Quantitative Aptitude Mock Test 2 Practice

1. If n is an odd integer, then n^2 is:

• A. Always even
• B. Always odd (Correct)
• C. Sometimes even
• D. Always prime

Explanation: Let $n = 2k+1$. Then $(2k+1)^2 = 4k^2 + 4k + 1 = 2(2k^2+2k)+1$, which is of the form $2m+1$. So it is always odd.

2. A is 25% more than B. B is what percent less than A?

• A. 15%
• B. 18%
• C. 20% (Correct)
• D. 25%

Explanation: Use x/(100+x) x 100 = 25/125 x 100 = 20%.

3. Vani invests Rs 42000 at the start of the year. After 4 months, she changes it to Rs 54000. Kunal keeps Rs 36000 for 12 months. Their profit ratio is:

• A. 25:18 (Correct)
• B. 42000:36000
• C. 18:25
• D. 8:12

Explanation: Vani = 42000 x 4 + 54000 x 8 = 600000. Kunal = 36000 x 12 = 432000. Ratio = 25:18.

4. A leak at the bottom empties a full tank in 8 hours. An inlet fills it in 6 hours. If the tank is full and both start together, what happens?

• A. It empties in 24 hours
• B. It empties in 12 hours
• C. It never empties (Correct)
• D. It empties in 48 hours

Explanation: Inlet rate = 1/6, leak rate = 1/8. Net rate = 1/24 filling, not emptying. So the tank never empties while both operate.

5. Form the quadratic equation whose roots have sum 8 and product 15.

• A. $x^2 - 8x + 15 = 0$ (Correct)
• B. $x^2 + 8x + 15 = 0$
• C. $x^2 - 8x - 15 = 0$
• D. $x^2 + 8x - 15 = 0$

Explanation: If the roots have sum $S$ and product $P$, the equation is $x^2 - Sx + P = 0$. So it becomes $x^2 - 8x + 15 = 0$.

6. Two fair coins are tossed. Probability of exactly one head?

• A. $1/4$
• B. $1/2$ (Correct)
• C. $3/4$
• D. $1$

Explanation: Favourable outcomes are HT and TH, so probability $= \frac{2}{4} = \frac12$.

7. The area of a circle is 616 cm^2. Find its circumference. Use pi = 22/7.

• A. 88 cm (Correct)
• B. 44 cm
• C. 176 cm
• D. 132 cm

Explanation: From pi r^2 = 616, we get r^2 = 196 and r = 14. Circumference = 2pi r = 88 cm.

8. The difference between half-yearly and annual amount on Rs 20,000 for 1 year at 10% is:

• A. Rs 25
• B. Rs 50 (Correct)
• C. Rs 75
• D. Rs 100

Explanation: Half-yearly amount = 20000(1.05)^2 = 22050. Annual amount = 22000. Difference = 50.

9. A product goes from manufacturer to wholesaler to retailer at gains of 10%, 20%, and 25% respectively. If final price is Rs 3,300, manufacturing cost was:

• A. Rs 2,000 (Correct)
• B. Rs 2,100
• C. Rs 2,200
• D. Rs 2,250

Explanation: Original cost $=\frac{3300}{1.1\times1.2\times1.25}=2000$.

10. What is the distance of the point (6,8) from the origin?

• A. 8
• B. 10 (Correct)
• C. 12
• D. 14

Explanation: Distance from origin $=\sqrt{6^2+8^2}=\sqrt{100}=10$.

11. How many prime numbers lie between 10 and 20?

• A. 3
• B. 4 (Correct)
• C. 5
• D. 6

Explanation: Prime numbers between 10 and 20 are 11, 13, 17 and 19. Total = 4.

12. A is 40% less than B. B is what percent more than A?

• A. 50%
• B. 60%
• C. 66 2/3% (Correct)
• D. 80%

Explanation: Take B = 100, then A = 60. Increase = 40/60 x 100 = 66 2/3%.

13. Aarav invests Rs 36000 for 12 months and Meera invests Rs 24000 for 9 months. Total profit is Rs 18000. Aarav's share is:

• A. Rs 12000 (Correct)
• B. Rs 6000
• C. Rs 13200
• D. Rs 10800

Explanation: Capital-months = 432000 and 216000. Aarav gets 432000/648000 of 18000 = Rs 12000.

14. Pipe A fills 1/3 of a tank in 5 hours. In how many hours will Pipe A fill the whole tank?

• A. 10 hours
• B. 12 hours
• C. 15 hours (Correct)
• D. 18 hours

Explanation: If 1/3 tank is filled in 5 hours, the full tank is filled in 5 x 3 = 15 hours.

15. Solve: $2x - 5 > 9$

• A. $x > 5$
• B. $x > 6$
• C. $x > 7$ (Correct)
• D. $x > 8$

Explanation: Add 5: $2x > 14$. Divide by 2 to get $x > 7$.

