</output>
<gadget id="calculator">22 - 17</gadget>
<output>5</output>
<gadget id="calculator">5 / 5</gadget>
<output>1</output>
<result>1</result>


exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 9 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?

Explanation: "the total number of the people in the room must be a multiple of both 7 and 9 ( in order 3 / 7 and 5 / 9 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 9 , which is 63 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 91 people in the room . therefore there are 3 / 7 * 63 = 27 people in the room under the age of 21 . answer : a ."

<gadget id="calculator">7 * 9</gadget>
<output>63</output>
<gadget id="calculator">63 * 3</gadget>
<output>189</output>
<gadget id="calculator">189 / 7</gadget>
<output>27</output>
<result>27</result>


the product of two successive numbers is 7832 . which is the smaller of the two numbers ?

Explanation: "c 88 from the given alternatives , 88 × 89 = 7832 ∴ smaller number = 88"

<gadget id="calculator">7_832 ** (1/2)</gadget>
<output>2*sqrt(1958) = around 88.498588</output>
<result>2*sqrt(1958) = around 88.498588</result>


Explanation: "solution therefore = 3.6 x 0.48 x 2.50 / 0.12 x 0.09 x 0.5 = 36 x 48 x 250 / 12 x 9 x 5 = 800 answer b"

divide(multiply(multiply(3.6, 0.48), 2.50), multiply(multiply(0.12, 0.09), 0.5))

<gadget id="calculator">3.6 * 0.48</gadget>
<output>1.728</output>
<gadget id="calculator">1.728 * 2.5</gadget>
<output>4.32</output>
<gadget id="calculator">0.12 * 0.09</gadget>
<output>0.0108</output>
<gadget id="calculator">0.0108 * 0.5</gadget>
<output>0.0054</output>
<gadget id="calculator">4.32 / 0.0054</gadget>
<output>800</output>
<result>800</result>


two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 30 hr . if all pipes are opened simultaneously , then the cistern will be filled in

Explanation: "solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 − 1 / 30 = 3 / 20 hence , tank will be filled in 20 / 3 = 6.67 hour option ( a )"

inverse(subtract(add(divide(const_1, 10), divide(const_1, 12)), divide(const_1, 30)))

<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/10) + (1/12)</gadget>
<output>11/60 = around 0.183333</output>
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(11/60) - (1/30)</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 / (3/20)</gadget>
<output>20/3 = around 6.666667</output>
<result>20/3 = around 6.666667</result>


if 1 / 8 of a pencil is black 1 / 2 of the remaining is white and the remaining 7 / 2 is blue find the total length of the pencil ?

Explanation: ( 1 / 8 ) p + ( 1 / 2 ) p + ( 7 / 2 ) = p on solving the above for p we get 9.333 now checking for the answer : 9.333 / 8 = 1.166 cm 9.333 / 2 = 4.665 cm now 1.166 + 4.665 + ( 7 / 2 ) = 9.33 cm answer : d

add(divide(multiply(divide(7, 2), add(divide(1, 8), divide(1, 2))), subtract(const_1, add(divide(1, 8), divide(1, 2)))), divide(7, 2))

<gadget id="calculator">7 / 2</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/8) + (1/2)</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">(7/2) * (5/8)</gadget>
<output>35/16 = around 2.1875</output>
<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(35/16) / (3/8)</gadget>
<output>35/6 = around 5.833333</output>
<gadget id="calculator">(35/6) + (7/2)</gadget>
<output>28/3 = around 9.333333</output>
<result>28/3 = around 9.333333</result>


the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 42 degrees . find the temperature on friday ?

Explanation: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 42 tu + w + th = 192 - 42 = 150 f = 184 – 150 = 34 . answer : a"

subtract(42, subtract(multiply(48, const_4), multiply(46, const_4)))

<gadget id="calculator">48 * 4</gadget>
<output>192</output>
<gadget id="calculator">46 * 4</gadget>
<output>184</output>
<gadget id="calculator">192 - 184</gadget>
<output>8</output>
<gadget id="calculator">42 - 8</gadget>
<output>34</output>
<result>34</result>


Explanation: "a certain taxi company charges $ 2.10 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.10 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.1 + $ 15.6 = $ 17.7 . answer : c ."

add(2.10, multiply(subtract(divide(8, divide(1, 5)), 1), 0.40))

<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">8 / (1/5)</gadget>
<output>40</output>
<gadget id="calculator">40 - 1</gadget>
<output>39</output>
<gadget id="calculator">39 * 0.4</gadget>
<output>15.6</output>
<gadget id="calculator">2.1 + 15.6</gadget>
<output>17.7</output>
<result>17.7</result>


two cyclist start from the same places in opposite directions . one is going towards north at 30 kmph and the other is going towards south 40 kmph . what time will they take to be 50 km apart ?

Explanation: "to be ( 30 + 40 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 70 * 50 = 0.714 hrs answer is b"

<gadget id="calculator">30 + 40</gadget>
<output>70</output>
<gadget id="calculator">50 / 70</gadget>
<output>5/7 = around 0.714286</output>
<result>5/7 = around 0.714286</result>


in x - y plane , there is a right triangle abc ( ∠ b = 90 o ) . if the length of ac is 25 and the slope of line segment ac is 4 / 3 , what is the length of ab ?

Explanation: "slope = change in vertical direction / change in horizontal direction = 4 / 3 change in vertical direction = 4 x = ab change in horizontal direction = 3 x = bc ab ^ 2 + bc ^ 2 = 25 ^ 2 16 x ^ 2 + 9 x ^ 2 = 625 25 x ^ 2 = 625 x ^ 2 = 25 x = 5 therefore ab = 5 * 4 = 20 answer : d"

multiply(4, divide(25, sqrt(add(power(4, const_2), power(3, const_2)))))

<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">16 + 9</gadget>
<output>25</output>
<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>
<gadget id="calculator">25 / 5</gadget>
<output>5</output>
<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<result>20</result>


the average of 5 consecutive odd numbers a , b , c , d and e is 13 . what percent of b is c ?

Explanation: explanation : in such a case the middle number ( c ) is the average ∴ c = 13 and b = 11 required percentage = 13 / 11 x 100 = 118.2 answer : option d

multiply(divide(add(add(divide(multiply(5, 13), 5), const_2), const_2), add(divide(multiply(5, 13), 5), const_2)), const_100)

<gadget id="calculator">5 * 13</gadget>
<output>65</output>
<gadget id="calculator">65 / 5</gadget>
<output>13</output>
<gadget id="calculator">13 + 2</gadget>
<output>15</output>
<gadget id="calculator">15 + 2</gadget>
<output>17</output>
<gadget id="calculator">17 / 15</gadget>
<output>17/15 = around 1.133333</output>
<gadget id="calculator">(17/15) * 100</gadget>
<output>340/3 = around 113.333333</output>
<result>340/3 = around 113.333333</result>


a palindrome is a number that reads the same forward and backward , such as 343 . how many odd , 8 - digit numbers are palindromes ?

