# GRE Quantitative Reasoning Important Questions and Answers

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## Important Questions and Answers on Quantitative Reasoning

**Directions for questions 1 to 10: Answer the questions independently of each other.**

1. There are seven persons — A, B, C, D, E, F and G, standing in a row and three distinct articles P, Q and R are to be given to three people. No three neighbouring persons receive an article, Find the number of ways for distribution in the above manner?

(a) 320 ways

(b) 180 ways

(c) 210 ways

(d) None of these

2. Find DE : DB, if *l*(BC) = 3 units, *l*(EB) = 1 unit and DE is ‘an angle bisector of \angle CDB and DB is an angle bisector of \angle ADE.

(a) \frac{2}{3}

(b) \frac{1}{3}

(c) 1

(d) Cannot be determined

3. An alloy ‘A’ of gold and copper contains gold and copper in the ratio 7 : 2 and another alloy ‘B’ has gold and copper in the ratio 7 : 8. How much of each alloys should be mixed together to form a third alloy weighing 28 kg such that it has gold and copper in equal proportion?

(a) 7 kg and 21 kg

(b) 3 kg and 25 kg

(c) 8 kg and 20 kg

(d) None of these

4. Find the sum of the series 0, 8, 24, 48, 80 ….up to 50 terms.

(a) 183620

(b) 143251

(c) 198120

(d) 166600

5. A man was asked to make 216 baskets in certain number of days. He started his work by making equal number of baskets per day. He did this for 8 days and then started making 8 baskets more than his initially planned number of baskets per day. He continued this till the earlier decided number of days and found that he had made 232 baskets. How many days did he work?

(a) 10 days

(b) 20 days

(c) 15 days

(d) None of these

6. Two persons A and B could finish a work in x days. Initially, B worked for y days and was later joined by A. The remaining work was completed by them in Z days. In how many days could each of them finish the work?

(a) A\equiv \frac{y[1+xz+z^{2}]}{z(y+z-x)}, B\equiv \frac{y[1+xz+z^{2}]}{z(x-z)}

(b) A\equiv \frac{y[1+xz+z^{2}]}{z(y+3-x)}, B\equiv \frac{y[1+xz-z^{2}]}{z(x-z)}

(c) A\equiv \frac{y}{zx}, B\equiv \frac{y}{z}(1-x)

(d) None of these

7. The product of the three sides of \Delta ABC is 64. Which one of the following best represents the perimeter, P, of the triangle?

(a) P\ge 12

(b) P = 12

(c) P = 14

(d) P\le 13

8. For every positive integer n, (1 + \frac{3}{n^{2}}) < x\le 7+\frac{1}{n^{3}}, where ‘x’ is a real number. Find ‘x’.

(a) 1\lt x\le 8

(b) 5 < x < 8

(c) 4\lt x\le 8

(d) 5\lt x\le 7

9. Eight dice are thrown simultaneously. What is the probability that the sum of the outcomes of all the eight dice is 9?

(a) \frac{5}{6^{8}}

(b) \frac{8}{6^{8}}

(c) \frac{1^5}{6^{8}}

(d) \frac{1}{6}

10. A man sells a shirt at a certain price and earns 5% profit. Had he sold it for Rs.200 more, he would have earned a profit of 15%: What was‘ the cost price of the shirt?

(a) Rs.1600

(b) Rs.2400

(c) Rs.3300

(d) Rs.2000

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**Directions for questions 11 and 12: Answer the questions on the basis of the information given below.**

Given two circles with centres O1 and O2. OC and OD are tangents to both the circles. OD = 12 cm and O2D = 3\frac{1}{2} cm.

11. Find OL

(a) 5 cm

(b) 6 cm

(c) 7 cm

(d) 9 cm

12. If O1A = 1.75 cm. Find O1O.

(a) 6\frac{1}{2} cm

(b) 7\frac{3}{5} cm

(c) 6\frac{1}{4} cm

(d) 8\frac{2}{7} cm

**Directions for questions 13 to 20: Answer the questions independently of each other.**

13. In the given circle with centre O and radius 4, AC = \log _{3} and BC = \log _{4}1836. Which of the following best represents the length of side AB?

(a) 1\lt AB\le 8

(b) 1\lt AB\le 10

(c) \log_{3}29\lt AB\le \log_{4}1836

(d) 3\le AB\le 5

14. If \alpha and \beta are the roots of the quadratic equation \frac{1}{x-1}+\frac{1}{x-b}=\frac{1}{c} and \alpha\beta=0, then find \alpha^{3}+\beta^{3} in terms of a and b.

(a) (\frac{a^{2}+b^{2}}{a+b})^{3}

(b) -(\frac{a^{2}+b^{2}}{a+b})^{3}

(c) (\frac{2a^{2}+b^{2}}{a+b})^{3}

(d) (\frac{a^{2}b^{2}}{a+b})^{3}

15. Two cars A and B race on a track of length z km at average speeds of x kmph and y kmph, respectively. Car A takes two breaks of duration \frac{x}{10} hours each while car B takes two breaks of duration \frac{y}{8} hours each. If car A ﬁnishes 10 minutes after car B, then z can be:

(a) \frac{9y}{8}+\frac{11x}{10}-1

(b) \frac{9y+12x-15}{8(y-x)}

(c) \frac{15y+10-12x}{60(\frac{1}{x}-\frac{1}{y})}

(d) \frac{5y+3-4x}{60(x-y)}

16. What is the difference in the areas enclosed by the inequations -n\le (x^{2}+y^{2})^{\frac{1}{2}}\le n, if n takes integer values such that 0\lt n\le 2?

(a) \pi

(b) 2\pi

(c) 3\pi

(d) None of these

17. Okha express runs from Mumbai to Okha at a constant speed of 50 kmph. It halts at Baroda which is 400 km from Mumbai. The distance between Mumbai to Okha is 900 km. Today, it reached Baroda 30 minutes late, what should be the speed of the train approximately so that it reaches Okha in time?

(a) 53 kmph

(b) 55 kmph

(c) 48 kmph

(d) 51 kmph

18. The functions f(x) and g(x) are related as f(g(x)) = xg(f(f(x))), where f(x) = \frac{x}{x-1}. What could be the functional form of g(x)?

(a) \frac{x}{x+1}

(b) \frac{x+1}{x}

(c) \frac{x}{x-1}

(d) \frac{x-1}{x}

19. If ab + bc + ca = 0, find \sqrt{\frac{a+b}{a+c}}

(a) \frac{c}{a}

(b) \frac{b}{c}

(c) \frac{a}{b}

(d) None of these

20. Find the area of \Delta ABC in the above figure.

(a) 25 cm^{2}

(b) 2.5cm^{2}

(c) 12.5cm^{2}

(d) Cannot be determined