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aqua_rat__Gbpt4Dcq9gMWwu0q

X Y +Y X ________ The sum of the two digit numbers above is a three digit number PQ1, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X? I) 7 II) 8 III) 9 Choose the correct choice A) I only B) II only C) III only D) I and II only E) all I , II and III

it can be a combination of 9,2 or 8,3 or 7,4 I choose all I , II and III as an answer. <result>E</result>

E

X Y +Y X ________ The sum of the two digit numbers above is a three digit number PQ1, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X? I) 7 II) 8 III) 9

aqua_rat__dVZY2Px2L0W3c1O8

What is the probability that a leap year has 53 Sundays and 52 Mondays? Pick: A) 1/9 B) 1/8 C) 1/3 D) 1/7 E) 1/2

A leap year has 52 weeks and two days Total number of cases = 7 Number of favourable cases = 1 i.e., {Saturday, Sunday} Required Probability = 1/7 Answer:1/7 <result>D</result>

D

What is the probability that a leap year has 53 Sundays and 52 Mondays?

aqua_rat__g0YHS0tbeog4U58Q

Machine Z can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N? Choices: A) 1/2 B) 1/3 C) 4/13 D) 8/29 E) 6/33

Let the following be true: Z makes x in time t Then the following follows: N makes x in 4t/3 O makes x in 3/2(4t/3) = 2t M:N:O = 1:4/3:2=3:4:6 So N=4/(3+4+6)=4/13=4/13 <result>C</result>

C

Machine Z can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?

aqua_rat__vDbEPDil2wuiB4TF

If cement, gravel and sand are to be mixed in 7:10:13 and 7 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available. Answers A) 35 7/8 B) 30 C) 34 2/7 D) 34 5/7 E) 34 6/7

Cement:Gravel:Sand = 7:10:13 --&gt; total of 7+10+13= <gadget id="calculator"> 7+10+13</gadget> <output>30</output> 30 parts. If we use 7 tons of cement, then we'll get 7/7*30= <gadget id="calculator"> 7/7*30</gadget> <output>30</output> 30 tons of mixture. Answer: 30. <result>B</result>

B

If cement, gravel and sand are to be mixed in 7:10:13 and 7 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available.

aqua_rat__mRIBSf0Fv06JP7yH

If the cost price is 90% of the selling price, then what is the profit percent? Options. A) 5% B) 11% C) 13% D) 21% E) 19%

Let S.P. = $100 C.P. = $90 Profit = $10 Profit% = 10/90 * 100 = 25/6 = 11% approximately Answer is 11% <result>B</result>

B

If the cost price is 90% of the selling price, then what is the profit percent?

aqua_rat__pSQo6s0hN3mZwaUL

If w and y are positive integer and w/y is an even integer, which of the following can be an odd integer? Select the correct option: A) x B) xy C) x−y D) x+2y E) w/3

C w-Y Let says w =12 Y=3 iT BECOMES w-Y =9 This is odd True w = 12 Y = 6 THEN w-Y = 2, Which is even hence this is False. so both Yes and NO situations are exists for this Option. C can't be the correct answer same logic goes for E. I believe this question is incomplete b'coz of Irrelevant Options. <result>E</result>

E

If w and y are positive integer and w/y is an even integer, which of the following can be an odd integer?

aqua_rat__yX0bY0nNwrnFcVyJ

Which of the following is equal to 3.14 x 10^6) ? Select: A) 3.14 B) 3140000 C) 31400 D) 314 E) 314000

= 3.14 x 10^6 = 3.14 x 1000000 = 3140000. Answer is 3140000. <result>B</result>

B

Which of the following is equal to 3.14 x 10^6) ?

aqua_rat__k2tvPRofctsiC3OU

9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days? Choose the correct choice A) 19 days B) 18 days C) 12 days D) 27 days E) 26 days

9M + 12B ----- 12 days 12M + 12B ------- 10 days 10M + 10B -------? 108M + 144B = 120M +120B 24B = 12M =&gt; 1M = 2B 18B + 12B = 30B ---- 12 days 20B + 10B 18 + 12= <gadget id="calculator"> 18 + 12</gadget> <output>30</output> 30B ---- 12 days 20B + 10B = 30B -----? 20 + 10= <gadget id="calculator"> 20 + 10</gadget> <output>30</output> 30B -----?=&gt; 12 days Answer: 12 days <result>C</result>

C

9 men and 12 boys finish a job in 12 days, 12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days?

aqua_rat__eRoI1ZzIA8qyiQAs

A box contains 10 tablets of medicine A and 17 tablets of medicine B. What is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted. Choose the correct choice from the following answers A) 12 B) 15 C) 17 D) 19 E) 21

The worst case scenario will be if we remove all 17 tablets of medicine B first. The next 2 tablets we remove have to be of medicine A, so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 17+2= <gadget id="calculator"> 17+2</gadget> <output>19</output> 19 tablets. Answer:19. <result>D</result>

D

A box contains 10 tablets of medicine A and 17 tablets of medicine B. What is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted.

aqua_rat__QjS0ZpEVc1WQt611

Which is better investment 11% stock at 143 or 9 ¾% stock at 117 Pick: A) 11 % stock at 143 B) 9 3/4 stock at 117 C) both D) cannot be compared E) none of these

Let the investment in each (143*117) Income in first case = (11/143*143*117)= <gadget id="calculator">(11/143*143*117)</gadget> <output>1_287</output> 1287 Income in second case=((39/117*4)*143*117)=1394.25 Clearly, 9 ¾% stock at 117 ANSWER 9 3/4 stock at 117 <result>B</result>

B

Which is better investment 11% stock at 143 or 9 ¾% stock at 117

aqua_rat__iHR4pljNwQh5NLIr

96% of the population of a village is 23040. The total population of the village is? Choose the correct choice from the following choices A) 26799 B) 24000 C) 26682 D) 29973 E) 12312

X * (96/100) = 23040 X = 240 * 100= <gadget id="calculator">240 * 100</gadget> <output>24_000</output> 24000 Answer: 24000 <result>B</result>

B

96% of the population of a village is 23040. The total population of the village is?

aqua_rat__xK7y79rhNuVvG9PC

Simplify:935421 x 625 Answers: A) 594983125 B) 584932715 C) 584938125 D) 584638125 E) 584641258

935421 x 625 = 935421 x 54 = 935421 x (10/2)^ 4 935421 x 10^4/2^4=9354210000/16= <gadget id="calculator">9354210000/16</gadget> <output>584_638_125</output> 584638125 Answer is 584638125 <result>D</result>

D

Simplify:935421 x 625

aqua_rat__n2r34GXi2cXpqxCp

1. Internet: $80, with no sales tax, plus $10 shipping fee 2. Store X: $90, a 10% discount, plus 10% tax on discounted price 3. Store Y: $90, no tax 4. Store Z: $90, a 10% sales tax, and $10 rebate after tax Isaac can purchase a certain item in four different ways, as shown in the table. What is the lowest price for which he can purchase this item? Select: A) 88.1 B) 89.0 C) 89.1 D) 89.50 E) 90.0

1. Internet: $80, with no sales tax, plus $10 shipping fee --&gt; 80+10=90; 2. Store X: $90, a 10% discount, plus 10% tax on discounted price --&gt; 90*0.9*1.1 -- 80+10= <gadget id="calculator"> -- 80+10</gadget> <output>90</output> 90; 2. Store X: $90, a 10% discount, plus 10% tax on discounted price --&gt; 90*0.9*1.1=89.1 3. Store Y: $90, no tax --&gt; 90; 4. Store Z: $90, a 10% sales tax, and $10 rebate after tax --&gt; 90*1.1-10 -- 90*0.9*1.1= <gadget id="calculator"> -- 90*0.9*1.1</gadget> <output>89.1</output> 89.1 3. Store Y: $90, no tax --&gt; 90; 4. Store Z: $90, a 10% sales tax, and $10 rebate after tax --&gt; 90*1.1-10=89. So the lowest price is $89. Answer: 89.0.-- 90*1.1-10= <gadget id="calculator">-- 90*1.1-10</gadget> <output>89</output> 89. So the lowest price is $89. Answer: 89.0. <result>B</result>

