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

# Solved Examples 1(Quantitative Ability)

1. 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
2. 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
3. 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.
4. 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
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. 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.
7. 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
8. 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
9. 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
10. 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 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 basket that contains 2 apples, 3 bananas, 6 oranges, and 4 pears is in the workroom. When Ms. Hutchinson went to the workroom, other workers had already taken 1 banana, 2 oranges, and 1 pear. From the remaining fruit, Ms. Hutchinson randomly took 3 pieces of fruit separately from the basket. If each fruit is equally likely to be chosen, what is the probability that the third piece was an orange if the first two she took were also oranges? 1. 4/165 2. 9/11 3. 4/11 4. 3/11 5. 2/9 Ms. Hutchinson randomly takes the 3 pieces of fruit from the basket, there are 2 apples, 3 -1 = 2 bananas, 6 - 2 = 4 oranges, and 4 - 1 = 3 pears. Assuming that the first 2 pieces of fruit Ms. Hutchinson takes are oranges, there will be 2 apples, 2 bananas, 4 - 2 = 2 oranges, and 3 pears left in the basket when she selects the third piece of fruit. The probability that the third piece of fruit she selects will be an orange is $$\frac{2}{2 + 2 + 2 + 3} = \frac{2}{9}$$. 13. 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 14. 25% of 4/4% of 1/25 = ? 1. 1 2. 3 3. 0 4. 67 5. 25 25% of 4/4% of 1/25 = 1/.04/25 = 25/25 = 1 15. 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. 16. 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 $$\frac{6𝑥^2 + 4𝑥}{2𝑥} = 3𝑥 + 2$$ 17. 5873 + 12034 + 1106 = ? 1. 19016 2. 20001 3. 19013 4. 2018 5. 19010 5873 + 12034 + 1106 = 17907 + 1106 = 19013 18. 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 19. 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 20. 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 21. 8 : ? :: 1 : 4 1. 24 2. 16 3. 0 4. 32 5. 20 ? × 1 = 8 × 4 ? = 32 22. 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 23. 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
24. 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
25. A man sells two houses for \$ 2 lac each. On one he gained 20% and on the other he lost 20%. His total profit or loss % in the transaction will be

1. 4% profit
2. 5% loss
3. no profit, no loss
4. 4% loss
5. 3% loss
% loss = (% loss X % profit)/100 = (20 X 20)/100 = 4%