16. Two dice are rolled. What is the probability that the sum is 8?

• A. $1/9$
• B. $5/36$ (Correct)
• C. $1/6$
• D. $7/36$

Explanation: The favourable ordered pairs are $(2,6),(3,5),(4,4),(5,3),(6,2)$, so the probability is $\frac{5}{36}$.

17. The diagonals of a rhombus are 16 cm and 12 cm. Find its area.

• A. 96 cm^2 (Correct)
• B. 192 cm^2
• C. 48 cm^2
• D. 72 cm^2

Explanation: Area of a rhombus = 1/2 x d1 x d2. So area = 1/2 x 16 x 12 = 96 cm^2.

18. At 10% annual CI, in how many years will a sum become 1.331 times?

• A. 1
• B. 2
• C. 3 (Correct)
• D. 4

Explanation: Since $1.1^3=1.331$, the time is 3 years.

19. A dealer quotes Rs 45 for an article costing Rs 30. A fake Rs 50 note is used and Rs 5 change is returned. Total loss is:

• A. Rs 35 (Correct)
• B. Rs 45
• C. Rs 50
• D. Rs 80

Explanation: Loss consists of article cost and returned change, so total loss is Rs 35.

20. Which point is the midpoint of (1,1) and (5,7)?

• A. (2,3)
• B. (3,4) (Correct)
• C. (4,5)
• D. (3,5)

Explanation: Midpoint $=\left((1+5)/2,(1+7)/2\right)=(3,4)$.

21. Which set correctly represents integers?

• A. {1, 2, 3, ...}
• B. {0, 1, 2, 3, ...}
• C. {..., -2, -1, 0, 1, 2, ...} (Correct)
• D. {3/4, 5/6, 7/8}

Explanation: Integers include negative whole numbers, zero, and positive whole numbers. So the correct set is $\{..., -2, -1, 0, 1, 2, ...\}$.

22. If P is 20% more than Q and Q = 250, then P =

• A. 280
• B. 290
• C. 300 (Correct)
• D. 320

Explanation: 20% of 250 = 50, so P = 300.

23. Aarav invests Rs 20000 for 8 months and Meera invests Rs 30000 for 12 months. Total profit is Rs 15600. Meera's share is:

• A. Rs 10800 (Correct)
• B. Rs 4800
• C. Rs 12000
• D. Rs 9600

Explanation: Capital-months = 160000 and 360000. Meera gets 360000/520000 of 15600 = Rs 10800.

24. Pipe A fills 1/3 of a tank in 5 hours and Pipe B fills 2/5 of the same tank in 8 hours. Working together, they fill the tank in:

• A. 8 4/7 hours (Correct)
• B. 9 hours
• C. 9 1/2 hours
• D. 10 hours

Explanation: Pipe A fills full tank in 15 hours, Pipe B fills full tank in 20 hours. Combined rate = 1/15 + 1/20 = 7/60. Time = 60/7 = 8 4/7 hours.

25. Solve: $3x + 4 \le 19$

• A. $x \le 4$
• B. $x \le 5$ (Correct)
• C. $x \le 6$
• D. $x \le 7$

Explanation: Subtract 4: $3x \le 15$. Divide by 3 to get $x \le 5$.

26. Two dice are thrown. What is the probability that the sum is prime?

• A. $1/3$
• B. $5/12$ (Correct)
• C. $1/2$
• D. $7/12$

Explanation: Prime sums are 2, 3, 5, 7, and 11, with total count 15. Hence probability $= \frac{15}{36} = \frac{5}{12}$.

27. A circular ring has outer radius 10 cm and inner radius 6 cm. Find the area of the ring. Use pi = 3.14.

• A. 200.96 cm^2 (Correct)
• B. 251.2 cm^2
• C. 113.04 cm^2
• D. 400 cm^2

Explanation: Area of annulus = pi(R^2 - r^2). So 3.14 x (100 - 36) = 200.96 cm^2.

28. The population of a village is 80,000 and grows by 5% every year. Find the population after 2 years.

• A. 88,000
• B. 88,200 (Correct)
• C. 88,400
• D. 88,600

Explanation: Population after 2 years = $80000(1.05)^2=88200$.

29. A trader sells 40% of his stock at 20% loss. At what markup on the remaining stock should he sell to gain 25% overall?

• A. 45%
• B. 50%
• C. 55% (Correct)
• D. 60%

Explanation: Take total CP $=100$. 40% sold at 20% loss gives SP $=32$. Needed total SP $=125$. So remaining 60 must sell for 93, giving gain $=\frac{33}{60}\times100=55\%$.

30. Which of the following equals cos 30deg?

• A. 1/2
• B. 1/sqrt(2)
• C. sqrt(3)/2 (Correct)
• D. sqrt(3)

Explanation: $\cos 30^\circ = \sqrt{3}/2$.