Explanation: "first recognize you only need to consider the first four digits ( because the second four are just the first four flipped ) there are 9000 possibilities for the first four digits of a 8 digit number , 1000 - 9999 inclusive . everything starting with a 1 , 3,5 , 7,9 will be odd , which is 5 / 9 ths of the combinations . 5 / 9 * 9000 = 5000 answer : d"

divide(power(const_10, divide(8, const_2)), const_2)

<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">10 ** 4</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 / 2</gadget>
<output>5_000</output>
<result>5_000</result>


a person borrows rs . 7000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year .

Explanation: "gain in 2 years = [ ( 7000 * 6 * 2 ) / 100 ] - [ ( 7000 * 4 * 2 ) / 100 ] 840 - 560 = 280 gain in 1 year = ( 280 / 2 ) = 140 rs answer : c"

divide(subtract(divide(multiply(multiply(7000, 6), 2), const_100), divide(multiply(multiply(7000, 4), 2), const_100)), 2)

<gadget id="calculator">7_000 * 6</gadget>
<output>42_000</output>
<gadget id="calculator">42_000 * 2</gadget>
<output>84_000</output>
<gadget id="calculator">84_000 / 100</gadget>
<output>840</output>
<gadget id="calculator">7_000 * 4</gadget>
<output>28_000</output>
<gadget id="calculator">28_000 * 2</gadget>
<output>56_000</output>
<gadget id="calculator">56_000 / 100</gadget>
<output>560</output>
<gadget id="calculator">840 - 560</gadget>
<output>280</output>
<gadget id="calculator">280 / 2</gadget>
<output>140</output>
<result>140</result>


what is the difference between the local value of 1 and 2 in the number 2124 ?

Explanation: explanation : 100 â € “ 20 = 80 answer : d

subtract(multiply(1, const_100), multiply(2, const_10))

<gadget id="calculator">1 * 100</gadget>
<output>100</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<result>80</result>


in 10 years , a will be twice as old as b was 10 years ago . if a is now 7 years older than b the present age of b is

Explanation: "let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 7 = > 2 b - b - 7 = 30 b = 37 so the present age of b is 37 years answer : a"

<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 + 10</gadget>
<output>30</output>
<gadget id="calculator">30 + 7</gadget>
<output>37</output>
<result>37</result>


you buy a piece of land with an area of â ˆ š 1600 , how long is one side of the land plot ?

Explanation: "try filling the numbers into the answer y x y = find the closest to 900 . answer b"

<gadget id="calculator">1_600 ** (1/2)</gadget>
<output>40</output>
<result>40</result>


a can do a work in 15 days b in 14 days and c in 16 days . if they work on it together then in how many days required to complete the work ?

Explanation: person ( a ) ( b ) ( c ) ( a + b + c ) time - ( 15 ) ( 14 ) ( 16 ) rate - ( 224 ) ( 240 ) ( 210 ) ( 674 ) work - ( 3360 ) ( 3360 ) ( 3360 ) ( 3360 ) therefore a + b + c requires ( 3360 / 674 ) days to complete entire work = 3360 / 674 answer is c

divide(multiply(multiply(15, 14), 16), multiply(add(add(15, 14), 16), 15))

<gadget id="calculator">15 * 14</gadget>
<output>210</output>
<gadget id="calculator">210 * 16</gadget>
<output>3_360</output>
<gadget id="calculator">15 + 14</gadget>
<output>29</output>
<gadget id="calculator">29 + 16</gadget>
<output>45</output>
<gadget id="calculator">45 * 15</gadget>
<output>675</output>
<gadget id="calculator">3_360 / 675</gadget>
<output>224/45 = around 4.977778</output>
<result>224/45 = around 4.977778</result>


tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 10 meters and a circumference of 9 meters , and the interior of tank b has a height of 9 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?

Explanation: "the radius of tank a is 9 / ( 2 * pi ) . the capacity of tank a is 10 * pi * 81 / ( 4 * pi ^ 2 ) = 405 / ( 2 * pi ) the radius of tank b is 10 / ( 2 * pi ) . the capacity of tank b is 9 * pi * 100 / ( 4 * pi ^ 2 ) = 450 / ( 2 * pi ) tank a / tank b = 405 / 450 = 9 / 10 = 90 % the answer is b ."

multiply(multiply(power(divide(9, 10), const_2), divide(10, 9)), const_100)

<gadget id="calculator">9 / 10</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(9/10) ** 2</gadget>
<output>81/100 = around 0.81</output>
<gadget id="calculator">10 / 9</gadget>
<output>10/9 = around 1.111111</output>
<gadget id="calculator">(81/100) * (10/9)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(9/10) * 100</gadget>
<output>90</output>
<result>90</result>


a cistern can be filled by a tap in 6 hours while it can be emptied by another tap in 12 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?

Explanation: "net part filled in 1 hour = ( 1 / 6 - 1 / 12 ) = 1 / 12 the cistern will be filled in 12 / 1 hrs i . e . , 12 hrs . answer : c"

divide(const_1, subtract(divide(const_1, 6), divide(const_1, 12)))

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/6) - (1/12)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>12</result>


seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 40 percent ryegrass , what percent of the weight of this mixture is x ?

Explanation: "- - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 40 % 0.4 x + ( m - x ) 0.25 = 0.4 m 0.15 x = 0.15 m x = 1 m x = 100 % of m a"

divide(subtract(40, 25), subtract(divide(40, const_100), divide(25, const_100)))

<gadget id="calculator">40 - 25</gadget>
<output>15</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(2/5) - (1/4)</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">15 / (3/20)</gadget>
<output>100</output>
<result>100</result>


the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if y 12 = 110 , what is the value of y ?

Explanation: ab = ( a - 1 ) ( b - 1 ) y 12 = ( y - 1 ) ( 12 - 1 ) = 110 - - > y - 1 = 10 - - > y = 11 answer : a

<gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">110 / 11</gadget>
<output>10</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<result>11</result>


each month a retailer sells 100 identical items . on each item he makes a profit of $ 60 that constitutes 10 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the discount ?

Explanation: "for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 60 sell price = $ 600 + $ 60 thus , the sell price is $ 660 for each item . selling all 100 items gives the retailer . . . 100 ( $ 60 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 660 ) = $ 33 discount $ 627 = $ 600 + $ 27 now , the retailer makes a profit of just $ 27 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 27 ( x ) = $ 2,000 x = 2,000 / 27 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d"

divide(multiply(100, 60), subtract(60, divide(multiply(add(divide(multiply(100, 60), 10), 60), 5), 100)))

<gadget id="calculator">100 * 60</gadget>
<output>6_000</output>
<gadget id="calculator">6_000 / 10</gadget>
<output>600</output>
<gadget id="calculator">600 + 60</gadget>
<output>660</output>
<gadget id="calculator">660 * 5</gadget>
<output>3_300</output>
<gadget id="calculator">3_300 / 100</gadget>
<output>33</output>
<gadget id="calculator">60 - 33</gadget>
<output>27</output>
<gadget id="calculator">6_000 / 27</gadget>
<output>2_000/9 = around 222.222222</output>
<result>2_000/9 = around 222.222222</result>


a and b go around a circular track of length 200 m on a cycle at speeds of 36 kmph and 72 kmph . after how much time will they meet for the first time at the starting point ?