B

1. Internet: $80, with no sales tax, plus $10 shipping fee 2. Store X: $90, a 10% discount, plus 10% tax on discounted price 3. Store Y: $90, no tax 4. Store Z: $90, a 10% sales tax, and $10 rebate after tax Isaac can purchase a certain item in four different ways, as shown in the table. What is the lowest price for which he can purchase this item?

aqua_rat__CpwEFluSg6V4DGYe

3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 2 men and 3 women will do that task. Choose the correct choice from the following options: A) 1/2 B) 1/10 C) 1/18 D) 1/16 E) 1/11

3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w Therefore 3 m + 8 w = 14 w 2 m + 3 w =7 w 1/2nswer is 7/14 =1/2 1/2nswer: 1/2 <result>A</result>

A

3 men and 8 women complete a task in same time as 6 men and 2 women do. How much fraction of work will be finished in same time if 2 men and 3 women will do that task.

aqua_rat__u3Gn8QrkgWDvYaEg

There are 10 cans in the refrigerator. 5 of them are red and 5 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator. Choose the correct choice. A) 410 B) 490 C) 493 D) 455 E) 445

410nswer: 410. <result>A</result>

A

There are 10 cans in the refrigerator. 5 of them are red and 5 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator.

aqua_rat__Uy06weH9fGkPVL5T

If W is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of W? Choose the correct option: A) 10 B) 12 C) 14 D) 16 E) 18

W = 30! 8 W = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 Out of these 30 , 27 , 24 , 21 , 18, 15 , 12 , 09 , 06 , 3 are factors of 3 3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2, 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3 So we have a total of 14 three's ... Therefore the maximum value of K can be 14 (14) <result>C</result>

C

If W is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of W?

aqua_rat__aYLwJlLY0h10Wrjh

At what rate percent per annum will a sum of money double in 6 years. Choose the correct choice from the following choices. A) 12.5% B) 13.5% C) 11.5% D) 14.5% E) 16.6%

Let principal = P, Then, S.I.=P and Time=8 years Rate = [(100 x P)/ (P x 6)]% = 16.6% per annum. Answer: 16.6% <result>E</result>

E

At what rate percent per annum will a sum of money double in 6 years.

aqua_rat__S5WEYrWqqc0rB1sr

What decimal fraction is 70 ml of a litre ? Choose the correct choice from the following answers. A) .7 B) .07 C) .05 D) 0.07 E) None of these

Answer Required fraction = 70/1000 = 7/100= <gadget id="calculator">7/100</gadget> <output>7/100 = around 0.07</output> .07 Correct Option: .07 <result>B</result>

B

What decimal fraction is 70 ml of a litre ?

aqua_rat__kJpxbpBM16eV4Rcb

There are 8 baskets numbered from 1 to 8 and filled with apples. 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket. If there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process, how many apples were left in the end? Select the correct option A) 640 B) 680 C) 720 D) 760 E) 800

Each child takes a total of 1+2+3+4+5+6+7+8 = 8*9/2= <gadget id="calculator">8*9/2</gadget> <output>36</output> 36 apples. The total number of apples taken by 10 children is 10*36= <gadget id="calculator"> 10*36</gadget> <output>360</output> 360 The number of apples left in the end is 1000 - 360= <gadget id="calculator"> 1000 - 360</gadget> <output>640</output> 640 apples. The answer is 640. <result>A</result>

A

There are 8 baskets numbered from 1 to 8 and filled with apples. 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket. If there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process, how many apples were left in the end?

aqua_rat__OvFYYREtwRo0qu8t

If two numbers x, a perfect square and y, a perfect cube are added results a two digit number, whose digits if reversed, difference is 9, Find x and y ? Choose the most appropriate option: A) x=4,y=8 B) x=4,y=9 C) x=4,y=7 D) x=4,y=9 E) x=5,y=8

4+8= <gadget id="calculator">4+8</gadget> <output>12</output> 12 when reversed 21 21-12= <gadget id="calculator">21-12</gadget> <output>9</output> 9 x=4,y=8 x=4,y=8NSWER:x=4,y=8 <result>A</result>

A

If two numbers x, a perfect square and y, a perfect cube are added results a two digit number, whose digits if reversed, difference is 9, Find x and y ?

aqua_rat__sXGvEmzHSMSil8HA

The food in a camp lasts for 40 men for 35 days. If ten more men join, how many days will the food last? Options: A) 34days B) 32days C) 30days D) 28days E) 26days

one man can consume the same food in 40*35= <gadget id="calculator">40*35</gadget> <output>1_400</output> 1400 days. 10 more men join, the total number of men= 50 The number of days the food will last = 1400/50= <gadget id="calculator">1400/50</gadget> <output>28</output> 28 days. Answer: 28days <result>D</result>

D

The food in a camp lasts for 40 men for 35 days. If ten more men join, how many days will the food last?

aqua_rat__wtK7whl8QE7uTqkb

The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago ? Select. A) 71 years B) 72 years C) 73 years D) 74 years E) 75 years

Answer : A. Required sum = (80 - 3 x 3) years = (80 - 9)= <gadget id="calculator">(80 - 9)</gadget> <output>71</output> 71 years. <result>A</result>

A

The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago ?

aqua_rat__gKgYtFYYxWV7gYLg

If (x+4)^2/(x+10)=8, then the difference between the two possible values of x is: Choose the correct answer: A) 2 B) 6 C) 12 D) 16 E) 24

(x+4)^2/(x+10)=8 (x+4)^2=8(x+10) x^2+8x+16=8x+80 x^2-64=0 (x-8)(x+8)=0 x=8 or x=-8 The answer is 16. <result>D</result>

D

If (x+4)^2/(x+10)=8, then the difference between the two possible values of x is:

aqua_rat__1RQtwSjXTMWhXUes

If m and n are nonzero integers and 390m = 150n, then mn must be divisible by Select the correct option: A) 10 B) 45 C) 50 D) 65 E) 75

390m = 150n; m/n = 5/13. m is a multiple of 5 and n is a multiple of 13, therefore mn must be a multiple of 5*13= <gadget id="calculator">5*13</gadget> <output>65</output> 65. Answer: 65. <result>D</result>

D

If m and n are nonzero integers and 390m = 150n, then mn must be divisible by

aqua_rat__m3GGCW7emjzSoyDz

A is the average (arithmetic mean) of the first 7 positive multiples of 6 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n? Choose the correct choice. A) 8 B) 10 C) 12 D) 16 E) 24

If A^2 - B^2 = 0, then let's assume that A = B. A must equal the 4th positive multiple of 4, thus A = 24, which also equals B. B is the second positive multiple of n, thus n = 24/2= <gadget id="calculator">24/2</gadget> <output>12</output> 12. The answer is 12. <result>C</result>

C

A is the average (arithmetic mean) of the first 7 positive multiples of 6 and B is the median of the first 3 positive multiples of positive integer n. If the value of A^2 – B^2 is zero, what is the value of n?

aqua_rat__pJGQhQRgdvsaORNg

Two pipes P and Q can fill a cistern in 10 and 25 minutes respectively. Both are opened together, but at the end of 5 minutes the first is turned off. How much longer will the cistern take to fill? Choose the correct option: A) 12 1/7 B) 12 1/4 C) 12 1/3 D) 12 1/2 E) 12 1/5

