Solved Examples Set 3 (Quantitative Ability)

1. 72 + 679 + 1439 + 537+ ? = 4036

   1. 1309
   2. 1208
   3. 2308
   4. 2423
   5. 1309

   72 + 679 + 1439 + 537+ ? = 4036
   2727 + ? = 4036
   ? = 4036 - 2727 = 1309

2. A man takes 50 minutes to cover a certain distance at a speed of 6 km/hr. If he walks with a speed of 10 km/hr, he covers the same distance in

   1. 1 hour
   2. 30 minutes
   3. 20 minutes
   4. 10 minutes
   5. 40 minutes

   \( 50 × 6 \over 10 \) = 30 minutes

3. A bank increased the rate of interest which it paid to depositors from 3.5% to 4% per annum. Find how much more interest a man would receive if he deposited $ 64000 in the bank for 6 months at the new interest rate

   1. $ 160
   2. $ 180
   3. $ 200
   4. $ 220
   5. $ 150

   If the interest rate is 3.5% then interest amount is
   3.5% of 6400 = 0.035 × 6400 = $ 2240
   If the interest rate is 4% then interest amount is
   4% of 6400 = 0.04 × 6400 = $ 2560
   Now the difference of both interests = 2560 - 2240 = $ 320 per annum
   Interest for half year (6 months) = \(320 \over 2\) = $ 160

4. 10 men can complete a job in 14 days. How long will it take 4 men to finish the same job if they work at the same rate?

   1. 33 days
   2. 35 days
   3. 37 days
   4. 39 days
   5. 31 days

   \(14 × 10 \over 4 \) = 35 days

5. 5.41 - 3.29 × 1.6 = ?

   1. 14.6
   2. 0.3392
   3. 0.146
   4. 3.392
   5. 1.46

   5.41 - 3.29 × 1.6 = 5.41 - 5.264 = 0.146

6. A man bought a flat for $ 820000. He borrowed 55% of this money from a bank. How much money did he borrow from the bank?

   1. $ 451000
   2. $ 452000
   3. $ 453000
   4. $ 454000
   5. $ 450000

   55% of 820000 = 0.55 × 820000 = $ 451000

7. Matthew’s age (𝑚) is three years more than twice Rita’s age (𝑟). Which equation shows the relationship between their ages?

   1. 𝑚 = 𝑟 − 32
   2. 𝑚 = 𝑟 + 32
   3. 𝑚 = 2(𝑟 + 3)
   4. 𝑚 = 2𝑟 − 3
   5. 𝑚 = 2𝑟 + 3

   As Matthew's age (𝑚) is three more years (+3) than twice Rita's age (2𝑟). Therefore, 𝑚 = 2𝑟 + 3.

8. By selling a fan for $ 475, a person loses 5%. To get a gain of 5%, he should sell the fan for:

   1. $ 500
   2. $ 525
   3. $ 535
   4. $ 575
   5. $ 505

   cost price = 100/(100 - 5) x 475 = $ 500
   sale price = (100 + 5)/100 x 500 = $ 525

9. A man is 5 times as old as his son. 2 years ago the sum of the squares of their ages was 1114. Find the present age of son.

   1. 7 years
   2. 9 years
   3. 8 years
   4. 8 1/2 years
   5. 6 years

   Let son's age = x, then
   father's age = 5x
   As before 2 years ago the sum of the squares of their ages was 1114, the equation becomes as
   \((x - 2)^2 + (5x - 2)^2 = 1114 \)
   By simplifying the equation, we have
   \(13x^2 -12x -553 = 0\)
   Now solving the equation, we have
   \(13x^2 - 12x - 553 = 0\)
   \(13x^2 - 91x + 79x -553 = 0\)
   13x(x - 7) + 79(x - 7) = 0
   (x - 7)(13x + 79) = 0
   x = 7 and x = -6.077
   As age could not be negative, hence the present age of the son is 7 years.

10. A boy scored 90 marks for his mathematics test. This was 20% more than what he had scored for the geography test. How much did he score in geography?