Explanation: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 200 / ( 36 * 5 / 18 ) , 200 / ( 72 * 5 / 18 ) } = lcm ( 20 , 10 ) = 20 sec . answer : d"

divide(200, subtract(multiply(72, const_0_2778), multiply(36, const_0_2778)))

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">20 - 10</gadget>
<output>10</output>
<gadget id="calculator">200 / 10</gadget>
<output>20</output>
<result>20</result>


if x and y are both odd prime numbers and x < y , how many distinct positive r integer factors does 2 xy have ?

Explanation: since 2 xy prime r factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer .

multiply(multiply(2, add(const_1, const_1)), add(const_1, const_1))

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


a man can row 8 kmph in still water . when the river is running at 3 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?

Explanation: "m = 8 s = 3 ds = 11 us = 5 x / 11 + x / 5 = 1 x = 3.4 d = 3.4 * 2 = 6.8 answer : e"

multiply(divide(multiply(add(8, 3), subtract(8, 3)), add(add(8, 3), subtract(8, 3))), const_2)

<gadget id="calculator">8 + 3</gadget>
<output>11</output>
<gadget id="calculator">8 - 3</gadget>
<output>5</output>
<gadget id="calculator">11 * 5</gadget>
<output>55</output>
<gadget id="calculator">11 + 5</gadget>
<output>16</output>
<gadget id="calculator">55 / 16</gadget>
<output>55/16 = around 3.4375</output>
<gadget id="calculator">(55/16) * 2</gadget>
<output>55/8 = around 6.875</output>
<result>55/8 = around 6.875</result>


the length of a train and that of a platform are equal . if with a speed of 36 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?

Explanation: "speed = [ 36 * 5 / 18 ] m / sec = 10 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 10 ã ¨ x = 10 * 60 / 2 = 300 answer : c"

divide(divide(multiply(36, const_1000), divide(const_60, const_1)), const_2)

<gadget id="calculator">36 * 1_000</gadget>
<output>36_000</output>
<gadget id="calculator">60 / 1</gadget>
<output>60</output>
<gadget id="calculator">36_000 / 60</gadget>
<output>600</output>
<gadget id="calculator">600 / 2</gadget>
<output>300</output>
<result>300</result>


the overall age of x and y is 19 year greater than the overall age of y and z . z is how many decades younger that x ?

Explanation: "d 19 ( x + y ) â € “ ( y + z ) = 19 x â € “ z = 19"

<gadget id="calculator">19 / 1</gadget>
<output>19</output>
<result>19</result>


for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 16 , then v =

Explanation: "( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 16 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 36 the answer is c ."

divide(divide(16, 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">16 / (2/3)</gadget>
<output>24</output>
<gadget id="calculator">24 / (2/3)</gadget>
<output>36</output>
<result>36</result>


a group of men decided to do a work in 55 days , but 15 of them became absent . if the rest of the group did the work in 60 days , find the original number of men ?

Explanation: "original number of men = 15 * 60 / ( 60 - 55 ) = 180 answer is a"

divide(multiply(15, 60), subtract(60, 55))

<gadget id="calculator">15 * 60</gadget>
<output>900</output>
<gadget id="calculator">60 - 55</gadget>
<output>5</output>
<gadget id="calculator">900 / 5</gadget>
<output>180</output>
<result>180</result>


a train 250 m long , running with a speed of 50 km / hr will pass a tree in ?

Explanation: "speed = 50 * 5 / 18 = 125 / 9 m / sec time taken = 250 * 9 / 125 = 18 sec answer : a"

multiply(divide(250, multiply(50, const_1000)), const_3600)

<gadget id="calculator">50 * 1_000</gadget>
<output>50_000</output>
<gadget id="calculator">250 / 50_000</gadget>
<output>1/200 = around 0.005</output>
<gadget id="calculator">(1/200) * 3_600</gadget>
<output>18</output>
<result>18</result>


country x imposes a two - tiered tax on imported cars : the first tier imposes a tax of 25 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 15 % . if ron imported a $ 30000 imported car and ended up paying $ 5500 in taxes , what is the first tier ' s price level ?

Explanation: let t be the tier price , p be total price = 30000 per the given conditions : 0.25 t + 0.15 ( p - t ) = 5500 0.25 t + 0.15 * 30000 - 0.15 t = 5500 0.10 t + 4500 = 5500 0.10 t = 5500 - 4500 = 1000 t = 1000 / 0.10 = 10000 answer a

divide(subtract(5500, multiply(divide(15, const_100), 30000)), subtract(divide(25, const_100), divide(15, const_100)))

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) * 30_000</gadget>
<output>4_500</output>
<gadget id="calculator">5_500 - 4_500</gadget>
<output>1_000</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) - (3/20)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1_000 / (1/10)</gadget>
<output>10_000</output>
<result>10_000</result>


in the faculty of reverse - engineering , 230 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?

Explanation: "answer is d : 649 solution : total number of students studying both are 423 + 230 - 134 = 519 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 519 , so 100 % is approx . 649 ."

<gadget id="calculator">230 + 423</gadget>
<output>653</output>
<result>653</result>


the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 48 . what is a possible value for the mean of the distribution ?

Explanation: "the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 48 : { mean } - 3 * { sd } > 48 ; { mean } - 6 > 48 ; { mean } > 54 . answer : d ."

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">48 + 6</gadget>
<output>54</output>
<gadget id="calculator">54 + 1</gadget>
<output>55</output>
<result>55</result>


a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 9 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?

Explanation: "let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 9 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 9 ) = 0.08 t - - > 60 + 6 ( t - 9 ) = 8 t - - > t = 3 . answer : a ."

divide(subtract(0.60, multiply(0.06, 9)), subtract(0.08, 0.06))

<gadget id="calculator">0.06 * 9</gadget>
<output>0.54</output>
<gadget id="calculator">0.6 - 0.54</gadget>
<output>0.06</output>
<gadget id="calculator">0.08 - 0.06</gadget>
<output>0.02</output>
<gadget id="calculator">0.06 / 0.02</gadget>
<output>3</output>
<result>3</result>


zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 9 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 9 questions did zachary answer correctly ?

Explanation: "i got two equations : 3 x - 2 y = 25 x + y = 9 3 x - 2 ( 9 - x ) = 25 3 x - 18 + 2 x = 25 5 x = 43 x = 8.6 or between 8 and 9 . ( ans c )"

divide(add(subtract(multiply(2, subtract(9, 2)), multiply(3, 2)), 31), add(3, 2))

<gadget id="calculator">9 - 2</gadget>
<output>7</output>
<gadget id="calculator">2 * 7</gadget>
<output>14</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">14 - 6</gadget>
<output>8</output>
<gadget id="calculator">8 + 31</gadget>
<output>39</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">39 / 5</gadget>
<output>39/5 = around 7.8</output>
<result>39/5 = around 7.8</result>


if the average of 5 positive integers is 60 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?