5/10+ x/25 = 1 x= 12 1/2 Answer: 12 1/2 <result>D</result>

D

Two pipes P and Q can fill a cistern in 10 and 25 minutes respectively. Both are opened together, but at the end of 5 minutes the first is turned off. How much longer will the cistern take to fill?

aqua_rat__FZhy1iUc5gOX4G0w

4 litres of water is mixed in certain amount of pure milk whose cost is Rs. 3 per litre. If the dishonest milkman earns a profit of 20% by selling the mixture at initial price then what is the quantity of pure milk obtained by the customer? Choose the correct choice: A) 24 B) 20 C) 18 D) 25 E) None of these

cost given = Rs 3/ltr. i.e cost earned through water mixture= 4*3= <gadget id="calculator">4*3</gadget> <output>12</output> 12 rs therefore earned 20%, that is on water .. therefore total earned= 12*100/20= <gadget id="calculator">12*100/20</gadget> <output>60</output> 60 rs. hence 60/3= <gadget id="calculator">60/3</gadget> <output>20</output> 20 ltr overall mixture! ANSWER:20 <result>B</result>

B

4 litres of water is mixed in certain amount of pure milk whose cost is Rs. 3 per litre. If the dishonest milkman earns a profit of 20% by selling the mixture at initial price then what is the quantity of pure milk obtained by the customer?

aqua_rat__1vMvpRudvK77R9Ks

When two coins are tossed,Find the probability of getting all tails? Choose one: A) 1/3 B) 3/4 C) 1/8 D) 3/8 E) 1/4

When two coins are tossed, S = {HH, HT, TH, TT} where H = Head and T = Tail Let 1/4 = event of getting all tails Then 1/4 = {TT} so, P(1/4) = n(1/4)/n(S) =1/4 <result>E</result>

E

When two coins are tossed,Find the probability of getting all tails?

aqua_rat__WY3hRzxb0AXZ2in4

Ravi purchased 20 dozens of toys at the rate of Rs. 340 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit? Choose one: A) 16.4% B) 1.2% C) 5.6% D) 34.1% E) 12.2%

A C.P. of 1 toy = 340/12 = Rs. 28.3 S.P of 1 toy = Rs. 33 Profit = 4.6/31.25 * 100 = 16.4% 16.4%nswer is 16.4% <result>A</result>

A

Ravi purchased 20 dozens of toys at the rate of Rs. 340 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?

aqua_rat__LCmqTuvQ6Slle63M

Let x, y and z be distinct integers, x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true? Choose the correct choice from the following answers: A) (x – z)^2 * y is even B) (x – z)*y^2 is odd C) (x – z)*y is odd D) (x – y)^2 * z is even E) none

Explanation : Let x = 5, y= 3, z = 2 (according to the given condition) (x – z)2 * y :- ( 5 - 2)2 * 3 = 27 (x – z) * y2 :- (5 - 2) * 32 = 27 (x – z) * y :- (5 - 2) * 3 = 9. (x – y)2 * z :- (5 - 3)2 * 2 = 8. (x – z)^2 * y is evennswer : (x – z)^2 * y is even <result>A</result>

A

Let x, y and z be distinct integers, x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?

aqua_rat__na3XrGQeVKP9CTaX

Boy sells a book for Rs. 450 he gets a loss of 10%, find CP of the book? Pick: A) Rs.300 B) Rs.400 C) Rs.500 D) Rs.550 E) Rs.600

Find cost price Let C.P. of book = x and S.P. = Rs. 450 S.P. of book = C.P. – (10% of C.P.) S.P. = x – (0.10x) 450 = 0.9 x x i.e cost price = Rs.500 Rs.500 <result>C</result>

C

Boy sells a book for Rs. 450 he gets a loss of 10%, find CP of the book?

aqua_rat__B0VTQifqdDx7Cr0s

The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder? Choose the correct choice from the following options. A) 520 sq cm B) 840 sq cm C) 440 sq cm D) 120 sq cm E) 5 sq cm

Explanation: r = 7 h = 3 2πr(h + r) = 2 * 22/7 * 7(10) = 440 sq cm Answer: 440 sq cm <result>C</result>

C

The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?

aqua_rat__A3uXNmxuhxvPZudi

What will $2000 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually? Choose the correct answer. A) $3124 B) $3260 C) $3328 D) $3456 E) $3680

After one year: 1.2 * $2000 After two years: (1.2)^2 * $2000 After three years: (1.2)^3 * $2000 = $3456 The answer is $3456. <result>D</result>

D

What will $2000 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually?

aqua_rat__Xiurcqf66qSQ9huM

Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in: Choose the correct choice from the following options. A) 3 9/17 hours B) 1 13 /17 hours C) 2 8/11 hours D) 4 1/ 2 hours E) 5 1/ 2 hours

Explanation: Pipes A and B can fill the tank in 5 and 6 hours respectively. Therefore, part filled by pipe A in 1 hour =1/5 part filled by pipe B in 1 hour = 1/6 Pipe C can empty the tank in 12 hours. Therefore, part emptied by pipe C in 1 hour =1/12 Net part filled by Pipes A,B,C together in 1 hour =1/5+1/6-1/12=17/60 i.e., the tank can be filled in 60/17=3 9/17 hours. 3 9/17 hoursnswer: Option 3 9/17 hours <result>A</result>

A

Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:

aqua_rat__m6ljlC2PxhZnOi6e

In a certain store, the profit is 320% of the cost. If the cost increases by 40% but the selling price remains constant, approximately what percentage of the selling price is the profit Answers: A) 67% B) 80% C) 90% D) 100% E) None of above

Explanation: Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420. New C.P. = 140% of Rs. 100 = Rs. 140 New S.P. = Rs. 420. Profit = Rs. (420 - 140) = Rs. 280 Required percentage = (280/420) * 100 = 66.67%(approx) =67% 67%nswer: 67% <result>A</result>

A

In a certain store, the profit is 320% of the cost. If the cost increases by 40% but the selling price remains constant, approximately what percentage of the selling price is the profit

aqua_rat__dUctsYLQendmJjmK

A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 37 years and that of the grandchildren is 6 years. What is the average age of the family? Select the correct option: A) 28 4⁄7 years B) 31 5⁄7 years C) 32 2⁄7 years D) 27 1⁄2 years E) None of these

Required average = (67×2+37×2+6×3/2+2+3) =226/7 = 32 2⁄7 years Answer 32 2⁄7 years <result>C</result>

C

A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 37 years and that of the grandchildren is 6 years. What is the average age of the family?

aqua_rat__gf7BbBcG5g4aLjUp

A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1? Choose the correct choice from the following answers A) 5 months B) 6 months C) 7 months D) 8 months E) 9 months

Explanation: Let B joined for x months. Then 85000×12:42500 × x = 3:1 ⇒850×12:425x=3:1 ⇒850×12×1=3×425x Answer: Option 8 months ⇒850×4=425x ⇒x=8 <result>D</result>

D

A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?

aqua_rat__UPY8AYpNocGxWB23

A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is? Options. A) 77 kmph B) 55 kmph C) 54 kmph D) 58 kmph E) 76 kmph

S = 240/16 * 18/5= <gadget id="calculator">240/16 * 18/5</gadget> <output>54</output> 54 kmph Answer: 54 kmph <result>C</result>

C

A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?

aqua_rat__i1AtywxvzeUxrLVM

A & B throws a pair of dice and winner is one who gets a sum of 9 first.if A starts throwing first Then what is the ratio of A winning over B? Choose the most appropriate option: A) 8/9 B) 9/8 C) 7/8 D) 6/9 E) 5/9

probability of a person throwing first and winning is given by 1/(2-p) 1/(2-(1/9))=9/17 prob of a prob of b is 8/17 prob (a/b) 9/8 ANSWER:9/8 <result>B</result>

