Quantitative Aptitude Mock Test 3 Practice

1. 53724 is divisible by 11 because:

• A. Sum of digits is 21
• B. Difference of alternate digit sums is 11 (Correct)
• C. Last digit is 4
• D. It is divisible by 2 and 9

Explanation: Using the divisibility rule of 11: $5 - 3 + 7 - 2 + 4 = 11$. Since 11 is divisible by 11, the number is divisible by 11.

2. After a 20% decrease, a value becomes 360. Original value was:

• A. 400
• B. 420
• C. 440
• D. 450 (Correct)

Explanation: 80% = 360, so 100% = 450.

3. Tea worth Rs 24/kg is mixed with tea worth Rs 40/kg to obtain a blend worth Rs 30/kg. The ratio of cheaper to dearer tea is:

• A. 10:6 (Correct)
• B. 6:10
• C. 11:6
• D. 10:7

Explanation: By alligation, cheaper:dearer = (40 - 30):(30 - 24) = 10:6.

4. Two buses start from opposite ends of a 420 km road at 70 km/hr and 60 km/hr. They meet after:

• A. 3 hours
• B. 3 hr 14 min (Correct)
• C. 3 hr 30 min
• D. 4 hours

Explanation: Relative speed = 70 + 60 = 130 km/hr. Time = 420/130 = 42/13 hours, which is about 3 hours 14 minutes.

5. Solve: $|x + 4| = 2$

• A. $x = -2$ or $-6$ (Correct)
• B. $x = 2$ or $-6$
• C. $x = -2$ or $6$
• D. $x = 2$ or $6$

Explanation: $x + 4 = 2$ gives $x = -2$, and $x + 4 = -2$ gives $x = -6$.

6. A coin and a die are used together. Probability of head and a number greater than 4?

• A. $1/12$
• B. $1/6$ (Correct)
• C. $1/4$
• D. $1/3$

Explanation: The events are independent. So probability $= \frac12 \times \frac26 = \frac16$.

7. A cone has base radius 7 cm and slant height 25 cm. Find its lateral surface area. Use pi = 22/7.

• A. 550 cm^2 (Correct)
• B. 1100 cm^2
• C. 275 cm^2
• D. 154 cm^2

Explanation: Lateral surface area of cone = pi r l. So (22/7) x 7 x 25 = 550 cm^2.

8. Present worth of Rs 12,100 due after 2 years at 10% CI is:

• A. Rs 9,500
• B. Rs 10,000 (Correct)
• C. Rs 10,500
• D. Rs 11,000

Explanation: Present worth = $12100/(1.1)^2 = 10000$.

9. If an article listed at Rs 900 is sold at two successive discounts of 8% and 8%, the price paid is:

• A. Rs 756.44
• B. Rs 761.76 (Correct)
• C. Rs 768
• D. Rs 774

Explanation: $SP=900\times0.92\times0.92=761.76$.

10. What is tan 45deg?

• A. 0
• B. 1/sqrt(2)
• C. 1 (Correct)
• D. sqrt(3)

Explanation: $\tan 45^\circ = 1$ because $\sin 45^\circ = \cos 45^\circ$.

11. The smallest digit that can replace a in 8a36 so that the number is divisible by 11 is:

• A. 3
• B. 4
• C. 5 (Correct)
• D. 6

Explanation: Apply the rule of 11: $8 - a + 3 - 6 = 5 - a$. This must be 0 or a multiple of 11. For the smallest digit, take $5-a=0$, so $a=5$.

12. If Arjun has 80 marks and Priya has 100 marks, Arjun is less than Priya by:

• A. 15%
• B. 20% (Correct)
• C. 25%
• D. 30%

Explanation: Difference = 20. Base = 100. So 20/100 x 100 = 20%.

13. How many litres of a 45% solution must be mixed with a 15% solution to make 20 L of a 30% solution?

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

Explanation: Alligation gives 15%:45% = 15:15, so both quantities are equal. Therefore the 45% solution is 10 L.

14. Diya drives at 90 km/hr and catches Arjun driving at 60 km/hr after 4 hours. What was Arjun's head start?

• A. 60 km
• B. 90 km
• C. 120 km (Correct)
• D. 150 km

Explanation: Relative speed = 90 - 60 = 30 km/hr. Head start = 30 x 4 = 120 km.

15. The solution set of $|x - 1| \ge 4$ is:

• A. $x \le -3$ or $x \ge 5$ (Correct)
• B. $-3 \le x \le 5$
• C. $x \ge -3$
• D. $x \le 5$

Explanation: Distance from 1 is at least 4, so move 4 units left and right: $x \le -3$ or $x \ge 5$.

16. If $A=\{2,4,6,8\}$ and $B=\{4,8,10\}$, find $A \cap B$.

• A. $\{2,10\}$
• B. $\{4,8\}$ (Correct)
• C. $\{2,4,8\}$
• D. $\{4,6,8,10\}$

Explanation: The common elements in both sets are 4 and 8, so $A \cap B = \{4,8\}$.