Explanation: "sum of 5 integer ( a , b , c , d , e ) = 5 * 60 = 300 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 300 i . e . 5 a = 290 i . e . a = 58 i . e . largest e = 58 + 10 = 68 answer : option d"

add(divide(subtract(multiply(60, 5), 10), 5), 10)

<gadget id="calculator">60 * 5</gadget>
<output>300</output>
<gadget id="calculator">300 - 10</gadget>
<output>290</output>
<gadget id="calculator">290 / 5</gadget>
<output>58</output>
<gadget id="calculator">58 + 10</gadget>
<output>68</output>
<result>68</result>


in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 160 of the workers of that company are men , how many of the workers are women ?

Explanation: "set up equation : x = total number of workers 160 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 160 = 16 / 30 x x = 300 300 - 160 = 140 answer e"

multiply(divide(160, add(subtract(divide(const_1, const_3), multiply(divide(const_1, const_3), divide(20, const_100))), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100)))), add(multiply(divide(const_1, const_3), divide(20, const_100)), subtract(subtract(const_1, divide(const_1, const_3)), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100)))))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/3) * (1/5)</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/3) - (1/15)</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/3) * (2/5)</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">(4/15) + (4/15)</gadget>
<output>8/15 = around 0.533333</output>
<gadget id="calculator">160 / (8/15)</gadget>
<output>300</output>
<gadget id="calculator">(2/3) - (4/15)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(1/15) + (2/5)</gadget>
<output>7/15 = around 0.466667</output>
<gadget id="calculator">300 * (7/15)</gadget>
<output>140</output>
<result>140</result>


Explanation: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 53 odd numbers = 53 ^ 2 = 2809 answer : b"

multiply(multiply(53, const_2), divide(53, const_2))

<gadget id="calculator">53 * 2</gadget>
<output>106</output>
<gadget id="calculator">53 / 2</gadget>
<output>53/2 = around 26.5</output>
<gadget id="calculator">106 * (53/2)</gadget>
<output>2_809</output>
<result>2_809</result>


find the value of 5 + 2 â € ¢ ( 8 â € “ 3 )

Explanation: 5 + 2 â € ¢ ( 8 â € “ 3 ) = 5 + 2 ( 5 ) = 5 + 2 * 5 = 5 + 10 = 15 correct answer e

<gadget id="calculator">8 - 3</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<result>15</result>


what least number should be added to 1057 , so that the sum is completely divisible by 23

Explanation: "explanation : ( 1057 / 23 ) gives remainder 22 22 + 1 = 23 , so we need to add 1 answer : option b"

<gadget id="calculator">1_057 % 23</gadget>
<output>22</output>
<gadget id="calculator">23 - 22</gadget>
<output>1</output>
<result>1</result>


. in digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be ?

Explanation: 20 * 10 * 5 = 1000 answer : b

<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<gadget id="calculator">200 * 5</gadget>
<output>1_000</output>
<result>1_000</result>


when 1 / 20 % of 8,000 is subtracted from 1 / 10 of 8,000 , the difference is

Explanation: 1 / 20 % of 8000 = 4 1 / 10 of 8000 = 800 800 - 2 = 798 ans : d

multiply(inverse(10), multiply(multiply(const_100, const_10), add(const_4, const_4)))

<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">1_000 * 8</gadget>
<output>8_000</output>
<gadget id="calculator">(1/10) * 8_000</gadget>
<output>800</output>
<result>800</result>


35 % of the employees of a company are men . 60 % of the men in the company speak french and 40 % of the employees of the company speak french . what is % of the women in the company who do not speak french ?

Explanation: no of employees = 100 ( say ) men = 35 women = 65 men speaking french = 0.6 * 35 = 21 employees speaking french = 0.4 * 100 = 40 therefore women speaking french = 40 - 21 = 19 and women not speaking french = 65 - 19 = 46 % of women speaking french = 46 / 65 * 100 = 70.77 % answer e

multiply(divide(subtract(divide(subtract(const_100, 35), const_100), subtract(divide(40, const_100), multiply(divide(35, const_100), divide(60, const_100)))), divide(subtract(const_100, 35), const_100)), const_100)

<gadget id="calculator">100 - 35</gadget>
<output>65</output>
<gadget id="calculator">65 / 100</gadget>
<output>13/20 = around 0.65</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(7/20) * (3/5)</gadget>
<output>21/100 = around 0.21</output>
<gadget id="calculator">(2/5) - (21/100)</gadget>
<output>19/100 = around 0.19</output>
<gadget id="calculator">(13/20) - (19/100)</gadget>
<output>23/50 = around 0.46</output>
<gadget id="calculator">(23/50) / (13/20)</gadget>
<output>46/65 = around 0.707692</output>
<gadget id="calculator">(46/65) * 100</gadget>
<output>920/13 = around 70.769231</output>
<result>920/13 = around 70.769231</result>


a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 45 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ?

Explanation: "a - b = 120 miles b - c = 60 miles avg speed = 45 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 45 = 180 / 4 t t = 60 b - c = 60 mph answer e"

multiply(divide(divide(add(divide(120, const_2), 120), 45), const_4), divide(120, const_2))

<gadget id="calculator">120 / 2</gadget>
<output>60</output>
<gadget id="calculator">60 + 120</gadget>
<output>180</output>
<gadget id="calculator">180 / 45</gadget>
<output>4</output>
<gadget id="calculator">4 / 4</gadget>
<output>1</output>
<gadget id="calculator">1 * 60</gadget>
<output>60</output>
<result>60</result>


dick and jane each saved $ 5,000 in 1989 . in 1990 dick saved 10 percent more than in 1989 , and together he and jane saved a total of $ 10,000 . approximately what percent less did jane save in 1990 than in 1989 ?

Explanation: "1990 dick saved = $ 5500 jane saved = $ 4500 ( jane saved $ 500 less than she did the prior year ) jane saved approximately $ 500 / 5000 $ ( 10 % ) less in 1990 answer : a"

multiply(subtract(const_1, subtract(const_2, add(divide(10, const_100), const_1))), const_100)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) + 1</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">2 - (11/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">1 - (9/10)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 100</gadget>
<output>10</output>
<result>10</result>


robert ate 7 chocolates , nickel ate 5 chocolates . how many more chocolates did robert ate than nickel ?

Explanation: 7 - 5 = 2 . answer is e

<gadget id="calculator">7 - 5</gadget>
<output>2</output>
<result>2</result>


a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 600 feet . what is its area , in square feet ?

Explanation: you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 600 , you can deduce the following a = 360 b = 480 360 x 480 = 172,800 a is the answer .

multiply(multiply(divide(600, add(const_2, const_3)), const_3), multiply(divide(600, add(const_2, const_3)), const_4))

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">600 / 5</gadget>
<output>120</output>
<gadget id="calculator">120 * 3</gadget>
<output>360</output>
<gadget id="calculator">120 * 4</gadget>
<output>480</output>
<gadget id="calculator">360 * 480</gadget>
<output>172_800</output>
<result>172_800</result>


on dividing 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor

Explanation: "d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 12 a )"

<gadget id="calculator">109 / 9</gadget>
<output>109/9 = around 12.111111</output>
<gadget id="calculator">floor(109/9)</gadget>
<output>12</output>
<result>12</result>


find compound interest on $ 10000 at 15 % per annum for 2 years 4 months , compounded annually .