B

A & B throws a pair of dice and winner is one who gets a sum of 9 first.if A starts throwing first Then what is the ratio of A winning over B?

aqua_rat__vX21GczOKhO8eKlY

A boy wants to go abroad by boat and return by flight. He has a choice of 8 different boat to go and 6 flight to return. In how many ways, can the boy perform his journey? Choose the correct choice from the following answers: A) 20 B) 48 C) 46 D) 50 E) 70

Ans.(B) Sol. Number of choices to go by ship = 8 Number of choices to return by airline = 6 From, fundamental principle, total number of ways of performing the journey = 8 x 6 = 48 ways <result>B</result>

B

A boy wants to go abroad by boat and return by flight. He has a choice of 8 different boat to go and 6 flight to return. In how many ways, can the boy perform his journey?

aqua_rat__rX4AHZ7JO2xVxveq

A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed. Choose one A) 10 m/sec B) 15 m/sec C) 18 m/sec D) 19 m/sec E) 25 m/sec

If length of train is l and speed of train is s, then l/s = 8 (l+180)/s = 20 (l+180)/l = 20/8 =5/2 2l+360 =5*l 3*l= 360 l=120 mtrs s= l/8 = 120/8= <gadget id="calculator">120/8</gadget> <output>15</output> 15 m/sec ANSWER:15 m/sec <result>B</result>

B

A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.

aqua_rat__mDAPz7k4L0l9HM01

How many ways are there to arrange the letters in the word accessibility ? Choose the most appropriate option. A) 1 B) 1260 C) 3780 D) 7560 E) 778377600

13 total words, 2C, 2S, 2I = 13! / 2! 2! 2! = 778377600 Answer 778377600 <result>E</result>

E

How many ways are there to arrange the letters in the word accessibility ?

aqua_rat__adExElKCVE3hKhIy

Sam and Nik start from A and B respectively at the same time and travel towards each other at constant speeds along the same route. Sam meets Nik at point C on the road which is 600m away from starting point A and 400m away from point B. The speed of Sam is 50 m/m(meter/minute). How much time did Sam take to cover the distance between A and B? Select A) 10 minutes B) 15 minutes C) 20 minutes D) 22 minutes E) 17 minutes

total distance from A to B- A - C = 600m, B - C = 400m; therefore A-B = 1000m; Vs=50 m/m; therefore, t = 1000/50= <gadget id="calculator">1000/50</gadget> <output>20</output> 20 minutes. option 20 minutes <result>C</result>

C

Sam and Nik start from A and B respectively at the same time and travel towards each other at constant speeds along the same route. Sam meets Nik at point C on the road which is 600m away from starting point A and 400m away from point B. The speed of Sam is 50 m/m(meter/minute). How much time did Sam take to cover the distance between A and B?

aqua_rat__c3iRL3YyRDPUhNa4

A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent? Choose one. A) 27% B) 20% C) 25% D) 40% E) 28%

900 ---- 180 100 ---- ? =&gt; 20% Answer: 20% <result>B</result>

B

A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?

aqua_rat__bZ138xoXwHYcDenC

The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest)? Options A) 28 years B) 11 years C) 20 years D) 17 years E) 16 years

Present total age of the members = 26(5) = 130 years. Present age of the youngest member = 10 years Present total age of the remaining four members = 130 -10= <gadget id="calculator">130 -10</gadget> <output>120</output> 120 years Their average age at the time of the birth of the youngest member= [120 - (4 * 10)] / 4 = 30 - 10= <gadget id="calculator">30 - 10</gadget> <output>20</output> 20 years. Answer: 20 years <result>C</result>

C

The present average age of a family of five members is 26 years. If the present age of the youngest member in the family is ten years, then what was the average age of the family at the time of the birth of the youngest member ? (Assume no death occurred in the family since the birth of the youngest)?

aqua_rat__wn752fbVz5Gu7YEv

In a school the number of girls is 15 more that that of the boys. now if 19% of the girls were newly joined and 25% of the boys were newly joined the number of girls is 9 more than that of the boys how many girls and boys were there? Choose the correct choice from the following choices. A) 156 B) 157 C) 158 D) 159 E) 160

In a school the number of girls is 15 more that that of the boys. Means G = 15 + B ------ 1 now if 19% of the girls were newly joined and 25% of the boys were newly joined Total Girls are 1.19G Total Boys are 1.25B girls is 9 more than that of the boys. 1.19G = 9 + 1.25B ------ 1 Solving 1 and 2 B= 147 G= 147 + 9= <gadget id="calculator">147 + 9</gadget> <output>156</output> 156 156NSWER:156 <result>A</result>

A

In a school the number of girls is 15 more that that of the boys. now if 19% of the girls were newly joined and 25% of the boys were newly joined the number of girls is 9 more than that of the boys how many girls and boys were there?

aqua_rat__kJMoEwqNTio9o04t

Rose made a part payment of $300 toward buying a brand new car, which represents 5% of the total cost of the car, how much remains to be paid? Choose the correct choice from the following. A) $5700 B) $5500 C) $5800 D) $5200 E) $5880

Explanation: Let's start with what the total price of the car would be. If 5% is equal to $300 then 100% equals $x. We just have to multiply $300 by 20 to get total amount=$6000. Out of this amount we then need to deduct the amount already paid which was $300 so we have $6000-$300=$5700 $5700nswer: Option $5700 6000- 300= <gadget id="calculator"> 6000- 300</gadget> <output>5_700</output> $5700 $5700nswer: Option $5700 <result>A</result>

A

Rose made a part payment of $300 toward buying a brand new car, which represents 5% of the total cost of the car, how much remains to be paid?

aqua_rat__k35XSp3ZP8vAzSUs

A certain list of 100 data has an average (arithmetic mean) of 7 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 104 data with standard deviation less than d? Select the correct option A) -7 and 0 B) 0 and 0 C) 0 and 7 D) 0 and 14 E) 7 and 7

Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller. According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount. Closest to the mean are 7 and 7 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD. Answer: 7 and 7. <result>E</result>

E

A certain list of 100 data has an average (arithmetic mean) of 7 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 104 data with standard deviation less than d?

aqua_rat__MOze4h800sZJ8ouh

If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is? Choose the correct choice from the following A) 1/8 B) 1/2 C) 7/9 D) 1/6 E) 1/1

The number of exhaustive outcomes is 36. Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2 P(E) = 1 - 1/2 = 1/2. Answer:1/2 <result>B</result>

B

If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?

aqua_rat__ZcGtxLGbhs3bPyXS

Pipe A can fill a tank in 16 hrs and pipe B can fill it in 24 hrs. If both the pipes are opened in the empty tank. In how many hours will it be fill 5/4th of that tank? Choose the correct choice: A) 10 B) 12 C) 14 D) 16 E) 18

Part filled A in 1 hr= (1/16) Part filled 12 in 1 hr= (1/24) Part filled by (A+12) together in 1 hr=(1/16)+(1/24)=5/48 So, The tank will be full in 48/5 hrs Time taken to fill Exact quarter tank = (48/5) * (5/4)= <gadget id="calculator">(48/5) * (5/4)</gadget> <output>12</output> 12 hrs Answer : 12 <result>B</result>

B

Pipe A can fill a tank in 16 hrs and pipe B can fill it in 24 hrs. If both the pipes are opened in the empty tank. In how many hours will it be fill 5/4th of that tank?

