In the name of ALLAH, the most beneficient, the most merciful

# Solved Examples 1(Quantitative Ability)

1. 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 $$\frac{6𝑥^2 + 4𝑥}{2𝑥} = 3𝑥 + 2$$
2. A train takes 50 minutes for a journey if it runs at 48 km/hr. The rate at which the train must run to reduce the time to 40 minutes will be

1. 50 km/hr
2. 55 km/hr
3. 60 km/hr
4. 57 km/hr
5. 65 km/hr
(50 × 48)/40 = 60 km/hr
3. 1015 / 0.05 / 40 = ?

1. 50.75
2. 507.5
3. 506
4. 2056
5. 5075
1015 / 0.05 / 40 = 20300 / 40 = 507.5
4. $${𝑥 - 8 \over 24} = {3 \over 4}$$ What is the value of 𝑥 in the equation?

1. 10
2. 20
3. 26
4. 31
5. 40
By cross multiplying, 4(𝑥 – 8) =3 × 24. Thus, 4𝑥 – 32 = 72, and so 4𝑥 = 104 and 𝑥 = 26.
5. In the figure above, AB is one edge of a cube. If AB equals 5, what is the surface area of the cube?

1. 25
2. 100
3. 125
4. 150
5. 300
Since one edge of the cube is 5, all edges equal 5. Therefore, the area of one face of the cube is:
(5)(5) = 25
Since a cube has 6 equal faces, its surface area will be:
(6)(25) = 150
6. ? % of 60 = 24

1. 40
2. 48
3. 45
4. 42
5. 38
x = (24 × 100)/60 = 40
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. The closest approximation of $$\frac{69.28 × .004}{.03}$$ is

1. 0.092
2. 0.92
3. 9.2
4. 92
5. 920
This problem is most easily completed by rearranging and approximating as follows:
(69.28 x .004)/.03 ≅ 69 x .1 = 6.9
which is the only reasonably close answer to 9.2
9. 8 : ? :: 1 : 4

1. 24
2. 16
3. 0
4. 32
5. 20
? × 1 = 8 × 4
? = 32
10. 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)/4 = 35 days
11. 5.76/1.6 - 2.4 = ?

1. 1.2
2. 2.4
3. 7.2
4. 0.12
5. 0.012
5.76/1.6 - 2.4 = 3.6 - 2.4 =1.2
12. A shopkeeper sold two articles for $48 each. He made a 25% profit on one article and a loss of 20% on the other. What was his net gain or loss on the sale of the two articles? 1. loss of$ 1.40
2. gain of $2.40 3. loss of$ 2.40
4. gain of $1.40 5. gain of$ 2.60
25% profit at selling price $48 = 48 x .25 =$ 12
20% loss at selling price $48 = 48 x 0.2 =$ 9.6
gain = profit - loss = 12 - 9.6 = $2.4 13. A car traveled 100 km with half the distance at 40 km/h and the other half at 80 km/h. Find the average speed of the car for the whole journey. 1. 53 km/hr 2. 53.33 km/hr 3. 54 1/4 km/hr 4. 55 km/hr 5. 56 km/hr The time, car took for the first half, 50/40 = 1.25 hrs and for the second half 50/80 = 0.625 hrs Total time = 1.25 + 0.625 = 1.875 hrs Average speed = 100/1.875 = 53.3 km/hr 14. How much would I have to pay for a book which cost$ 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
15. 396/11 + 19 = ?

1. 19.8
2. 36
3. 55
4. 33
5. 50
396/11 + 19 = 36 + 19 = 55
16. 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)/10 = 30 minutes
17. $$\frac{\frac{7}{10} × 14 × 5 × \frac{1}{28}}{\frac{10}{17} × \frac{3}{5} × \frac{1}{6} × 17} =$$

1. 4/7
2. 1
3. 7/4
4. 2
5. 17/4 18. A and B can reap a field in 30 days, working together. After 20 days, however, B is called away and A takes 20 days more to complete the work. B alone could do the whole work in

1. 48 days
2. 50 days
3. 56 days
4. 60 days
5. 64 days
(A + B)'s 20 day's work = (1/30 × 20) = 2/3
Remaining work = (1 - 2/3) = 1/3
Now, 1/3 work is done by A in 20 days.
Therefore, the whole work will be done by B in 20 × 3 = 60 days.
19. 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
20. 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.
21. The amount of hot cocoa powder remaining in a can is 6 1⁄4 tablespoons. A single serving consists of 1 3⁄4 tablespoons of the powder. What is the total number of servings of the powder remaining in the can?

1. 3 1⁄2
2. 3 4⁄7
3. 4 3⁄7
4. 4 1⁄2
5. 6
As $$6\frac{1}{4} = \frac{25}{4}$$ and $$1\frac{3}{4} = \frac{7}{4}$$. Therefore,
$$\frac{6\frac{1}{4} \text{ tsp}}{1\frac{3}{4} \text{ } \frac{tsp}{ serving}} = \frac{\frac{25}{4}}{\frac{7}{4}} \text{ servings} = \frac{25}{7} \text{ servings} = 3\frac{4}{7} \text{ servings}$$
22. 5873 + 12034 + 1106 = ?

1. 19016
2. 20001
3. 19013
4. 2018
5. 19010
5873 + 12034 + 1106 = 17907 + 1106 = 19013
23. 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
24. 40 men can build a wall 4 metres high in 15 days. The number of men required to build a similar wall 5 metres high in 6 days is

1. 115
2. 125
3. 105
4. 135
5. 130
(40 × 15 × 5)/(6 × 4) = 125 men
25. 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