17. A cube has total surface area 384 cm^2. Find its volume.

• A. 384 cm^3
• B. 256 cm^3
• C. 512 cm^3 (Correct)
• D. 768 cm^3

Explanation: 6a^2 = 384 gives a^2 = 64, so a = 8 cm. Volume = a^3 = 512 cm^3.

18. A student deposits Rs 25,000 at 8% annual CI. What will be the amount after 3 years?

• A. Rs 31,492
• B. Rs 31,493 (Correct)
• C. Rs 31,496
• D. Rs 31,500

Explanation: $A=25000(1.08)^3=31492.8$, approximately Rs 31,493.

19. A trader wants 33% gain after allowing 5% discount. Required markup percentage is closest to:

• A. 35%
• B. 38%
• C. 40% (Correct)
• D. 43%

Explanation: Take $CP=100$ and needed $SP=133$. $MP=\frac{133}{95}=1.4$ of CP, so markup is about 40%.

20. What is sin 30deg + cos 60deg?

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

Explanation: $\sin 30^\circ = 1/2$ and $\cos 60^\circ = 1/2$. So the sum is 1.

21. A number is divisible by 6 if it is divisible by:

• A. 2 only
• B. 3 only
• C. Both 2 and 3 (Correct)
• D. Both 3 and 9

Explanation: Since 6 = 2 x 3, a number must be divisible by both 2 and 3 to be divisible by 6.

22. If Priya has 100 marks and Arjun has 80 marks, Priya is more than Arjun by:

• A. 20%
• B. 22.5%
• C. 25% (Correct)
• D. 30%

Explanation: Difference = 20. Base = 80. So 20/80 x 100 = 25%.

23. A container has 16 L of milk. 4 L is removed and replaced with water, and the process is repeated 2 times. Milk left is:

• A. 9 L (Correct)
• B. 7 L
• C. 10 L
• D. 8 L

Explanation: Fraction left each time = 12/16. Milk left = 16 x (12/16)^2 = 9 L.

24. A train covers the first 180 km at 90 km/hr and the next 120 km at 60 km/hr. The average speed for the whole journey is:

• A. 70 km/hr
• B. 72 km/hr
• C. 75 km/hr (Correct)
• D. 78 km/hr

Explanation: Total distance = 300 km. Time = 180/90 + 120/60 = 2 + 2 = 4 hours. Average speed = 300/4 = 75 km/hr.

25. Solve: $7 - x > 1$

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

Explanation: Subtract 7: $-x > -6$. Multiply by -1 and reverse the sign to get $x

26. If $A=\{1,2,3\}$ and $B=\{3,4,5\}$, find $A \cup B$.

• A. $\{1,2,3\}$
• B. $\{3,4,5\}$
• C. $\{1,2,3,4,5\}$ (Correct)
• D. $\{1,2,4,5\}$

Explanation: The union contains all distinct elements from both sets.

27. How many small spheres of radius 1 cm can be formed from a solid sphere of radius 4 cm?

• A. 16
• B. 32
• C. 64 (Correct)
• D. 128

Explanation: Volume ratio equals the cube of the radius ratio. So the number of small spheres is (4/1)^3 = 64.

28. An article depreciates from Rs 50,000 to Rs 40,500 in 2 years. The annual depreciation rate is:

• A. 8%
• B. 9%
• C. 10% (Correct)
• D. 11%

Explanation: $(1-r)^2=40500/50000=0.81$. So $1-r=0.9$ and $r=10\%$.

29. An article is sold for Rs 2,875 at a profit of 15%. What is its cost price?

• A. Rs 2,400
• B. Rs 2,450
• C. Rs 2,500 (Correct)
• D. Rs 2,550

Explanation: $SP=115\%$ of CP. $CP=2875\times\frac{100}{115}=2500$.

30. What is sec²θ - tan²θ equal to?

• A. 0
• B. 1 (Correct)
• C. 2
• D. -1

Explanation: From $1+\tan^2\theta=\sec^2\theta$, we get $\sec^2\theta-\tan^2\theta=1$.

31. Which of the following numbers is divisible by 5?

• A. 462
• B. 731
• C. 980 (Correct)
• D. 847

Explanation: A number is divisible by 5 if its last digit is 0 or 5. Among the options, only 980 ends in 0.

32. Price of wheat rises by 25%. To keep spending fixed, consumption must fall by:

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

Explanation: Required reduction = 25/125 x 100 = 20%.

33. 6 kg of rice worth Rs 28/kg is mixed with 9 kg of rice worth Rs 40/kg. The mean price of the mixture is:

• A. Rs 35.2/kg (Correct)
• B. Rs 36.2/kg
• C. Rs 34.2/kg
• D. Rs 34/kg

Explanation: Weighted mean = (28 x 6 + 40 x 9) / 15 = Rs 35.2/kg.