aqua_rat__W1tJIOvo1ROwk3Ff

The area of the Rest room is 40 m2 that of a longer wall 10 m2 and of the shorter wall 1 m2, find the edge of the new cube? Select: A) 40 m3 B) 10 m2 C) 80 m3 D) 20 m3 E) 50 m3

lb = 40 ; lh = 10 ; fh = 1 (lbh)2 = 40 * 10 * 1 =&gt; lbh = 20 m3 ANSWER:20 m3 <result>D</result>

D

The area of the Rest room is 40 m2 that of a longer wall 10 m2 and of the shorter wall 1 m2, find the edge of the new cube?

aqua_rat__NTrO5AGhO4Yw7qf2

A parts store is having a store-wide sale of 10% off all merchandise. An out-of-stock part can be backordered, but at a 20% fee. If a customer orders an out-of-stock part whose presale price was $40, how much will he pay? Choose the correct choice from the following choices: A) $41.40 B) $42.00 C) $42.60 D) $43.20 E) $43.80

price = (original price - 10% decrease) + 20% increase price = [40 * (90/100)] * (120/100) = 40 * (.90) * (1.2) = 36 * 1.2= <gadget id="calculator">36 * 1.2</gadget> <output>43.2</output> 43.20 The answer is $43.20. <result>D</result>

D

A parts store is having a store-wide sale of 10% off all merchandise. An out-of-stock part can be backordered, but at a 20% fee. If a customer orders an out-of-stock part whose presale price was $40, how much will he pay?

aqua_rat__y105iHTYHIdPrssu

An ice cream store received shipments of ingredients on Tuesday and Wednesday. Tuesday's shipment had 6 different packages, with an average (arithmetic mean) of 11 and 2/3 pounds. Wednesday's shipment included 7 packages, weighing an average of 9 and 3/7 pounds. What was the average package weight, in pounds, of the shipments received on both days? Choose the correct choice from the following answers: A) 9 and 6/7 pounds B) 10 and 1/10 pounds C) 10 and 2/5 pounds D) 136/13 pounds E) 11 and 1/7 pounds

Solution: Average weight = Total weight/number of packages. The total weight on Tuesday was 6 * (11 and 2/3 pounds), or 70 pounds. The total weight on Wednesday was 7 * (9 and 3/7 pounds), or 66 pounds. The sum of the weights for both days is 66 + 70, or 136 pounds. The average is 136 pounds/13 packages. answer: 136/13 pounds <result>D</result>

D

An ice cream store received shipments of ingredients on Tuesday and Wednesday. Tuesday's shipment had 6 different packages, with an average (arithmetic mean) of 11 and 2/3 pounds. Wednesday's shipment included 7 packages, weighing an average of 9 and 3/7 pounds. What was the average package weight, in pounds, of the shipments received on both days?

aqua_rat__AKVbUaIdRD6LJfhr

Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 25 kg of fresh grapes? Choose the correct choice from the following answers: A) 2 kg B) 2.4 kg C) 3.12 kg D) 10 kg E) none of these

The weight of non-water in 25 kg of fresh grapes (which is 100-90= <gadget id="calculator">100-90</gadget> <output>10</output> 10% of whole weight) will be the same as the weight of non-water in x kg of dried grapes (which is 100-20= <gadget id="calculator">100-20</gadget> <output>80</output> 80% of whole weight), so 25∗0.1=x∗0.8--&gt; x=3.12 Answer: 3.12 kg. <result>C</result>

C

Fresh grapes contain 90% by weight while dried grapes contain 20% water by weight. What is the weight of dry grapes available from 25 kg of fresh grapes?

aqua_rat__0QNG0rF0ZnMprmsy

On flipping 3 coins together what is the outcomes for at least One tail and three heads? Choose the most appropriate option: A) 1/7 B) 3/8 C) 3/11 D) 4/8 E) 5/13

Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Favorable outcomes for at least two heads = favorable outcomes for exactly two heads and favorable outcomes for more than two heads = {HHT, HTH, THH,HHH} 4/8 4/8 <result>D</result>

D

On flipping 3 coins together what is the outcomes for at least One tail and three heads?

aqua_rat__ep4CMjqXMr06qtmK

An agent wants to sell x% of a list of 10,000 apartments in a residential area. After market price decreases, the agent must reduce this selection by (x − 8)%. In terms of x, how many apartments will he be able to sell? Select the correct option A) x*x – 8x B) (x)(108 – x) C) (100)(108 – x) D) (100)(92 – x) E) (x-8)/100

Based on the answer choices and the question, this question begs the use of x=8 as a sample number. Initial = 8%*10000 = 800 Reduction = 8-8= <gadget id="calculator">8-8</gadget> <output>0</output> 0%, so no math required here to calculate the reduction; just make sure that you can calculate 800 in your answer. A. x*x – 8x= 0; No B. (x)(108 – x) = 800; Winner! C. (100)(108 – x) &gt; 800; No D. (100)(92 – x) &gt; 800; No E. (x-8)/100 = 0; No (x)(108 – x) <result>B</result>

B

An agent wants to sell x% of a list of 10,000 apartments in a residential area. After market price decreases, the agent must reduce this selection by (x − 8)%. In terms of x, how many apartments will he be able to sell?

aqua_rat__j2Uc1GO7qmK0IoDM

If four coins are tossed, the probability of getting two heads and two tails i Answers: A) 3/8 B) 3/6 C) 3/9 D) 3/1 E) 3/2

Since four coins are tossed, sample space = 24 Getting two heads and two tails can happen in six ways. n(E) = six ways p(E) = 6/24 = 3/8 3/8nswer:3/8 <result>A</result>

A

If four coins are tossed, the probability of getting two heads and two tails i

aqua_rat__V22wI21ERqTtDVKs

A boat crossed a lake from North to East at the speed of 7 km/h, entered a river and covered twice as much distance going upstream at 6 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.8 km/h that day, what was its approximate downstream speed? Choose the correct answer: A) 4 B) 5 C) 6 D) 7 E) 8

One way of solving this is: Speed of boat on still water (lake)=7kmph Speed upstream = 6kmph = speed in still water - speed of river =&gt; speed of river = 1kmph =&gt;Speed downstream = speed in still water + speed of river = 7+1= <gadget id="calculator">7+1</gadget> <output>8</output> 8kmph Ans is 8 <result>E</result>

E

A boat crossed a lake from North to East at the speed of 7 km/h, entered a river and covered twice as much distance going upstream at 6 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.8 km/h that day, what was its approximate downstream speed?

aqua_rat__2PF8wtGsoACjdDtO

At a dinner party,3 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group? Choose the correct answer. A) 1) 5 B) 2) 10 C) 3) 24 D) 4) 2 E) 5) 120

for number of distinct arrangements of 'n' items around a circular table, we get the arrangements by way of (n-1)! in this case, there are 3 guests, so number of distinct arrangements = 2! = 2 Answer : 4) 2 <result>D</result>

D

At a dinner party,3 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?

aqua_rat__Q2O8hGIlmlnJi6TM

A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is? Choose the correct choice A) 1.7 B) 1.9 C) 3 D) 1.5 E) 1.2

M = 9 S = x DS = 9 + x US = 9 - x 9 + x = (9 - x)2 9 + x = 18 -2x 3x = 9 x = 3 Answer:3 <result>C</result>

C

A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?

aqua_rat__6nsaxhU03S0EIqbT

If w/x = 1/3 and w/y = 4/15, then (x + y)/y = Choose the correct option: A) 4/5 B) 6/5 C) 7/5 D) 8/5 E) 9/5

W/X = 1/3=&gt;x=3w and W/Y = 4/15=&gt;y=15/4w (X+Y)/Y = (3w+15/4w)/(15/4w) = (27/4w)/(15/4w) = 9/5 Correct Option: 9/5 <result>E</result>

