# GRE Quantitative Reasoning Mock Test Questions and Answers

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## Mock Test Questions and Answers on Quantitative Reasoning

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

1. A square and rhombus have the same base. If the rhombus is inclined at 60°, find the ratio of area of square to the area of the rhombus,

(a) 1

(b) 2\sqrt{3}:3

(c) \sqrt{3}:1

(d) None of these

2. A man’s total expenses for 10 years from 1951 to 1960 amounted to Rs.45000. He spent Rs.3200 in 1951 and Rs.57OO in 1961. What was his average annual expenditure for the years from 1952 to 1961?

(a) Rs.4450

(b) Rs.4750

(c) Rs.4180

(d) Rs.5700

3. There is a 90% probability that m > 0, 10% probability that n < 0, then what is the probability that m x n is negative? (given that m and n\# 0)
(a) 0.09

(b) 0.18

(c) 0.5

(d) 0.75

4. S1 and S2 are two light rays. Both the rays originate from a single point (0, 1) and travel along linear paths. S1 passes through (1, -2) and S2 passes through (-1, 2). The paths of S1 and S2 are:

(a) x + 3y = 1, x + y = 1

(b) 3x + y = 1, x – y = 1

(c) 3x + y = 1, x + y = 1

(d) x – 3y = 1, x + 3y = 1

5. If the sum of the radius and the height of a closed cylinder is 35 cm and the total surface area of the cylinder is 1505 cm2, then the circumference of the base of the cylinder is:
(a) 43 cm

(b) 34 cm

(c) 23 cm

(d) Cannot be determined

6. Find x

(a) a + b + c

(b) b – a – c

(c) c – a – b

(d) None of these

7. For functions of the nature y=a^{x}, where x is a real number and 0 < a < 1, which of the following statement/s is/are true?
I. They are increasing in nature.
II. They all meet at (0, 1)

(a) Only I is true

(b) Only II is true

(c) I and II are true

(c) Neither I nor II is true

8. Harish purchased a motorcycle for Rs.19725 in the year 1992. Due to some financial problems, he wanted to sell it in the year 1995. He displayed the selling price as Rs.19200. Ram wanted to purchase it and negotiated for a 10% discount on the price. But Harish sold him the motorcycle after giving 2 consecutive discounts of 7% and then 3% on the displayed selling price. The depreciation for the motorcycle is 10% per annum. What is the net discount that Harish offered Ram?

(a) 10%

(b) 13.79%

(c) 9.79%

(d) 10.21%

9. \Delta ABC\angle A and \angle B are 50° and 60° respectively. If O is the orthocentre, find angle \angle AOB.

(a) 100°

(b) 90°

(c) 110°

(d) 120°

10. A certain city has a wall around it. The shape of the wall is that -of a regular hexagon and this wall has six gates, each one exactly at the centre of the each wall of the hexagon. A house stands  outside the city, 4 kms in front of one of the gates such that it can be just seen from the two gates on the adjacent sides. What is the total length of the wall that surrounds the city?

(a) \frac{8}{\sqrt{3}}

(b) 8\sqrt{3}

(c) 12\sqrt{3}

(d) 16\sqrt{3}

Directions f0r questions 11 to 15: Each of the following questions is followed by two statements.

Mark [a], if the question can be [answered by using any of the statements alone but not by using the other statement alone.
Mark [b], if the question can be answered by using either of the statements alone.
Mark [c], if the question can be answered only by using both the statements together.
Mark [d], if the question cannot be answered.

11. I have a total of Rs.5 in 5 paise, 10 paise, and 25 paise coins. How many 10 paise coins do I have?
I. The number of 25 paise coins is 10.
II. The number of 10 paise coins exceeds that of 5 paise coins.

12. What is _area of the circle shown?

I. ABCD is a square of side = 5.
II. AC = \sqrt{2} x diameter of circle

13. How many cars pass a lamp-post in one hour?
I. Number of cars passing the lamp-post in one direction is twice the number of cars passing the lamp-post in the other direction.
II. Average speed of a car passing the lamp-post is 50 kins/hr.

14. * denotes x or ÷, # denotes + or —. What do * and # denote?
I. 1 * O = 1 # 1
II. 1 # 0 = 1 * 1

15. In a certain colony of 500 people how many read only newspaper ‘A’, given that there is only l other newspaper ‘B’? ‘
I. 300 people read only ‘B’.

Directions for questions 16 to 20: Each of the following questions are followed by three statements Determine the statement/s that are sufficient to answer the questions.

16. A bag contains 15 balls of the same size. Each ball is either white, red or blue in colour How many red balls are there in the bag?
I. The probability of drawing a red ball is the same as that of drawing a blue ball.
II. The bag contains more blue balls than white ones.
III. The probability of randomly drawing a white ball from the bag is 20 percent.

(a) All three

(b) Only III

(c) I and III

(d) (I and II) or (II and III)

17. A fishing ship was moving towards a light house on the shore with uniform speed. A mar standing on the lighthouse observes the ship. Six minutes later he finds that the angle of depression was 60°. Find the time taken by the ship to reach the lighthouse.
I. Initially, the man standing on the lighthouse observes the ship at an angle of depression of 30°.
II. The speed of the ship was 5 km/hr.
III. The height of the lighthouse was 350 m.

(a) Any one of the three

(b) I and II

(c) I only

(d) I or (II and III)

18. What is the value of xyz? (a # 0, b # 0, c #0).

I. x^{a}=y^{b}=z^{c}
II. a^{x}=b, b^{y}=c, c^{z}=a
III. ab + bc + ca = 0

(a) I and II

(b) II and III

(c) II or (I and III)

(d) None of these

19. In a girls college, each girl student is intelligent or beautiful or a player. How many girls are there in the college?
I. A survey of the college discloses that 300 students are intelligent, 150 are players and 91 are beautiful.
II. 100 girls are both beautiful and intelligent, 70 are both players and intelligent.
III.In a team of 100 girls, the ratio of players, intelligent and beautiful girls is 3 : 5 : 6

(a) All three

(b) I and II

(c) II and III

(d) Data insufficient

20. Rajdhani Express runs between Delhi and Mumbai. What is the revenue from the sale of second class tickets of this train?
I. The first class and second class fares between Mumbai and Delhi are in the ratio of 6 :4
II. The number of passengers in the first and second classes is in the ratio 3 : 5.
III. The total collection between the two stations in a single run is Rs.72000.

(a) II and III

(b) I and II

(c) II or (I and III)

(d) None of these