Quantitative Aptitude Mock Test 1 Practice

1. Which of the following is a whole number but not a natural number?

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

Explanation: Natural numbers begin from 1, while whole numbers begin from 0. So 0 belongs to whole numbers, but it is not a natural number.

2. 12.5% as a fraction is:

• A. 1/4
• B. 1/6
• C. 1/8 (Correct)
• D. 1/10

Explanation: 12.5% = 12.5/100 = 1/8.

3. 16 workers can finish a job in 18 days. In how many days will 24 workers finish it?

• A. 12 days (Correct)
• B. 13 days
• C. 11 days
• D. 15 days

Explanation: Workers and days are inversely proportional. 16 x 18 = 24 x d, so d = 12 days.

4. Kiran can do 2/3 of a task in 16 days. In how many days will she complete the full task?

• A. 20 days
• B. 22 days
• C. 24 days (Correct)
• D. 26 days

Explanation: If 2/3 of the task takes 16 days, then the full task takes 16 x 3/2 = 24 days.

5. Find the roots of $x^2 - 5x + 6 = 0$.

• A. 1 and 6
• B. 2 and 3 (Correct)
• C. -2 and -3
• D. 3 and 4

Explanation: Factorize: $x^2 - 5x + 6 = (x-2)(x-3)$. So the roots are 2 and 3.

6. How many diagonals does a nonagon have?

• A. 18
• B. 24
• C. 27 (Correct)
• D. 36

Explanation: Total pairs of vertices $= ^9C_2 = 36$. Subtract 9 sides to get 27 diagonals.

7. Two triangles have angles 40deg, 60deg, 80deg and 40deg, 60deg, 80deg respectively. They are:

• A. Congruent
• B. Similar (Correct)
• C. Neither
• D. Both congruent and similar

Explanation: Equal angles guarantee AA similarity, but not necessarily congruency.

8. CI on Rs 25,000 for 6 months at 8% p.a. compounded half-yearly is:

• A. Rs 800
• B. Rs 1,000 (Correct)
• C. Rs 1,200
• D. Rs 1,400

Explanation: One half-year period at 4% gives CI = 25000 x 4 / 100 = 1000.

9. A stock is sold: 40% at 20% gain and the rest at 10% loss. Overall result is:

• A. 2% loss
• B. 2% gain (Correct)
• C. 4% loss
• D. 4% gain

Explanation: Overall\% $=0.4\times20+0.6\times(-10)=2\%$ gain.

10. The points (2,-k), (0,-5), and (5/2,0) are collinear. Find k.

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

Explanation: Using the area-zero condition for collinear points gives $k=1$.

11. Which of the following is an irrational number?

• A. 3/7
• B. 0.25
• C. sqrt(5) (Correct)
• D. -8

Explanation: A rational number can be written in the form $p/q$. $3/7$, 0.25 and -8 are all rational. $\sqrt{5}$ is non-terminating and non-repeating, so it is irrational.

12. 60% of 500 is:

• A. 250
• B. 280
• C. 300 (Correct)
• D. 320

Explanation: 0.60 x 500 = 300.

13. The fraction 63/84 expressed as a ratio in simplest form is:

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

Explanation: 63:84 reduces by 21 to 3:4.

14. Pipe A fills a tank in 10 hours and Pipe B fills it in 15 hours. If both are opened together, how long will the tank take to fill?

• A. 5 hours
• B. 6 hours (Correct)
• C. 7 hours
• D. 8 hours

Explanation: Combined rate = 1/10 + 1/15 = 5/30 = 1/6. So the tank fills in 6 hours.

15. For $x^2 - 7x + 10 = 0$, the sum of roots is:

• A. 7 (Correct)
• B. 10
• C. -7
• D. -10

Explanation: For $ax^2+bx+c=0$, sum of roots $= -b/a$. Here it is $-(-7)/1 = 7$.

16. How many triangles can be formed from 7 non-collinear points?

• A. 21
• B. 28
• C. 35 (Correct)
• D. 42

Explanation: Choose any 3 points: $^7C_3 = 35$.