Explanation: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 10000 x ( 1 +  ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 10000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 13886.25 . : . c . i . = rs . ( 13886.25 - 10000 ) = $ 3886.25 answer a ."

add(add(multiply(10000, divide(15, const_100)), multiply(add(10000, multiply(10000, divide(15, const_100))), divide(15, const_100))), multiply(add(add(10000, multiply(10000, divide(15, const_100))), multiply(add(10000, multiply(10000, divide(15, const_100))), divide(15, const_100))), divide(divide(15, const_100), const_3)))

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">10_000 * (3/20)</gadget>
<output>1_500</output>
<gadget id="calculator">10_000 + 1_500</gadget>
<output>11_500</output>
<gadget id="calculator">11_500 * (3/20)</gadget>
<output>1_725</output>
<gadget id="calculator">1_500 + 1_725</gadget>
<output>3_225</output>
<gadget id="calculator">11_500 + 1_725</gadget>
<output>13_225</output>
<gadget id="calculator">(3/20) / 3</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">13_225 * (1/20)</gadget>
<output>2_645/4 = around 661.25</output>
<gadget id="calculator">3_225 + (2_645/4)</gadget>
<output>15_545/4 = around 3_886.25</output>
<result>15_545/4 = around 3_886.25</result>


having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 1.28 at the candy store . what is john ’ s weekly allowance ?

Explanation: "total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 1.28 therefore , x = $ 4.80 . answer e"

divide(1.28, subtract(const_1, add(divide(3, 5), multiply(divide(const_1, 3), subtract(const_1, divide(3, 5))))))

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(1/3) * (2/5)</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">(3/5) + (2/15)</gadget>
<output>11/15 = around 0.733333</output>
<gadget id="calculator">1 - (11/15)</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">1.28 / (4/15)</gadget>
<output>4.8</output>
<result>4.8</result>


sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 60 ps per meter is ?

Explanation: "3 x * 2 x = 3750 = > x = 25 2 ( 75 + 50 ) = 250 m 250 * 0.60 = rs . 150 answer : c"

divide(multiply(60, rectangle_perimeter(sqrt(divide(multiply(3750, 2), 3)), divide(3750, sqrt(divide(multiply(3750, 2), 3))))), const_100)

<gadget id="calculator">3_750 * 2</gadget>
<output>7_500</output>
<gadget id="calculator">7_500 / 3</gadget>
<output>2_500</output>
<gadget id="calculator">2_500 ** (1/2)</gadget>
<output>50</output>
<gadget id="calculator">3_750 / 50</gadget>
<output>75</output>
<gadget id="calculator">2 * (50 + 75)</gadget>
<output>250</output>
<gadget id="calculator">60 * 250</gadget>
<output>15_000</output>
<gadget id="calculator">15_000 / 100</gadget>
<output>150</output>
<result>150</result>


if a person walks at 25 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :

Explanation: "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 25 25 x = 10 x + 200 15 x = 200 x = 13.3 km . answer : c"

multiply(10, divide(20, subtract(25, 10)))

<gadget id="calculator">25 - 10</gadget>
<output>15</output>
<gadget id="calculator">20 / 15</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">10 * (4/3)</gadget>
<output>40/3 = around 13.333333</output>
<result>40/3 = around 13.333333</result>


a big container is 30 % full with water . if 45 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?

Explanation: "a big container is 30 % full with water and after 45 liters of water is added , the container becomes 75 % full . hence these 45 liters account for 45 % of the container , which means that the capacity of it is 45 / 0.45 = 100 liters . or : if the capacity of the container is x liters then : 0.3 x + 45 = 0.75 x - - > x = 100 liters . answer : e ."

divide(45, subtract(divide(3, 4), divide(30, const_100)))

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/4) - (3/10)</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">45 / (9/20)</gadget>
<output>100</output>
<result>100</result>


find the smallest number that should be multiplied with 54000 to make it a perfect cube .

Explanation: 54000 = 2 ^ 1 * 3 ^ 3 * 10 ^ 3 to make it ps * 2 ^ 2 or 4 answer : a

multiply(divide(divide(divide(divide(54000, const_1000), const_3), const_3), const_3), divide(divide(divide(divide(54000, const_1000), const_3), const_3), const_3))

<gadget id="calculator">54_000 / 1_000</gadget>
<output>54</output>
<gadget id="calculator">54 / 3</gadget>
<output>18</output>
<gadget id="calculator">18 / 3</gadget>
<output>6</output>
<gadget id="calculator">6 / 3</gadget>
<output>2</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<result>4</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 500000 ?

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(divide(500000, multiply(const_1000, const_10)), const_4)

<gadget id="calculator">1_000 * 10</gadget>
<output>10_000</output>
<gadget id="calculator">500_000 / 10_000</gadget>
<output>50</output>
<gadget id="calculator">50 * 4</gadget>
<output>200</output>
<result>200</result>


the average of 7 numbers is 25 . if each number be multiplied by 5 . find the average of new set of numbers ?

Explanation: "explanation : average of new numbers = 25 * 5 = 125 answer : option d"

<gadget id="calculator">25 * 5</gadget>
<output>125</output>
<result>125</result>


a 90 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?

Explanation: "1 : 2 / 5 = 5 : 2 2 / 7 * 90 = 25 answer : a"

subtract(90, divide(90, add(divide(2, 5), const_1)))

<gadget id="calculator">2 / 5</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">90 / (7/5)</gadget>
<output>450/7 = around 64.285714</output>
<gadget id="calculator">90 - (450/7)</gadget>
<output>180/7 = around 25.714286</output>
<result>180/7 = around 25.714286</result>


a courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is :

Explanation: "explanation : number of bricks = courtyard area / 1 brick area = ( 2500 × 1600 / 20 × 10 ) = 20000 option c"

divide(multiply(multiply(25, const_100), multiply(16, const_100)), multiply(20, 10))

<gadget id="calculator">25 * 100</gadget>
<output>2_500</output>
<gadget id="calculator">16 * 100</gadget>
<output>1_600</output>
<gadget id="calculator">2_500 * 1_600</gadget>
<output>4_000_000</output>
<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<gadget id="calculator">4_000_000 / 200</gadget>
<output>20_000</output>
<result>20_000</result>


find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1008 ?

Explanation: "1008 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 900 answer : a"

divide(1008, add(divide(multiply(divide(add(multiply(2, 5), 2), 5), 5), const_100), const_1))

<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<gadget id="calculator">12 / 5</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">(12/5) * 5</gadget>
<output>12</output>
<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(3/25) + 1</gadget>
<output>28/25 = around 1.12</output>
<gadget id="calculator">1_008 / (28/25)</gadget>
<output>900</output>
<result>900</result>


if a sum of money doubles itself in 20 years at simple interest , the ratepercent per annum is

Explanation: "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 20 ) = 5 option d"

divide(divide(const_2, divide(20, const_100)), const_2)

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">2 / (1/5)</gadget>
<output>10</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<result>5</result>


at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 7.50 per hour , how much less than a manager does a chef earn each hour ?