34. A train running at 90 km/hr takes 9 seconds to pass a signal post. The length of the train is:

• A. 200 m
• B. 210 m
• C. 225 m (Correct)
• D. 240 m

Explanation: 90 km/hr = 25 m/s. Length = 25 x 9 = 225 m.

35. Solve: $|5x| = 25$

• A. $x = \pm 4$
• B. $x = \pm 5$ (Correct)
• C. $x = \pm 6$
• D. $x = 5$ only

Explanation: $5x = 25$ or $5x = -25$. So $x = \pm 5$.

36. If $U=\{1,2,3,4,5,6\}$ and $A=\{2,4,6\}$, find $A'$ with respect to $U$.

• A. $\{2,4,6\}$
• B. $\{1,3,5\}$ (Correct)
• C. $\{1,2,3\}$
• D. $\{4,5,6\}$

Explanation: Complement means elements of the universal set that are not in $A$.

37. The height of a cylinder is halved while radius stays the same. By what factor does the volume change?

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

Explanation: Volume of a cylinder is pi r^2 h. If h is halved and r is unchanged, the volume also becomes half.

38. At SI, a sum becomes four times in 15 years. In how many years will it become seven times?

• A. 25
• B. 30 (Correct)
• C. 35
• D. 40

Explanation: Four times means interest = 3P in 15 years. Seven times means interest = 6P, which needs double the time, i.e. 30 years.

39. A shopkeeper marks an item 60% above cost and gives a 25% discount. His profit percentage is:

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

Explanation: Take CP = 100. MP = 160 and SP after 25% discount = $160\times0.75=120$. Profit = 20%.

40. What is cos 0deg × sin 90deg + sin 0deg × cos 90deg?

• A. 0
• B. 1 (Correct)
• C. 2
• D. 1/2

Explanation: $\cos 0^\circ=1$, $\sin 90^\circ=1$, $\sin 0^\circ=0$, and $\cos 90^\circ=0$. So the value is $1\times1 + 0\times0 = 1$.

41. How many digits can replace x in 62x4 so that the number is divisible by 3?

• A. 2
• B. 3
• C. 4 (Correct)
• D. 5

Explanation: Digit sum = 6 + 2 + x + 4 = 12 + x. Since 12 is divisible by 3, x must also be divisible by 3. Possible digits: 0, 3, 6, 9. Total = 4 digits.

42. Price falls by 20%. Consumption can rise by:

• A. 20%
• B. 22%
• C. 25% (Correct)
• D. 30%

Explanation: Required rise = 20/80 x 100 = 25%.

43. Tea worth Rs 50/kg is mixed with tea worth Rs 80/kg to obtain a blend worth Rs 62/kg. The ratio of cheaper to dearer tea is:

• A. 18:12 (Correct)
• B. 12:18
• C. 19:12
• D. 18:13

Explanation: By alligation, cheaper:dearer = (80 - 62):(62 - 50) = 18:12.

44. A train passes a standing man in 12 seconds and a 240 m bridge in 36 seconds. The length of the train is:

• A. 100 m
• B. 120 m (Correct)
• C. 140 m
• D. 160 m

Explanation: Let train length be L and speed be v. Then L/v = 12 and (L + 240)/v = 36. So 12v + 240 = 36v, hence 240 = 24v and v = 10. Therefore L = 12 x 10 = 120 m.

45. Evaluate $\log_2 32$

• A. 4
• B. 5 (Correct)
• C. 6
• D. 7

Explanation: $2^5 = 32$, so $\log_2 32 = 5$.

46. In a class, 24 students study English, 18 study Maths, and 7 study both. How many study at least one?

• A. 31
• B. 35 (Correct)
• C. 42
• D. 49

Explanation: Use $n(E \cup M) = n(E) + n(M) - n(E \cap M)$, so $24 + 18 - 7 = 35$.

47. A cone and a cylinder have the same base and height. What is the ratio of their volumes?

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

Explanation: Volume of cone = (1/3)pi r^2 h, while volume of cylinder = pi r^2 h. So the ratio is 1:3.

48. If Rs 10,000 under CI grows to Rs 12,100 in 2 years, what is the annual rate?

• A. 8%
• B. 9%
• C. 10% (Correct)
• D. 11%

Explanation: $(1+r)^2=12100/10000=1.21$. So $r=10\%$.

49. A single discount equivalent to successive discounts of 12.5% and 20% is:

• A. 30% (Correct)
• B. 32.5%
• C. 35%
• D. 37.5%

Explanation: Use multiplier: $0.875\times0.8=0.7$. Customer pays 70%, so equivalent discount is 30%.

50. Find the value of 4cos²60deg - sin⁴30deg.

• A. 15/16 (Correct)
• B. 1
• C. 3/4
• D. 7/8

Explanation: $4\times(1/2)^2 - (1/2)^4 = 4\times1/4 - 1/16 = 1 - 1/16 = 15/16$.