# GRE Quantitative Reasoning Practice Questions and Answers

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## Practice Questions and Answers on Quantitative Reasoning

Directions f0r questions 1 to 20: Answer the questions independently of each other.

1. If 20! = 20 x 19 x 18 x 17 x ……… x  3  x 2 x 1, the maximum power of 3 which will divide 20! is:

(a) 5

(b) 6

(c) 7

(d) 8

2. The population of a town is 311250. The ratio of population of women to men is 1075 : 1000.  There are 24% literate among men and 8% literate among women. What percentage of persons in the town is illiterate? »

(a) 84.3%

(b) 83.7%

(c) 72.6%

(d) 79%

3. Five friends Jayesh, Karteek, Lakshman, Mayur and Nitin wanted to buy clothes from Arrow. Jayesh has more than thrice the amount that Lakshman has. Karteek has a lesser amount as compared to Mayur. Nitin has twice as much as Mayur. Lakshman has as much as Mayur. They each have to buy at-least a shirt or a T-shirt or a sweater or a tie or a pair of trousers, which are  priced at Rs.1200, Rs.400, Rs.800, Rs.600 and Rs.1400 respectively. Karteek borrows Rs.300 from Jayesh and buys a tie and is left with no money. Mayur borrows Rs.300 from Nitin, buys a  sweater and is left with no money. Lakshman borrows equal amounts from Nitin and Jayesh and buys a shirt. Then, Jayesh gives Rs.50 to Nitin and they buy the remaining two items, and both are left with no money. What is the maximum number of items that Jayesh can buy with his own money?

(a) 1

(b) 2

(c) 3

(d) 4

4. What is the area of the figure below, given that all the six whorls drawn here are equal semicircles with diameter 7 cm.? (Take π = 3.14)

(a) 213.5 cm^{2}

(b) 425 cm^{2}

(c) 231 cm^{2}

(d) 854 cm^{2}

5. A manufacturing company uses 10 machines, the annual output of which amounts to Rs.42000 and pays 10% of the profit to its share holders. The annual manufacturing expenses are Rs.18000  and the establishment charges Rs.9000. The output and manufacturing expenses are in proportion to the number of machines ‘and the shareholders are paid in proportion to the profit.  What will the company pay its shareholders if one machine breaks down and it remains idle for one year?

(a) Rs.1260

(b) Rs.1500

(c) Rs. 1480

(d) Rs. 1320

6. The price of sugar for 6  consecutive days was Rs.6, Rs.5.5, Rs.6.2, Rs.7.1, Rs.6.8 and Rs.5.5 per kg. The increase in average price for the last 4 days over the first 4 days is equal to:

(a) 25 paise

(b) 20 paise

(c) 30 paise

(d) 35 paise

7. If the traditional order in ‘BODMAS’ is redefined as ‘BSOMAD’, find the value of the following expression as per the precedence of operations.
3 x 4 0f 5 – 2 ÷ 4 + 9 -5

(a) \frac{127}{2}

(b) 34

(c) \frac{9}{2}

(d) None of these

8. Balan borrowed Rs.1000 at 10 percent per annum simple interest. He immediately lent the whole sum at 10 percent per annum compounded annually. At the end of 2 year, he would gain.

(a) Rs.1

(b) Rs.10

(c) Rs.11

(d) Rs.100

9. If (221)^{k}=(13)^{p}=(17)^{q} and p, k, q are non zero then which of the following is true?

(a) p^{2}k=p+q

(b) pqk^{-1}=p+q

(c) \frac{1}{p}+\frac{1}{q}=k

(d) \frac{1}{k}=p+q

10. A cup of milk contains 3 parts pure milk and 1 part water. How much of the mixture must be Withdrawn and substituted with Water in order that the resulting mixture may be half milk and half water?-

(a) \frac{1}{2}

(b) \frac{1}{3}

(c) \frac{1}{4}

(d) \frac{1}{5}

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11. For starting a business, I take a loan of Rs.4 lakhs from a bank at an interest rate of 10% compounded annually. I pay back the loan in the next 3 years by making equal payments at the end of  each year. Calculate the value of each equal payment.

(a) Rs.1.6 lakhs

(b) Rs.1.8 lakhs

(c) Rs.2.1 lakhs

(d) Rs.2.4 lakhs

12. Under given condition, the pressure of a definite mass of a gas varies inversely with volume and directly with the temperature of the gas. If volume of gas reduced by 20% and temperature falls by 25% then the pressure will:

(a) reduce by \frac{25}{4}%

(b) increase by \frac{15}{4}%

(c) reduce by 25%

(d) reduce by 8%

13. ABC (A # B # C) is a 3 digit number such that A! + B! + C! = ABC, the value of B.

(a) 5

(b) 4

(c) 2

(d) No unique value is possible

14. What can be said about ‘n’ if the sum of the numbers’ greater than 2^{n} and less than 2^{n+1} where n\varepsilon N is definitely divisible by 18 only?

(a) a power of 2

(b) a multiple of 3

(c) an even number

(d) an odd number greater than 3

15. P and Q entered into a partnership investing Rs.12000 and Rs.16000 respectively. After 3 months Q withdraws Rs.5000 while P invested Rs.5000 more. Out of a total profit of Rs.5’600 after 6  months, the share of P exceeds that of Q by:

(a) RS200

(b) RS.100

(c) RS300

(d) RS400

16. Given x α  z and y α z, which one of the following statements is incorrect?

(a) (x+y) α z

(b) (x—y) α z

(c) \sqrt{xy}\alpha z^{2}

(d) \frac{x}{4}\alpha z

17. Two circles of identical radii intersect each other such that each one passes through the centre of the other. The length of the line joining the centres is l cm. A square ABCD has its base on this  line joining the centres of the two circles. Find the areal (in cm2) that is outside the circles but inside the square.

(a) 1-\frac{\pi}{6}+\frac{\sqrt{3}}{4}

(b) 1-\frac{\pi}{6}+\frac{\sqrt{3}}{2}

(c) 1-\frac{\pi}{6}+\frac{4}{\sqrt{4}}

(d) 1-\frac{\pi}{6}+\frac{\sqrt{2}}{3}

18. If 5 x 6=(33)_{x}. Find y, if (y)_{10}=(100)_{x}.

(a) 90

(b) 81

(c) 100

(d) 110

19. If x + 3 is a factor of x^{3}-7x^{2}-7kx+9k, then k is:

(a) 6

(b) 2

(c) 3

(d) More than -3

20. There is an equation ax + by = c, which has solutions that are only positive integers. ‘a’ and ‘b’ can take values 1 or 2.” ‘c’ can take values 1, 2 or 3. How many different solution sets are possible?

(a) 1

(b) 2

(c) 3

(d) More than 3