Explanation: "manager wages per hour = $ 7.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 7.50 ) = = > $ 3.75 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 3.75 = ( 20 * ( $ 3.75 ) ) / 100 - - > ( $ 75 ) / 100 - - > $ 0.75 therefore , chef wages per hour = $ 3.75 + $ 0.75 = = > $ 4.5 difference of wages between manager and chef = $ 7.50 - $ 4.5 = = > $ 3 answer : b"

multiply(subtract(const_1, multiply(divide(add(const_100, 20), const_100), divide(const_1, const_2))), 7.50)

<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(6/5) * (1/2)</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">(2/5) * 7.5</gadget>
<output>3</output>
<result>3</result>


a person incurs a loss of 5 % be selling a watch for rs . 1140 . at what price should the watch be sold to earn 5 % profit

Explanation: "explanation : let the new s . p . be x , then . ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) = > ( 95 / 1140 = 105 / x ) = > x = 1260 option c"

multiply(divide(1140, divide(subtract(const_100, 5), const_100)), divide(add(const_100, 5), const_100))

<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">95 / 100</gadget>
<output>19/20 = around 0.95</output>
<gadget id="calculator">1_140 / (19/20)</gadget>
<output>1_200</output>
<gadget id="calculator">100 + 5</gadget>
<output>105</output>
<gadget id="calculator">105 / 100</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">1_200 * (21/20)</gadget>
<output>1_260</output>
<result>1_260</result>


a train is 400 meter long is running at a speed of 60 km / hour . in what time will it pass a signal post ?

Explanation: speed = 60 km / hr = 60 * ( 5 / 18 ) m / sec = 150 / 9 m / sec total distance = 400 meter time = distance / speed = 400 * ( 9 / 150 ) = 24 seconds answer : d

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">400 / (50/3)</gadget>
<output>24</output>
<result>24</result>


how long does a train 105 m long running at the speed of 68 km / hr takes to cross a bridge 90 m length ?

Explanation: "speed = 68 * 5 / 18 = 19 m / sec total distance covered = 105 + 90 = 205 m . required time = 205 / 19 = 10.7 sec . answer : b"

<gadget id="calculator">105 + 90</gadget>
<output>195</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">68 * (5/18)</gadget>
<output>170/9 = around 18.888889</output>
<gadget id="calculator">195 / (170/9)</gadget>
<output>351/34 = around 10.323529</output>
<result>351/34 = around 10.323529</result>


there are 6 people in the elevator . their average weight is 152 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .

Explanation: "solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 152 ) = 1057 - 912 = 145 . answer a"

subtract(multiply(151, 7), multiply(6, 152))

<gadget id="calculator">151 * 7</gadget>
<output>1_057</output>
<gadget id="calculator">6 * 152</gadget>
<output>912</output>
<gadget id="calculator">1_057 - 912</gadget>
<output>145</output>
<result>145</result>


ms . lopez deposits $ 150 in an account that pays 20 % interest , compounded semiannually . how much money will there be in the account at the end of one year ?

Explanation: "using formula - a = p ( 1 + r / n ) ^ nt given p = 150 n = 2 t = 1 r = 0.2 substituting value in formula a = 150 ( 1 + 0.2 / 2 ) ^ 2 a = 181.15 $ = c"

multiply(150, power(add(const_1, divide(divide(20, const_100), const_2)), const_2))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) / 2</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">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>
<gadget id="calculator">150 * (121/100)</gadget>
<output>363/2 = around 181.5</output>
<result>363/2 = around 181.5</result>


how much is 70 % of 40 is greater than 4 / 5 of 25 ?

Explanation: "( 70 / 100 ) * 40 – ( 4 / 5 ) * 25 = 8 answer : e"

subtract(multiply(40, divide(70, const_100)), multiply(divide(4, 5), 25))

<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">40 * (7/10)</gadget>
<output>28</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 25</gadget>
<output>20</output>
<gadget id="calculator">28 - 20</gadget>
<output>8</output>
<result>8</result>


one man adds 3 liters of water to 12 liters of milk and another 4 liters of water to 10 liters of milk . what is the ratio of the strengths of milk in 2 mixtures ?

Explanation: "strength of milk in the mixture = quantity of milk / total quantity of mixture strength of milk in the 1 st mixture = 12 / 15 strength of the milk 2 nd mixture = 10 / 14 the ratio of their strengths = 12 / 15 : 10 / 14 = 28 : 25 answer is c"

<gadget id="calculator">3 + 12</gadget>
<output>15</output>
<gadget id="calculator">12 / 15</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">4 + 10</gadget>
<output>14</output>
<gadget id="calculator">10 / 14</gadget>
<output>5/7 = around 0.714286</output>
<gadget id="calculator">(4/5) / (5/7)</gadget>
<output>28/25 = around 1.12</output>
<result>28/25 = around 1.12</result>


27 is a perfect cube . when x is added to the prime factor of 27 , the result is a prime number . what is x ?

Explanation: 27 is 3 * 3 * 3 then a 3 + 1 = 4 b 3 + 3 = 6 c 3 + 5 = 8 d 3 + 8 = 11 e 3 + 11 = 14 here d is the only addition that gives a prime number .

<gadget id="calculator">27 - 3</gadget>
<output>24</output>
<gadget id="calculator">24 / 3</gadget>
<output>8</output>
<result>8</result>


a part - time employee ’ s hourly wage was increased by 10 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?

Explanation: "let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 10 % wage increase , the employee makes $ 1.10 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.10 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.10 to get : new # of hours = 100 / 1.10 ≈ 90 hours so , the number of hours decreases from 100 hours to ( approximately ) 90 hours . this represents a 10 % decrease ( approximately ) . answer choice a is the closest answer ."

multiply(divide(divide(10, const_100), divide(add(10, const_100), const_100)), const_100)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">10 + 100</gadget>
<output>110</output>
<gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(1/10) / (11/10)</gadget>
<output>1/11 = around 0.090909</output>
<gadget id="calculator">(1/11) * 100</gadget>
<output>100/11 = around 9.090909</output>
<result>100/11 = around 9.090909</result>


the price of stock decreased by 5 % last year and rose by 10 % this year . what is the net percentage change in the price of the stock ?

Explanation: "( 100 % - 5 % ) * ( 100 % + 10 % ) = 0.95 * 1.10 = 1.045 = 104.5 % . the net percentage change in the price of the stock is ( + ) 4.5 % the answer is e"

multiply(subtract(multiply(add(divide(10, const_100), const_1), subtract(const_1, divide(5, const_100))), const_1), const_100)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) + 1</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 - (1/20)</gadget>
<output>19/20 = around 0.95</output>
<gadget id="calculator">(11/10) * (19/20)</gadget>
<output>209/200 = around 1.045</output>
<gadget id="calculator">(209/200) - 1</gadget>
<output>9/200 = around 0.045</output>
<gadget id="calculator">(9/200) * 100</gadget>
<output>9/2 = around 4.5</output>
<result>9/2 = around 4.5</result>


the speed of a subway train is represented by the equation z = s ^ 2 + 2 s for all situations where 0 ≤ s ≤ 7 , where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving . in kilometers per hour , how much faster is the subway train moving after 7 seconds than it was moving after 5 seconds ?

