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 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
3. 350 × ? = 4200

1. 12
2. 24
3. 15
4. 30
5. 16
? = 4200/350 =12
4. 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,
$$\frac{6\frac{1}{4} \text{ tsp}}{1\frac{3}{4} \text{ } \frac{tsp}{ serving}} = \frac{\frac{25}{4}}{\frac{7}{4}} \text{ servings} = \frac{25}{7} \text{ servings} = 3\frac{4}{7} \text{ servings}$$
5. 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 6. 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 7. 63.84 / ? = 21 1. 3.04 2. 3.4 3. 30.4 4. 300.4 5. 0.304 63.84 / ? = 21 ? = 63.84/21 = 3.04 8. 12% of ________ = 48 1. 250 2. 100 3. 400 4. 200 5. 300 $$12 \text{% of } x = 48$$ $$0.12x = 48$$ $$x = \frac{48}{0.12} = 400$$ 9. A man was 32 years old when his daughter was born. He is now five times as old as his daughter. How old is his daughter now? 1. 7 years 2. 8 years 3. 9 years 4. 10 years 5. 6 years Let's assume the daughter is d years old now. That means that the man is now (32 + d) years old, so that (32 + d) = 5d 32 = 4d d = 8 10. 60% of 37 = ? 1. 20 2. 21 3. 22.2 4. 22 5. none 60% of 37 = .6 × 37 = 22.2 11. A shopkeeper buys 300 identical articles at a total cost of$ 1500. He fixes the selling price of each article at 20% above the cost price and sells 260 articles at the price. As for the remaining articles, he sells them at 50% of the selling price. Calculate the shopkeeper's total profit.

1. $180 2.$ 185
3. $200 4.$ 190
5. $170 cost price of each item = 1500/300 =$ 5
selling price at 20% above the cost price = 5 + 5 × .2 = $6 selling price of 260 items = 260 × 6 =$ 1560
selling price of remaining 40 items = 40 × 6 × .5 = $120 Total profit = 1560 + 120 - 1500 =$ 180
12. 5873 + 12034 + 1106 = ?

1. 19016
2. 20001
3. 19013
4. 2018
5. 19010
5873 + 12034 + 1106 = 17907 + 1106 = 19013
13. 2244 / 0.88 = ? × 1122

1. 20.02
2. 20.2
3. 19.3
4. 2.27
5. 3.27
2244 / 0.88 = ? × 1122
? = 2550 / 1122 = 2.27
14. A boy of height 165 cm is replaced by another, which decreases the average height of the group of 34 students, by 1 cm. The height of the new student is

1. 129 cm
2. 130 cm
3. 131 cm
4. 132 cm
5. 133 cm
Total decreased height of 34 students = 1 × 34 = 34 cm
Height of the replaced student = 165 - 34 = 131 cm
15. 1.02 - 0.20 + ? = 0.842

1. 0.222
2. 232
3. 2
4. 0.022
5. 0.012
1.02 - 0.20 + ? = 0.842
0.82 + ? = 0.842
? = 0.842 - 0.82 = 0.022
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. 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.
18. 8 : ? :: 1 : 4

1. 24
2. 16
3. 0
4. 32
5. 20
? × 1 = 8 × 4
? = 32
19. 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,
$$\frac{𝑥^2 + 3x + 1}{x + 1} = \frac{𝑥^2 + 3x + 2}{x + 1} - \frac{1}{x + 1} = (𝑥 + 2) - \frac{1}{x + 1}$$
20. A third-grade class is composed of 16 girls and 12 boys. There are 2 teacheraides in the class. The ratio of girls to boys to teacher-aides is

1. 16:12:1
2. 8:6:2
3. 8:6:1
4. 8:3:1
5. 4:3:1
Girls to boys to teacher-aides are in proportion 16 to 12 to 2. Reduced to lowest terms, 16:12:2 equals 8:6:1.
21. 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/100 + bc/100 + ca/100 – abc/10000)
a = 20, b = 10, c = 25, solving we get, 46%.
22. 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
23. 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

24. 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
25. 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