E

If w/x = 1/3 and w/y = 4/15, then (x + y)/y =

aqua_rat__yCUMgrBAUcTGOxPD

In a city, 40% of the adults are illiterate while 85% of the children are literate. If the ratio of the adults to that of the children is 2 : 3, then what percent of the population is literate ? Choose the correct choice from the following choices: A) 20% B) 25% C) 50% D) 75% E) 80%

ET POPULATION 100 RATIO IS 2:3 So adults=2*100/5= <gadget id="calculator">2*100/5</gadget> <output>40</output> 40 chldren=3*100/5= <gadget id="calculator">3*100/5</gadget> <output>60</output> 60 illterate adult 40*40/100= <gadget id="calculator"> 40*40/100</gadget> <output>16</output> 16 literate adult 24 literate chldren 51 so total literate is 75 ANSWER:75% <result>D</result>

D

In a city, 40% of the adults are illiterate while 85% of the children are literate. If the ratio of the adults to that of the children is 2 : 3, then what percent of the population is literate ?

aqua_rat__aHRrhkH0ZgHu4nSK

If x+y=4 and x2y3 + y2x3=36, what is the value of xy? Answers. A) 1 B) 2 C) 3 D) 4 E) 5

xy=3 As x+y=4 x2y3+y2x3=36 x2y2(y+x)=36 Substituting x+y x2y2=4 xy=4 ANSWER:4 <result>D</result>

D

If x+y=4 and x2y3 + y2x3=36, what is the value of xy?

aqua_rat__boW5HpBUjMBXR17L

Trapezoid JKLM in the x-y plane has coordinates J = (–2, –1), K = (–2, 1), L = (6, 7), and M = (6, –1). What is its perimeter? Choose one A) 34 B) 36 C) 31 D) 40 E) (F) 42

JK =2 LM = 11 KL =using distance formula 10 JM = using distance formula 8 Sum of all is 31 31 <result>C</result>

C

Trapezoid JKLM in the x-y plane has coordinates J = (–2, –1), K = (–2, 1), L = (6, 7), and M = (6, –1). What is its perimeter?

aqua_rat__oHc2E6aOVtscJ9HI

The two lines y = x and x = -2 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z? Choices. A) 16 B) 8√2 C) 8 D) √2 E) (√2)/3

800score Official Solution: The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-2, -2) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height: A = (1/2)bh = (1/2)(2 × 2) = 2; so z = 2. The next step requires us to find the length of a side of a cube that has a face area equal to 2. As you know the 6 faces of a cube are squares. So, we can reduce the problem to finding the length of the side of a square that has an area of 2. Since the area of a square is equal to s², where s is the length of one of its side, we can write and solve the equation s² = 2. Clearly s = √2 , oranswer choice (√2). <result>D</result>

D

The two lines y = x and x = -2 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z?

aqua_rat__KYN8gWd5zlGQ9QXh

The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 6 ? Choose the correct choice from the following options. A) 96 B) 106 C) 158 D) 116 E) 122

Average = total runs / no.of innings = 32 So, total = Average x no.of innings = 32 * 20= <gadget id="calculator">32 * 20</gadget> <output>640</output> 640 Now increase in avg= 4 runs. So, new avg = 32+6= <gadget id="calculator">32+6</gadget> <output>38</output> 38 runs Total runs= new avg x new no. of innings = 38 * 21= <gadget id="calculator">38 * 21</gadget> <output>798</output> 798 Runs made in the 11th inning= 798-640= <gadget id="calculator">798-640</gadget> <output>158</output> 158 ANSWER:158 <result>C</result>

C

The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 6 ?

aqua_rat__oQO1o82BlpYt2zN0

300 × ? + (12 + 4) × 1/8 = 602 Choose one: A) A)4 B) B)3 C) C)5 D) D)2 E) E)8

Explanation: =&gt; 300 × ? + (12 + 4) × 1/8 = 602 =&gt; 300 × ? = 602 - (12 + 4) × 1/8 =&gt; 300 × ? = 602 - 2= <gadget id="calculator">602 - 2</gadget> <output>600</output> 600=&gt; ? = 600/300= <gadget id="calculator">600/300</gadget> <output>2</output> 2 Answer: Option 2 <result>D</result>

D

300 × ? + (12 + 4) × 1/8 = 602

aqua_rat__53nlGOBIuckp14wI

Walking at the rate of 4 kmph a man cover certain distance in 2 hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in. Pick: A) 12 min B) 25 min C) 40 min D) 60 min E) None of these

Explanation : Distance = Speed * time 4*11/4= <gadget id="calculator"> 4*11/4</gadget> <output>11</output> 11km New Speed= 16.5 kmph Therefore time = D/S = 11/16.5 = 40min Answer : 40 min <result>C</result>

C

Walking at the rate of 4 kmph a man cover certain distance in 2 hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in.

aqua_rat__IKkkHf0pjWb5m78I

If C is a whole number, C+1 is a whole number after that. If A is a whole number, what is a whole number before that? Select the correct option: A) -1 B) 1 C) 0 D) 2 E) -2

Solution: We know that the number ‘0’ together with the natural numbers gives us the numbers 0, 1, 2, 3, 4, 5, …………… which are called whole numbers. If A is a whole number and it is greater than 0 then the whole number before that is A – 1, which will always be a whole number. Again, when A is a whole number and it is equal to 0 then the whole number before that is A – 1 which means 0 – 1 = -1, which is not a whole number. Therefore, if A is a whole number then the number before that will not always be a whole number. -1nswer -1 <result>A</result>

A

If C is a whole number, C+1 is a whole number after that. If A is a whole number, what is a whole number before that?

aqua_rat__ODkTiE5yJUGvXtLQ

A can do a piece of work in 4 hours; B and C together can do it in 2 hours, which A and C together can do it in 2 hours. How long will B alone take to do it? Choose the correct choice from the following: A) 2hours B) 3hours C) 4hours D) 5hours E) 6hours

A's 1 hour work = 1/4; (B + C)'s 1 hour work = 1/2; (A + C)'s 1 hour work = 1/2 (A + B + C)'s 1 hour work = (1/4 + 1/2) = 3/4 B's 1 hour work = (3/4 - 1/2) = 1/4 B alone will take 4 hours to do the work. Answer:4hours <result>C</result>

C

A can do a piece of work in 4 hours; B and C together can do it in 2 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?

aqua_rat__5WrmLSb6AeXOnLw9

Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm. Choose the correct choice from the following A) 289 cm2 B) 285 cm2 C) 287 cm2 D) 267 cm2 E) 207 cm2

Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2 Answer: 285 cm2 <result>B</result>

B

Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.

aqua_rat__Dhyff9hUcdzavTe5

Adam borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond four years. If he pays a total interest of 11,900 at the end of nine years, how much money did he borrow? Choose the correct option. A) 10,526 B) 12,526 C) 14,000 D) 16,000 E) 16,536

Let the sum borrowed be x. Then, (x×6×21/00)+(x×9×3/100)+(x×14×4/100)= 11900 ⇒ (3⁄25x + 27⁄100x + 14⁄25x) = 11400 ⇒ 95⁄100x = 11900 ⇒ x = (11900×100/95)= 12526 Hence, sum borrowed = 12,526 Answer 12,526 <result>B</result>

B

Adam borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond four years. If he pays a total interest of 11,900 at the end of nine years, how much money did he borrow?

