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

# Solved Examples 1(Quantitative Ability)

1. 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.
2. 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
3. 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
4. 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
5. 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
6. A and B enter into a partnership contributing $800 and$ 1000 respectively. At the end of 6 months they admit C, who contributes $600. After 3 years they get a profit of$ 966. Find the share of each partner in the profit.

1. $336,$ 420, $210 2.$ 360, $400,$ 206
3. $380,$ 390, $196 4.$ 345, $405,$ 210
5. $325,$ 400, $200 A shares = 800 × 3 = 2400 B shares = 1000 × 3 = 3000 C shares = 600 × 2 1⁄2 = 1500 Total shares = 6900 A's profit = 2400/6900 × 966 =$ 336
B's profit = 3000/6900 × 966 = $420 C's profit = 1800/6900 × 966 =$ 210
7. 8 : ? :: 1 : 4

1. 24
2. 16
3. 0
4. 32
5. 20
? × 1 = 8 × 4
? = 32
8. 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
9. 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 10. 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 $$\frac{6𝑥^2 + 4𝑥}{2𝑥} = 3𝑥 + 2$$ 11. On a trip to visit friends, a family drives 65 miles per hour for 208 miles of the trip. If the entire trip was 348 miles and took 6 hours, what was the average speed, in miles per hour, for the rest of the trip? 1. 44 2. 50 3. 51 4. 58 5. 60 As the first part of the trip took $$\frac{208 \text{ miles}}{65 \text{ } \frac{miles}{hour}} = 3.2 \text{ hours},$$ so the remaining 140 miles (348 - 208) took 2.8 hours (6 - 3.2). The average speed for the rest of the trip was $$\frac {140 \text{ miles}}{2.8 \text{ hours}} = 50$$ miles per hour. 12. 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 13. 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 14. 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 15. 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 16. 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. 17. 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
18. Rashid buys three books for $16 each and four books for$ 23 each, what will be the average price of books

1. $18 2.$ 20
3. $22 4.$ 24
5. $16 Price of 3 books = 3 × 16 =$ 48
Price of 4 books = 4 × 23 = $92 Total price =$ 140
Total books = 3 + 4 = 7
Average price of books = 140/7 = $20 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. 42.98 + ? = 107.87 1. 64.89 2. 65.89 3. 64.98 4. 65.81 5. 63.89 ? = 107.87 - 42.98 = 64.89 21. 350 × ? = 4200 1. 12 2. 24 3. 15 4. 30 5. 16 ? = 4200/350 =12 22. ? % of 60 = 24 1. 40 2. 48 3. 45 4. 42 5. 38 x = (24 × 100)/60 = 40 23. if a > b and b > c then: 1. a = c 2. a > c 3. c > a 4. a < c 5. none As a > b > c so a > c 24. 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
25. 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