Explanation: "given : z = s ^ 2 + 2 s for 0 ≤ s ≤ 7 z ( 5 ) = 5 ^ 2 + 2 * 5 = 35 z ( 7 ) = 7 ^ 2 + 2 * 7 = 63 therefore z ( 7 ) - z ( 3 ) = 63 - 35 = 28 km / hr option b"

subtract(add(power(7, 2), multiply(7, 2)), add(power(5, 2), multiply(5, 2)))

<gadget id="calculator">7 ** 2</gadget>
<output>49</output>
<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">49 + 14</gadget>
<output>63</output>
<gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">25 + 10</gadget>
<output>35</output>
<gadget id="calculator">63 - 35</gadget>
<output>28</output>
<result>28</result>


a soccer team played 280 games and won 65 percent of them . how many games did it win ?

Explanation: "65 % of 280 = x 0.65 * 280 = x 182 = x answer : a"

<gadget id="calculator">65 * 280</gadget>
<output>18_200</output>
<gadget id="calculator">18_200 / 100</gadget>
<output>182</output>
<result>182</result>


the difference between two numbers is 2395 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is

Explanation: let the smaller number be x . then , larger number = ( 2395 + x ) therefore 2395 + x = ( 6 x + 15 ) ‹ = › 5 x = 2380 ‹ = › x = 476 . answer : c

divide(subtract(2395, 15), subtract(6, const_1))

<gadget id="calculator">2_395 - 15</gadget>
<output>2_380</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">2_380 / 5</gadget>
<output>476</output>
<result>476</result>


right triangle xyzs the base of the prism in the figure above . if xy = xz = â ˆ š 9 and the height of the prism is 6 , what is the volume of the prism ?

Explanation: volume of prism = area of base * height = 1 / 2 * ( square root of 9 ) * ( square root of 9 ) * 6 = 27 answer : b

<gadget id="calculator">9 ** (1/2)</gadget>
<output>3</output>
<gadget id="calculator">(3 * 3) / 2</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">(9/2) * 6</gadget>
<output>27</output>
<result>27</result>


on dividing 22 by a number , the quotient is 7 and the remainder is 1 . find the divisor .

Explanation: "d = ( d - r ) / q = ( 22 - 1 ) / 7 = 21 / 7 = 3 c"

<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>
<gadget id="calculator">floor(22/7)</gadget>
<output>3</output>
<result>3</result>


the smallest number which when diminished by 5 , is divisible by 12 , 16 , 18 , 21 and 28 is

Explanation: "required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 5 = 1008 + 5 = 1013 answer : b"

add(multiply(multiply(power(const_3, const_2.0), power(const_2.0, const_4)), add(const_3, const_4)), 5)

<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">2 ** 4</gadget>
<output>16</output>
<gadget id="calculator">9 * 16</gadget>
<output>144</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">144 * 7</gadget>
<output>1_008</output>
<gadget id="calculator">1_008 + 5</gadget>
<output>1_013</output>
<result>1_013</result>


the ratio between x and y is 7 / 5 ; x is multiplied by y and y is multiplied by x , what is the ratio between the new values of x and y ?

Explanation: ratio = 7 k / 5 k = 7 / 5 , 14 / 10 , etc . x is multiplied by y and y is multiplied by x - - > ( 7 k * 9 k ) / ( 9 k * 7 k ) = 1 answer : c

<gadget id="calculator">7 * 5</gadget>
<output>35</output>
<gadget id="calculator">5 * 7</gadget>
<output>35</output>
<gadget id="calculator">35 / 35</gadget>
<output>1</output>
<result>1</result>


when x is multiplied by 3 , the result is 14 more than the result of subtracting x from 26 . what is the value of x ?

Explanation: the equation that can be formed is : 3 x - 14 = 26 - x or , 4 x = 40 or , x = 10 . a answer .

divide(add(26, 14), add(const_3, const_1))

<gadget id="calculator">26 + 14</gadget>
<output>40</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">40 / 4</gadget>
<output>10</output>
<result>10</result>


raman , lakshmi and muthu enter into partnership . raman invests some money at the beginning , lakshmi invests double the amount after 6 months , and muthu invests thrice the amount after 8 months . if the annual gain be rs . 36000 . lakshmi ' s share is ?

Explanation: x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 36000 = 12000 answer : a

<gadget id="calculator">2 / 6</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 36_000</gadget>
<output>12_000</output>
<result>12_000</result>


in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 10 per square m ?

Explanation: length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 10 * 950 = rs . 9500 a

add(add(multiply(multiply(multiply(20, 15), const_2), 10), multiply(multiply(multiply(20, 5), const_2), 10)), multiply(multiply(multiply(15, 5), const_2), 10))

<gadget id="calculator">20 * 15</gadget>
<output>300</output>
<gadget id="calculator">300 * 2</gadget>
<output>600</output>
<gadget id="calculator">600 * 10</gadget>
<output>6_000</output>
<gadget id="calculator">20 * 5</gadget>
<output>100</output>
<gadget id="calculator">100 * 2</gadget>
<output>200</output>
<gadget id="calculator">200 * 10</gadget>
<output>2_000</output>
<gadget id="calculator">6_000 + 2_000</gadget>
<output>8_000</output>
<gadget id="calculator">15 * 5</gadget>
<output>75</output>
<gadget id="calculator">75 * 2</gadget>
<output>150</output>
<gadget id="calculator">150 * 10</gadget>
<output>1_500</output>
<gadget id="calculator">8_000 + 1_500</gadget>
<output>9_500</output>
<result>9_500</result>


31 of the scientists that attended a certain workshop were wolf prize laureates , and 18 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 50 of the scientists attended that workshop , how many of them were nobel prize laureates ?

Explanation: "lets solve by creating equation . . w = 31 . . total = 50 . . not w = 50 - 31 = 19 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 19 or x = 8 . . so who won nobel but not wolf = x + 3 = 11 . . but people who won both w and n = 13 . . so total who won n = 11 + 18 = 29 . . d"

add(add(3, divide(subtract(subtract(50, 31), 3), const_2)), 18)

<gadget id="calculator">50 - 31</gadget>
<output>19</output>
<gadget id="calculator">19 - 3</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">3 + 8</gadget>
<output>11</output>
<gadget id="calculator">11 + 18</gadget>
<output>29</output>
<result>29</result>


if 4 men can colour 48 m long cloth in 2 days , then 2 men can colour 36 m long cloth in

Explanation: "the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 36 / 6 × 2 = 3 day . c"

divide(36, multiply(divide(48, multiply(4, 2)), 2))

<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">48 / 8</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">36 / 12</gadget>
<output>3</output>
<result>3</result>


a library has an average of 540 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :

Explanation: "since the month begins with sunday , to there will be five sundays in the month average required = ( 540 x 5 + 240 x 25 ) / 30 ) = 290 answer : option c"

divide(add(multiply(add(floor(divide(30, add(const_3, const_4))), const_1), 540), multiply(subtract(30, add(floor(divide(30, add(const_3, const_4))), const_1)), 240)), 30)

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">30 / 7</gadget>
<output>30/7 = around 4.285714</output>
<gadget id="calculator">floor(30/7)</gadget>
<output>4</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 540</gadget>
<output>2_700</output>
<gadget id="calculator">30 - 5</gadget>
<output>25</output>
<gadget id="calculator">25 * 240</gadget>
<output>6_000</output>
<gadget id="calculator">2_700 + 6_000</gadget>
<output>8_700</output>
<gadget id="calculator">8_700 / 30</gadget>
<output>290</output>
<result>290</result>


when sold at a 70 % discount , a sweater nets the merchant a 40 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ?

