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

# Solved Examples 1(Quantitative Ability)

1. 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
2. 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
3. 396/11 + 19 = ?

1. 19.8
2. 36
3. 55
4. 33
5. 50
396/11 + 19 = 36 + 19 = 55
4. 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 5. 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 6. 8 : ? :: 1 : 4 1. 24 2. 16 3. 0 4. 32 5. 20 ? × 1 = 8 × 4 ? = 32 7. 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 8. ? % of 60 = 24 1. 40 2. 48 3. 45 4. 42 5. 38 x = (24 × 100)/60 = 40 9. 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, $$\frac{6\frac{1}{4} \text{ tsp}}{1\frac{3}{4} \text{ } \frac{tsp}{ serving}} = \frac{\frac{25}{4}}{\frac{7}{4}} \text{ servings} = \frac{25}{7} \text{ servings} = 3\frac{4}{7} \text{ servings}$$ 10. 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 = $210 11. A retailer bought a compact disc from a manufacturer for$ 200. In addition to that, he paid a 15% sales tax. If he sold the disc to a customer for $260, calculate the cash profit he made. 1.$ 30.00
2. $35.00 3.$ 32.50
4. $28.00 5.$ 30.50
price of a compact disc with sales tax = 200 + 0.15 × 200
= 200 + 30 = $230 As the selling price of the disc =$ 260
Hence, cash profit = 260 - 230 = $30 12. A shopkeeper buys 300 identical articles at a total cost of$ 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
13. 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
14. 15 men can complete a job in 10 days. How long will it take 8 men to finish the same job if they work at the same rate?

1. 14 3⁄4 days
2. 16 3⁄4 days
3. 18 3⁄4 days
4. 20 3⁄4 days
5. 22 3⁄4 days
(15 × 10)/8 = 18 3⁄4 days
15. 1015 / 0.05 / 40 = ?

1. 50.75
2. 507.5
3. 506
4. 2056
5. 5075
1015 / 0.05 / 40 = 20300 / 40 = 507.5
16. 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.

17. 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
18. 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
19. 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. (.5)(.3)(280) = 42
B. (.33)(.7)(160) = 36.96
C. (2)(.5)(30) = 30
D. (3)(.4)(40) = 48
E. (.6)(60) = 36
20. 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%
21. ? × 12 = 75% of 336

1. 48
2. 252
3. 28
4. 21
5. 23
? × 12 = 75% of 336
? × 12 = 0.75 × 336
? × 12 = 252
$$? = \frac{252}{12}$$
? = 21
22. 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
23. At a book fair, a book was reduced in price from $75 to$ 60. If the first price gives a 50% profit, find the percentage profit of the book sold at the reduced price.

1. 20%
2. 30%
3. 40%
4. 50%
5. 10%
As $75 (first price) gives a profit = 50%$ 1 gives a profit = (50/75)%
\$ 60 (reduced price) gives profit = (50/75 x 60)% = 40%
24. 350 × ? = 4200

1. 12
2. 24
3. 15
4. 30
5. 16
? = 4200/350 =12
25. 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