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A man has Rs. 544 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? Choose the correct choice from the following answers: A) 102 B) 38 C) 37 D) 90 E) 28

Let number of notes of each denomination be x. Then x + 5x + 10x = 544 ⇒ 16x = 544 ∴ x = 34. Hence, total number of notes = 3x = 102 102nswer:102 <result>A</result>

A

A man has Rs. 544 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

aqua_rat__jbfwBZQGRVEK7a1C

A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long? Choose the correct choice: A) 6 B) 3 C) 4 D) 9 E) 2

D = 25 * 60 + 1500= <gadget id="calculator">25 * 60 + 1500</gadget> <output>3_000</output> 3000 m T= 3000/60 * 18/5= <gadget id="calculator">3000/60 * 18/5</gadget> <output>180</output> 180 sec= 3 mins Answer:3 <result>B</result>

B

A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?

aqua_rat__LKbKNBpSchfJr87g

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 20 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? Answers: A) 40 B) 135 C) 50 D) 55 E) 60

A- 135 = 120 Miles 135 - C = 60 Miles Avg Speed = 20 Miles Time taken for A-135 3t and 135-C be t avg speed = (120+60) / Total time 20 = 180/4t t = 135 135-C = 135mph Answer 135 <result>B</result>

B

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 20 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?

aqua_rat__Vm18Wm9fPvNTRwBS

The average weight of a class is x pounds. When a new student weighing 90 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x? Options: A) 85 B) 86 C) 88 D) 90 E) 99

When the student weighs 90 pounds the average weight is x - 1 pounds; When the student weighs 110 pounds the average weight is x + 4 pounds. So, the increase in total weight of 110 - 90= <gadget id="calculator">110 - 90</gadget> <output>20</output> 20 pounds corresponds to the increase in average weight of (x + 4) - (x - 1) =5 pounds, which means that there are 20/5 ( + 4) - ( - 1)= <gadget id="calculator">( + 4) - ( - 1)</gadget> <output>5</output> 5 pounds, which means that there are 20/5= <gadget id="calculator"> 20/5</gadget> <output>4</output> 4 students (including the new one). So, initially there were 5 student. Total weight= 5x + 90 = 6(x-1) --&gt; x = 96 pounds. Answer: 99. <result>E</result>

E

The average weight of a class is x pounds. When a new student weighing 90 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?

aqua_rat__YYNKyfvzCUujVWLE

Margaret is 10 years more than twice the age of his son. The age of son is 12. Find the age of mother and find the difference between their ages Choose the correct choice from the following answers. A) 10yrs B) 22yrs C) 30yrs D) 40yrs E) 50yrs

Let, age of son x=12 Margaret is 10 years more than twice the age of his son, y = 10+2(x) =10+2(12) =10+24= <gadget id="calculator">10+24</gadget> <output>34</output> 34yrs Difference= 34 - 12= <gadget id="calculator">34 - 12</gadget> <output>22</output> 22yrs ANSWER:22yrs <result>B</result>

B

Margaret is 10 years more than twice the age of his son. The age of son is 12. Find the age of mother and find the difference between their ages

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Tina’s cat weighs 2.6 kilograms. Her dog weighs 6 times as much as her cat. How much does her dog weigh in kilograms? Choose one. A) A)10.4kg B) B)38kg C) C)22kg D) D)15.6kg E) E)20kg

2.6*6= <gadget id="calculator">2.6*6</gadget> <output>15.6</output> 15.6kg.Answer is 15.6kg. <result>D</result>

D

Tina’s cat weighs 2.6 kilograms. Her dog weighs 6 times as much as her cat. How much does her dog weigh in kilograms?

aqua_rat__HdUimfBkt2ERxqlD

If it takes 70 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job? Choose the correct option. A) 40/3 B) 11 C) 7 D) 7/3 E) 9/7

70 Workers = 3 hours then, 1 Worker = 3*70 Hours 30 Workers = (3*70) /(30)= <gadget id="calculator">(3*70) /(30)</gadget> <output>7</output> 7 ANSWER:7 <result>C</result>

C

If it takes 70 workers 3 hours to disassemble the exhibition rides at a small amusement park, how many hours would it take 30 workers to do this same job?

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g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(e) is divisible by 4^11, what is the smallest possible value for e? Choose the correct choice from the following options. A) 22 B) 24 C) 28 D) 32 E) 44

g(e)=4^11=2^22. So we have to find a product with atleast 22 2's in it. in option 1 22 the total no of 2's = [22/2] + [22/4] +[22/8] +[22/16] = 11+5+2+1= <gadget id="calculator">11+5+2+1</gadget> <output>19</output> 19 in option 2 24 the total no of 2's= [24/2] + [24/4] +[24/8] +[24/16] = 12+6+3+1= <gadget id="calculator">12+6+3+1</gadget> <output>22</output> 22 . Hence 24 <result>B</result>

B

g(x) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(e) is divisible by 4^11, what is the smallest possible value for e?

aqua_rat__6NX8DxDZWr233p4C

A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? Answers A) 2999 B) 1350 C) 2677 D) 2898 E) 2787

Area = (l + b +2d) 2d = (75 + 55 +2.5 * 2) 2*2.5 =&gt; 675 675 * 2 = Rs.1350 Answer1350 <result>B</result>

B

A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?

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Due to an increase in 30% in the price of eggs, 3 eggs less are available for Rs. 7.80. Find the present rate of eggs per dozen. Choose one A) Rs. 8.36 B) Rs. 9.36 C) Rs. 10.36 D) Rs. 11.36 E) Rs. 11.98

Let the original price per egg be Rs x Then increased price will be, (130/100 x) =7.80/x −7.80/(130/100) x =3 =7.80/x −780/130x =3 =390x=234 x=0.6 Actual price was Rs 0.6 Present price per dozen will be Rs.(12∗130/100 ∗0.6)=Rs.9.36 Answer : Rs. 9.36 <result>B</result>

B

Due to an increase in 30% in the price of eggs, 3 eggs less are available for Rs. 7.80. Find the present rate of eggs per dozen.

aqua_rat__QHJF0LXthrEL6XRK

Which of the following could be the value of x, if |-6x + 24| = 54? Choose the correct choice from the following answers: A) 5 B) 1 C) 1/5 D) 12 E) -12

|-6x + 24| = 54 =&gt; -6x + 24 = 54 or -6x + 24 = -54 =&gt; -6x = 30 or -6x = -78 =&gt; x = -5 or x = 12 Answer 12 <result>D</result>

D

Which of the following could be the value of x, if |-6x + 24| = 54?

aqua_rat__4XbJkl6n0ks61i3X

Juan is a gold medalist in athletics. In the month of May, if Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate? Choose the correct choice from the following choices: A) 10x/y B) 11x/y C) 9x/y D) 12x/y E) 13x/y

velocity=distance/time; since he ran at same rate both d tyms, y/11=x/t so t=11x/y ANSWER:11x/y <result>B</result>

B

Juan is a gold medalist in athletics. In the month of May, if Juan takes 11 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?

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Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2.5% more. She would get how much? Choose the correct choice from the following A) 9800 B) 96288 C) 26667 D) 1662 E) 2882

(8000*3*2.5)/100= <gadget id="calculator">(8000*3*2.5)/100</gadget> <output>600</output> 600 9200 -------- 9800 9800nswer:9800 <result>A</result>

A

Sonika deposited Rs.8000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2.5% more. She would get how much?

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There are between 500 and 510 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection? Choose the correct choice from the following choices. A) 501 B) 503 C) 506 D) 507 E) 510

Let number of cards = x If the cards are counted 3 at a time , there are 2 left over- x= 3p+2 x can take values 503 , 506 , 510 If the cards are counted 4 at a time , there is 1 left over x= 4q+1 x can take values 501 , 506 Therefore , x = 506 Answer 506 <result>C</result>

C

There are between 500 and 510 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?

