Solved Examples Set 1 (Quantitative Ability)

1. 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

2. 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

3. A single discount equivalent to a discount series of 20%, 10% and 25% is

   1. 55%
   2. 54%
   3. 46%
   4. 42%
   5. 50%

   If 3 succesive discounts are a%, b% and c%
   then single discount = a + b + c – (\(ab \over 100 \) + \(bc \over 100\) + \(ca \over 100 \) – \(abc \over 10000 \))
   a = 20, b = 10, c = 25, solving we get, 46%.

4. Which of the following is the largest?

   1. half of 30% of 280
   2. one-third of 70% of 160
   3. twice 50% of 30
   4. three times 40% of 40
   5. 60% of 60

   Let us calculate the value of each:
   A. 0.5 × 0.3 × 280 = 42
   B. 0.33 × 0.7 × 160 = 36.96
   C. 2 × 0.5 × 30 = 30
   D. 3 × 0.4 × 40 = 48
   E. 0.6 × 60 = 36

5. A man walked for 3 hours at 4.5 km/h and cycled for some time at 15 km/h. Altogether, he traveled 21 km. Find the time taken for cycling.

   1. 1/2 hour
   2. 1 hour
   3. 1 1⁄2 hours
   4. 2 hours
   5. 2 1⁄2 hours

   The man walked the distance = 3 x 4.5 = 13.5 km. The distance cycled by the man = 21 - 13.5 = 7.5 km
   As he cyled 15 km in 1 h
   he cycled 1 km in 1/15 h
   Finally, he cycled 7.5 km in 7.5/15 = 1/2 h

6. In the series 8, 9, 12, 17, 24 . . . the next number would be

   1. 29
   2. 30
   3. 33
   4. 35
   5. 41

   In the series, 8, 9, 12, 17, 24 . . .
   9 − 8 = 1
   12 − 9 = 3
   17 − 12 = 5
   24 − 17 = 7
   Hence, the difference between the next term and 24 must be 9 or
   x − 24 = 9, and
   x = 33
   Hence, the next term in the series must be 33

7. A shopkeeper bought a radio from a wholesaler for $ 250.00. In addition, he paid a sales tax of 15% on the cost price. He then sold the radio for $ 315.00. Calculate the cash profit made by the shopkeeper.

   1. $ 20.00
   2. $ 22.50
   3. $ 25.00
   4. $ 27.50
   5. $ 27.00

   cost price = $ 250
   sales tax = .15 × 250 = $ 37.5
   cash profit = 315 - 250 - 37.5 = $ 27.5

8. 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,
   \(\frac{𝑥^2 + 3x + 1}{x + 1} = \frac{𝑥^2 + 3x + 2}{x + 1} - \frac{1}{x + 1} = (𝑥 + 2) - \frac{1}{x + 1}\)

9. 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

10. 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

11. A can do a piece of work in 10 days and B can do it in 15 days. The number of days required by them to finish it, working together is

    1. 8
    2. 7
    3. 6
    4. 4
    5. 3

    A's 1 day work = \(1 \over 10\)
    B's 1 day work = \(1 \over 15\)
    Now both A and B's 1 day work = \({1 \over 10} + {1 \over 15}\) = \(3 + 2 \over 30\) = \(1 \over 6\)
    Hence the work by both A and B will be completed in 6 days.

12. if x% of 60 = 48 then x = ?

    1. 80
    2. 60
    3. 90
    4. 40
    5. 70

    x = \( {48 × 100 \over 60} \) = 80

13. \(\frac{\frac{7}{10} × 14 × 5 × \frac{1}{28}}{\frac{10}{17} × \frac{3}{5} × \frac{1}{6} × 17} = \)

    1. 4/7
    2. 1
    3. 7/4
    4. 2
    5. 17/4

    

14. 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

15. Which expression is equivalent to \(\frac{6𝑥^2 + 4𝑥}{2𝑥}\)?

    1. 7x
    2. 5x²
    3. 3x + 2
    4. 6x² + 2
    5. 3x² + 2x

    As \(\frac{6𝑥^2}{2𝑥} = 3𝑥,\) and \(\frac{4𝑥}{2𝑥} = 2,\) so then \(\frac{6𝑥^2 + 4𝑥}{2𝑥} = 3𝑥 + 2\)

16. By selling 60 chairs, a man gains an amount equal to selling price of 10 chairs. The profit percentage in the transaction is

    1. 10%
    2. 15%
    3. 16.67%
    4. 20%
    5. 22%

    selling price of 60 chairs = selling price of 10 chairs
    profit of 60 chairs = profit of 10 chairs
    profit of 6 chairs = profit of 1 chair
    profit of 1 chair = profit of 1/6 chair
    profit %age = 1/6 x 100 = 16.67%

17. Which set of ordered pairs represents a function?

    1. {(−5,5),(4,8),(−5,−6)}
    2. {(−1,−1),(−1,6),(−1,−10)}
    3. {(−3,7),(2,5),(−7,7)}
    4. {(2,3),(−2,4),(−2,−5)}
    5. {(2,3),(3,2),(2,5)}

    For a set of ordered pairs to be a function, no single 𝑥-coordinate can be mapped to two distinct 𝑦-coordinates. This is not the case for option A, where 𝑥=−5 is mapped to both 𝑦=5 and 𝑦=−6. Similarly, in options B (𝑥=−1), D (𝑥=−2), and E (𝑥=2), an 𝑥 value is mapped to two different 𝑦 values.

18. How much would I have to pay for a book which cost $ 72 to product, if the printing company sold it to a bookseller at 20% profit and in return the bookseller sold it to me at a profit of 25%?

    1. $ 104
    2. $ 106
    3. $ 108
    4. $ 110
    5. $ 109

    Cost of the book product = $ 72
    Profit of printing company = 20% of 72 = 0.2 x 72 = 14.4
    Now the cost of the book = 72 +14.4 = $ 86.4
    Profit of the bookseller = 25% of 86.4 = 21.4
    Finally, the cost of the book = 86.4 + 21.4 = $ 108

19. 5789 - 2936 + 1089 = ?

    1. 3942
    2. 4041
    3. 2626
    4. 3932
    5. 3940

    5789 - 2936 + 1089 = 6878 - 2936 = 3942

20. A rectangular room is 6 m long, 5 m wide and 4 m high. The total volume of the room in cubic meters is

    1. 24
    2. 30
    3. 120
    4. 240
    5. 140

    Total volume = length × width × height = 6 × 5 × 4 = 120

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