Explanation: "we should be careful about what are we measuring % on / what is the base . . let the marked up price = 100 . . selling price = 100 - 70 % of 100 = 30 . . profit = 40 % . . therefore the wholesale purchase cost = x . . . . 1.4 x = 30 or x = 21.42 . . . marked price was 100 so . . . so answer is 78.58 % . . e"

subtract(const_100, divide(subtract(const_100, 70), add(const_1, divide(40, const_100))))

<gadget id="calculator">100 - 70</gadget>
<output>30</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 + (2/5)</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">30 / (7/5)</gadget>
<output>150/7 = around 21.428571</output>
<gadget id="calculator">100 - (150/7)</gadget>
<output>550/7 = around 78.571429</output>
<result>550/7 = around 78.571429</result>


on a certain farm the ratio of horses to cows is 4 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 13 : 7 . after the transaction , how many more horses than cows would the farm own ?

Explanation: "originally , there were 4 k horses and k cows . 7 ( 4 k - 15 ) = 13 ( k + 15 ) 28 k - 13 k = 195 + 105 15 k = 300 k = 20 the difference between horses and cows is ( 4 k - 15 ) - ( k + 15 ) = 3 k - 30 = 30 the answer is a ."

subtract(subtract(multiply(4, divide(add(multiply(15, 13), multiply(15, 7)), subtract(multiply(4, 7), 13))), 15), add(divide(add(multiply(15, 13), multiply(15, 7)), subtract(multiply(4, 7), 13)), 15))

<gadget id="calculator">15 * 13</gadget>
<output>195</output>
<gadget id="calculator">15 * 7</gadget>
<output>105</output>
<gadget id="calculator">195 + 105</gadget>
<output>300</output>
<gadget id="calculator">4 * 7</gadget>
<output>28</output>
<gadget id="calculator">28 - 13</gadget>
<output>15</output>
<gadget id="calculator">300 / 15</gadget>
<output>20</output>
<gadget id="calculator">4 * 20</gadget>
<output>80</output>
<gadget id="calculator">80 - 15</gadget>
<output>65</output>
<gadget id="calculator">20 + 15</gadget>
<output>35</output>
<gadget id="calculator">65 - 35</gadget>
<output>30</output>
<result>30</result>


the total age of a and b is 12 years more than the total age of b and c . c is how many year younger than a

Explanation: "explanation : given that a + b = 12 + b + c = > a – c = 12 + b – b = 12 = > c is younger than a by 12 years answer : option b"

<gadget id="calculator">12 * 1</gadget>
<output>12</output>
<result>12</result>


if the diameter of circle r is 40 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?

Explanation: "let diameter of circle r , dr = 40 and diameter of circle s , ds = 100 radius of circle r , rr = 20 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 20 / 50 ) ^ 2 = ( 4 / 10 ) ^ 2 = 16 % answer : a"

<gadget id="calculator">pi * (40 ** 2)</gadget>
<output>1600*pi = around 5_026.548246</output>
<gadget id="calculator">(1600*pi) * 100</gadget>
<output>160000*pi = around 502_654.824574</output>
<gadget id="calculator">pi * (100 ** 2)</gadget>
<output>10000*pi = around 31_415.926536</output>
<gadget id="calculator">(160000*pi) / (10000*pi)</gadget>
<output>16</output>
<result>16</result>


if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer v that must divide n is ?

Explanation: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer v that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"

<gadget id="calculator">72 / 2</gadget>
<output>36</output>
<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<result>12</result>


mary can do a piece of work in 26 days . rosy is 30 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?

Explanation: "ratio of times taken by mary and rosy = 130 : 100 = 13 : 10 suppose rosy takes x days to do the work . 13 : 10 : : 26 : x = > x = 20 days . hence , rosy takes 20 days to complete the work . answer : b"

divide(26, add(const_1, divide(30, const_100)))

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">26 / (13/10)</gadget>
<output>20</output>
<result>20</result>


a student has to obtain 33 % of the total marks to pass . he got 175 marks and failed by 56 marks . the maximum marks are ?

Explanation: "let the maximum marks be x then , 33 % of x = 175 + 56 33 x / 100 = 231 x = 700 answer is e"

divide(add(175, 56), divide(33, const_100))

<gadget id="calculator">175 + 56</gadget>
<output>231</output>
<gadget id="calculator">33 / 100</gadget>
<output>33/100 = around 0.33</output>
<gadget id="calculator">231 / (33/100)</gadget>
<output>700</output>
<result>700</result>


if s and t are both odd prime numbers ands < t , then how many different positive integer factors does 2 sthave ?

Explanation: s and t are both odd prime numbers - it means either s or t is not 2 and since prime numbers have only two factors - 1 and the number itself s and t each will have ( 1 + 1 ) = 2 factors hence 2 st will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer

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


the maximum number of student amoung them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :

Explanation: "solution required number of student = h . c . f of 1001 and 910 = 91 . answer a"

<gadget id="calculator">gcd(1_001, 910)</gadget>
<output>91</output>
<result>91</result>


a class of 20 students took a science test . 10 students had an average ( arithmetic mean ) score of 80 . the other students had an average score of 60 . what is the average score of the whole class ?

Explanation: hear , 10 students had average score of 80 , so , 80 x 10 = 800 and 10 students had average score of 60 , so , 60 x 10 = 600 total no of student are 20 ( 800 + 600 ) / 20 = 70 correct ans is a

divide(add(multiply(10, 80), multiply(subtract(20, 10), 60)), 20)

<gadget id="calculator">10 * 80</gadget>
<output>800</output>
<gadget id="calculator">20 - 10</gadget>
<output>10</output>
<gadget id="calculator">10 * 60</gadget>
<output>600</output>
<gadget id="calculator">800 + 600</gadget>
<output>1_400</output>
<gadget id="calculator">1_400 / 20</gadget>
<output>70</output>
<result>70</result>


if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 900 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 922.50 . what is the value of x ?

Explanation: simple way to solve this question is to use options . from si , we know that x * y = 45,000 . now , put the value of x = 9000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 9000 + 5 % of 9000 = 9450 . 2 nd year , amount = 9450 + 5 % of 9450 = 9922.50 . we can see after 2 years interest = 9922.50 - 9000 = 922.50 . hence , it satisfies the question . hence a is the correct answer

divide(power(divide(900, const_2), const_2), subtract(922.5, 900))

<gadget id="calculator">900 / 2</gadget>
<output>450</output>
<gadget id="calculator">450 ** 2</gadget>
<output>202_500</output>
<gadget id="calculator">922.5 - 900</gadget>
<output>22.5</output>
<gadget id="calculator">202_500 / 22.5</gadget>
<output>9_000</output>
<result>9_000</result>