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

# Solved Examples Set 1 (Quantitative Ability)

1. In the series 8, 9, 12, 17, 24 . . . the next number would be

1. 29
2. 30
3. 33
4. 35
5. 41
In the series, 8, 9, 12, 17, 24 . . .
9 − 8 = 1
12 − 9 = 3
17 − 12 = 5
24 − 17 = 7
Hence, the difference between the next term and 24 must be 9 or
x − 24 = 9, and
x = 33
Hence, the next term in the series must be 33
2. 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 $$\frac{2}{2 + 2 + 2 + 3} = \frac{2}{9}$$.
3. $${0.027 \over 90} = ?$$

1. 0.0003
2. 0.03
3. 3
4. 0.00003
5. 0.003
$${0.027 \over 90} = {27 \over 1000 × 90} = {3 \over 10000} = 0.0003$$
4. $$25 \text{% of }{4 \over 4\text{%}} \text{ of }{1 \over 25} = ?$$

1. 1
2. 3
3. 0
4. 67
5. 25
$$25 \text{% of }{4 \over 4\text{%}} \text{ of }{1 \over 25}$$
$$= 25 \text{% } × {4 \over 4\text{%}} × {1 \over 25}$$
$$= 0.25 × {4 \over 0.04} × {1 \over 25}$$
$$= {25 \over 25}$$
= 1
5. 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
6. 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
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
$$50 × 48 \over 40$$ = 60 $$km \over hr$$
8. A third-grade class is composed of 16 girls and 12 boys. There are 2 teacher-aides 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.
9. A certain number was doubled and the result then multiplied by 3. If the product was 138, find the number.

1. 21
2. 23
3. 25
4. 27
5. 19
Let x be the number
the number is doubled, 2x
the result is multiplied by 3, 3 × 2x = 6x
6x = 138
x = $$138 \over 6$$ = 23
10. 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
11. if x% of 60 = 48 then x = ?

1. 80
2. 60
3. 90
4. 40
5. 70
x = $${48 × 100 \over 60}$$ = 80
12. 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 $$\frac{6𝑥^2 + 4𝑥}{2𝑥} = 3𝑥 + 2$$
13. A boy scored 90 marks for his mathematics test. This was 20% more than what he had scored for the geography test. How much did he score in geography?

1. 71 marks
2. 73 marks
3. 75 marks
4. 77 marks
5. 78 marks
20% of x + x = 90
0.2x + x = 90
1.2x = 90
x = $$90 \over 1.2$$
x = 75
14. $${396 \over 11}$$ + 19 = ?

1. 19.8
2. 36
3. 55
4. 33
5. 50
$${396 \over 11}$$ + 19 = 36 + 19 = 55
15. 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
16. 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
$$14 × 10 \over 4$$ = 35 days
17. A man earned an annual income of $245000 in 1990. He was allowed a deduction of$ 15000 relief for each of his three children and a personal relief of $30000. If he was charged a tax rate of 4% on first$ 50000 and 6% on his remaining income, calculate the total tax charged.

1. $9200 2.$ 8700
3. $9500 4.$ 9400
5. $9000 Total Income =$ 245000
Total relief = 3 × 15000 + 30000 = $75000 Rest income = 245000 - 75000 = 170000 Tax on 1st 50000 = 0.04 × 50000 =$ 2000
Tax on rest amount 120000 = 0.06 × 120000 = $7200 Total tax = 200 + 7200 =$ 9200
18. $${1250 \over 25} × 0.5 = ?$$

1. 250
2. 50
3. 2.5
4. 25
5. 125
$${1250 \over 25} × 0.5 = 50 × 0.5 = 25$$
19. 350 × ? = 4200

1. 12
2. 24
3. 15
4. 30
5. 16
$$? = {4200 \over 350} =12$$
20. 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, $$50 \over 40$$ = 1.25 hrs
and for the second half $$50 \over 80$$ = 0.625 hrs
Total time = 1.25 + 0.625 = 1.875 hrs
Average speed = $$100 \over 1.875$$ = 53.3 $$km \over hr$$