    1. 71 marks
    2. 73 marks
    3. 75 marks
    4. 77 marks
    5. 78 marks

    20% of x + x = 90
    0.2x + x = 90
    1.2x = 90
    x = \(90 \over 1.2\)
    x = 75

11. Which of the following expressions is equivalent to \(\frac{𝑥^2 + 3x + 1}{𝑥 + 1}\)?

    1. x + 2
    2. 𝑥 + 3
    3. 𝑥 + 2 - 1/(𝑥 + 1)
    4. 𝑥 + 3 + 1/(𝑥 + 1)
    5. 𝑥 + 4 + 5/(𝑥 + 1)

    As \(𝑥^2 + 3x + 1 = (𝑥^2 + 3x + 2) -1\)
    and
    \(\frac{𝑥^2 + 3x + 2}{x + 1} = \frac{(𝑥 + 2)(x + 1)}{x + 1} = 𝑥 + 2\)
    Therefore,
    \(\frac{𝑥^2 + 3x + 1}{x + 1} = \frac{𝑥^2 + 3x + 2}{x + 1} - \frac{1}{x + 1} = (𝑥 + 2) - \frac{1}{x + 1}\)

12. 5873 + 12034 + 1106 = ?

    1. 19016
    2. 20001
    3. 19013
    4. 2018
    5. 19010

    5873 + 12034 + 1106 = 17907 + 1106 = 19013

13. \( {0.027 \over 90} = ? \)

    1. 0.0003
    2. 0.03
    3. 3
    4. 0.00003
    5. 0.003

    \( {0.027 \over 90} = {27 \over 1000 × 90} = {3 \over 10000} = 0.0003 \)

14. \( {5.76 \over 1.6} - 2.4 = ? \)

    1. 1.2
    2. 2.4
    3. 7.2
    4. 0.12
    5. 0.012

    \( {5.76 \over 1.6} - 2.4 = \) 3.6 - 2.4 =1.2

15. If n! = n ⋅ (n − 1) ⋅ (n − 2) ⋅ (n − 3) . . . 2 ⋅ 1, what is the value of \(\frac{(6!)(4!)}{(5!)(3!)}\)

    1. 5/4
    2. 8/5
    3. 10
    4. 24
    5. 1152

    \(\frac{(6!)(4!)}{(5!)(3!)}\) = \(\frac{(6 . 5 . 4 . 3 . 2 . 1)(4 . 3 . 2. 1)}{(5 . 4 . 3 . 2 . 1)(3 . 2 . 1)}\) = \(\frac{6 . 4}{1}\) = 24

16. If 3x = −9, then 3x³ − 2x + 4 =

    1. -83
    2. -71
    3. -47
    4. -17
    5. 61

    First solving 3x = −9, x = −3. Now plug into 3x³ − 2x + 4:
    3x³ − 2x + 4
    = 3(-3)³ − 2(-2) + 4
    = 3(−27) + 6 + 4
    = −81 + 6 + 4
    = −71

17. A certain number was doubled and the result then multiplied by 3. If the product was 138, find the number.

    1. 21
    2. 23
    3. 25
    4. 27
    5. 19

    Let x be the number
    the number is doubled, 2x
    the result is multiplied by 3, 3 × 2x = 6x
    6x = 138
    x = \(138 \over 6\) = 23

18. A person's net income is $ 1373.70 and he pays an income tax of 5%. His gross income in dollars must be

    1. 1446
    2. 1118.96
    3. 1308.29
    4. 1438.25
    5. 1211.21

    Let gross income in dollars = x
    then according to the statement,
    x = 5% of x + 1373.70
    x - 0.05x = 1373.70
    0.95x = 1373.70
    x = \(137370 \over 95\) = 1446

19. A shop owner blends three types of coffees, A, B and C, in the ratio 3:5:7. Given that type A coffee costs $ 70 per kg, type B coffee costs $ 100 per kg and type C coffee costs $ 130 per kg, calculate the cost per kg of the blended mixture.

    1. $ 106
    2. $ 108
    3. $ 109
    4. $ 110
    5. $ 105

    Cost per kg = 70 x 1/5 + 100 x 1/3 + 130 x 7/15 = $ 108 per kg

20. A man sells two houses for $ 2 lac each. On one he gained 20% and on the other he lost 20%. His total profit or loss % in the transaction will be

    1. 4% profit
    2. 5% loss
    3. no profit, no loss
    4. 4% loss
    5. 3% loss

    % loss = (% loss X % profit)/100 = (20 X 20)/100 = 4%

Solved Examples Set 1
Solved Examples Set 2
Solved Examples Set 3