17. In which triangle do centroid, incenter, circumcenter, and orthocenter coincide?

• A. Right triangle
• B. Isosceles triangle
• C. Equilateral triangle (Correct)
• D. Scalene triangle

Explanation: In an equilateral triangle, all classical centers lie at the same point.

18. The difference between CI and SI on Rs 18,000 for 2 years at 10% is:

• A. Rs 160
• B. Rs 180 (Correct)
• C. Rs 200
• D. Rs 220

Explanation: For 2 years, difference = $P(R/100)^2$. = 18000 x 0.01 = 180.

19. A trader buys an article for Rs 2,400, spends Rs 180 on repair, then sells it for Rs 2,898. Gain percentage is:

• A. 10%
• B. 12%
• C. 12.33% (Correct)
• D. 15%

Explanation: Total CP $=2580$ and gain $=318$. Gain\% $=\frac{318}{2580}\times100=12.33\%$.

20. What is the slope of the line joining (2,6) and (-3,1)?

• A. 1 (Correct)
• B. 2
• C. -1
• D. 5

Explanation: $m=(6-1)/(2-(-3))=5/5=1$.

21. If one number is even and another is odd, then their sum is:

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

Explanation: Even + Odd = Odd. Example: 6 + 5 = 11, which is odd.

22. 20% of 15% equals:

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

Explanation: (20/100) x (15/100) = 3/100 = 3%.

23. A sum of Rs 1710 is divided between Aarav and Meera in the ratio 7:2. Aarav gets:

• A. Rs 1330 (Correct)
• B. Rs 380
• C. Rs 1339
• D. Rs 1321

Explanation: Total parts = 9. One part = 1710/9 = 190. Aarav gets 7 x 190 = Rs 1330.

24. A pipe fills a tank in 6 hours, but due to a leak it takes 8 hours. In how many hours can the leak empty the full tank?

• A. 20 hours
• B. 22 hours
• C. 24 hours (Correct)
• D. 26 hours

Explanation: Leak rate = 1/6 - 1/8 = 1/24 of the tank per hour. So the leak alone empties the tank in 24 hours.

25. For $2x^2 - 9x + 4 = 0$, the product of roots is:

• A. 1
• B. 2 (Correct)
• C. 3
• D. 4

Explanation: Product of roots is $c/a = 4/2 = 2$.

26. How many arrangements of LEVEL are possible?

• A. 24
• B. 30 (Correct)
• C. 36
• D. 60

Explanation: LEVEL has 5 letters with L repeated twice and E repeated twice, so count $= \frac{5!}{2!2!} = 30$.

27. The circumference of a circle exceeds its diameter by 30 cm. Find the radius. Use pi = 22/7.

• A. 7 cm (Correct)
• B. 14 cm
• C. 3.5 cm
• D. 10 cm

Explanation: 2pi r - 2r = 30. So 2r(pi - 1) = 30, and substituting pi = 22/7 gives r = 7 cm.

28. On what sum will the difference between CI and SI for 2 years at 5% be Rs 25?

• A. Rs 8,000
• B. Rs 9,000
• C. Rs 10,000 (Correct)
• D. Rs 12,000

Explanation: At 5%, difference for 2 years = $P\times25/10000=P/400$. So $P/400=25$ gives $P=10000$.

29. Out of total stock, one-third is sold at 10% loss. At what profit percent should the remaining stock be sold to gain 20% overall?

• A. 30%
• B. 35% (Correct)
• C. 40%
• D. 45%

Explanation: $\frac{1}{3}(-10)+\frac{2}{3}x=20$ gives $x=35\%$.

30. A point equidistant from (3,0) and (-3,0) must lie on which line?

• A. x-axis
• B. y-axis (Correct)
• C. line y=x
• D. line y=3

Explanation: The perpendicular bisector of the segment joining $(3,0)$ and $(-3,0)$ is the y-axis.