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Solve:- 555 x 555 x 555 + 555 x 555 x 555 = ?(555 x 555 - 555 x 555 + 555 x 555) Answers. A) 888 B) 333 C) 555 D) 988 E) 1110

Given Exp. = (a3 + b3) = (a + b) = (555 + 555)= <gadget id="calculator">(555 + 555)</gadget> <output>1_110</output> 1110(a2 - ab + b2) Answer 1110 <result>E</result>

E

Solve:- 555 x 555 x 555 + 555 x 555 x 555 = ?(555 x 555 - 555 x 555 + 555 x 555)

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A fair 2 sided coin is flipped 4 times. What is the probability that tails will be the result at least twice, but not more than 4 times? Answers: A) 1/8 B) 2/3 C) 5/8 D) 4/7 E) 3/7

at least twice, but not more than 4 timesmeans exactly 2 times, 3 times, 4 times The probability of getting exactly k results out of n flips is n5/8k/2^n 45/82/2^4+45/83/2^4=10/16=5/8 Option: 5/8 <result>C</result>

C

A fair 2 sided coin is flipped 4 times. What is the probability that tails will be the result at least twice, but not more than 4 times?

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Rs.590 is divided amongst A, B, C so that 5 times A's share, six times B's share and eight times C's share are all equal. Find C's share? Choose the correct choice from the following answers: A) 177 B) 150 C) 817 D) 716 E) 616

A+150+C = 590 5A = 6150 = 8C = x A:150:C = 1/5:1/6:1/8 = 24:20:15 15/59 * 590 = Rs.150 Answer: 150 <result>B</result>

B

Rs.590 is divided amongst A, B, C so that 5 times A's share, six times B's share and eight times C's share are all equal. Find C's share?

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Find the value of 72516 x 9999 = m? Choose the most appropriate option: A) 456578972 B) 436567874 C) 725087484 D) 725117481 E) 357889964

72516 x 9999 = 72516 x (10000 - 1) = 72516 x 10000 - 72516 x 1 = 725160000 - 72516= <gadget id="calculator">725160000 - 72516</gadget> <output>725_087_484</output> 725087484 725087484 <result>C</result>

C

Find the value of 72516 x 9999 = m?

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If a truck is traveling at a constant rate of 54 kilometers per hour, how many seconds will it take the truck to travel a distance of 600 meters? (1 kilometer = 1000 meters) Choose the correct answer A) 18 B) 24 C) 30 D) 36 E) 40

Speed = 54 Km/hr =&gt; 54,000 m/hr In one minute =&gt; 54000/60= <gadget id="calculator">54000/60</gadget> <output>900</output> 900 meters In one sec=&gt; 900/60= <gadget id="calculator">900/60</gadget> <output>15</output> 15 meters Time= Total distance need to be covered / Avg. speed =&gt; 600/ 15= <gadget id="calculator">600/ 15</gadget> <output>40</output> 40 and hence the Answer : 40 <result>E</result>

E

If a truck is traveling at a constant rate of 54 kilometers per hour, how many seconds will it take the truck to travel a distance of 600 meters? (1 kilometer = 1000 meters)

aqua_rat__CDgQq2KwyqOYixqL

When a number is divided by 6 &then multiply by 12 the answer is 15 what is the no.? Choices. A) 4.5 B) 5 C) 5.6 D) 7.5 E) 6.5

if $x$ is the number, x/6 * 12 = 15 =&gt; 2x = 15 =&gt; x = 7.5 7.5 <result>D</result>

D

When a number is divided by 6 &then multiply by 12 the answer is 15 what is the no.?

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For all even integers n, h(n) is defined to be the sum of the even integers between 4 and n, inclusive. What is the value of h(18)/h(10) ? Choose the correct choice from the following choices A) 3 B) 1.8 C) 6 D) 18 E) 60

CONCEPT: When terms are in Arithmetic Progression (A.P.) i.e. terms are equally spaced then Mean = Median =(First+Last)/2 and Sum = Mean*Number of terms h(18) = [(4+18)/2]*8 = 88 h(10) (4+18)/2 *8= <gadget id="calculator">(4+18)/2 *8</gadget> <output>88</output> 88 h(10)= (4+10)/2]*4 = 28 h(18)/h(10) (4+10)/2 *4= <gadget id="calculator">(4+10)/2 *4</gadget> <output>28</output> 28 h(18)/h(10)= (88) / (28) ~ 3 3nswer : 3 <result>A</result>

A

For all even integers n, h(n) is defined to be the sum of the even integers between 4 and n, inclusive. What is the value of h(18)/h(10) ?

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A is thrice as efficient as B and is, therefore, able to finish a piece of work 10 days earlier than B. In how many days A and B will finish it together? Choose the correct choice from the following A) 62 B) 78 C) 23 D) 5 E) 32

WC = 3:1 WT = 1:3 x 3x 1/x – 1/3x = 1/10 x = 20/3 3/20 + 1/20 = 1/5 =&gt; 5 days Answer: 5 <result>D</result>

D

A is thrice as efficient as B and is, therefore, able to finish a piece of work 10 days earlier than B. In how many days A and B will finish it together?

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On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is: Pick one: A) 48759 B) 51236 C) 47619 D) 6974 E) 1235

Explanation: By hit and trial, we find that 47619 x 7 = 333333. ANSWER:47619 <result>C</result>

C

On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is:

aqua_rat__DfHpZlag8iYtYSjv

By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent? Select A) 42 6/7 B) 35 C) 20 D) 25 E) 40

50 SP = 50 CP + 15 SP 35 SP = 50 CP 35 --- 15 CP gain 100 --- ? =&gt; 42 6/7% 42 6/7NSWER 42 6/7 <result>A</result>

A

By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?

aqua_rat__4V55DUyshKmIraq6

What decimal of an hour is a second ? Select. A) .0025 B) .0256 C) .00027 D) .000126 E) none of the above

Required decimal = 1/(60*60) =1/3600 = .00027 Answer = .00027 <result>C</result>

C

What decimal of an hour is a second ?

aqua_rat__OnvjZj9WMfNOsBJl

In an election a candidate who gets 84% of the votes is elected by a majority of 476 votes. What is the total number of votes polled? Options: A) 630 B) 700 C) 535 D) 450 E) 815

Let the total number of votes polled be x Then, votes polled by other candidate = (100-84)= <gadget id="calculator">(100-84)</gadget> <output>16</output> 16% of x 84% of x - 16% of x= 476 68x/100 = 476 x = 476*100/68= <gadget id="calculator">476*100/68</gadget> <output>700</output> 700 Answer is 700 <result>B</result>

B

In an election a candidate who gets 84% of the votes is elected by a majority of 476 votes. What is the total number of votes polled?

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The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 64% of the required amount. What is the net difference in the expenditure on that product? Choose the correct option: A) 12.5% B) 13% C) 15% D) 17% E) 20%

Quantity X Rate = Price 1 x 1 = 1 0.64 x 1.25 = 0.8 Decrease in price = (0.2/1) × 100 = 20% 20%) <result>E</result>

E

The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 64% of the required amount. What is the net difference in the expenditure on that product?

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When running a mile during a recent track meet, Nuria was initially credited with a final time of 3 minutes, 44 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile? Choose one: A) 5 minutes, 17.6 seconds B) 5 minutes, 21.8 seconds C) 4 minutes, 10.4 seconds D) 5 minutes, 44.44 seconds E) 5 minutes, 43.56 seconds

One approach: The watch starts to work after Nuria began his running. It means the time should be greater than credited 3 minutes, 44 seconds. The only number is 4 minutes, 10.4 seconds. Another approach: 11/25 close to 30 second when added to the 3 minutes, 44 seconds, it means it passes 4 minute. Answer: 4 minutes, 10.4 seconds <result>C</result>

C

When running a mile during a recent track meet, Nuria was initially credited with a final time of 3 minutes, 44 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile?