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

# Solved Examples Set 3 (Quantitative Ability)

1. $${1250 \over 25} × 0.5 = ?$$

1. 250
2. 50
3. 2.5
4. 25
5. 125
$${1250 \over 25} × 0.5 = 50 × 0.5 = 25$$
2. A person's net income is $1373.70 and he pays an income tax of 5%. His gross income in dollars must be 1. 1446 2. 1118.96 3. 1308.29 4. 1438.25 5. 1211.21 Let gross income in dollars = x then according to the statement, x = 5% of x + 1373.70 x - 0.05x = 1373.70 0.95x = 1373.70 x = $$137370 \over 95$$ = 1446 3. 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% 4. 40 arithmetic questions, each carrying equal marks, were given in a class test. A boy answered 25 questions correctly. What percentage was this? To pass a test a student must answer at least 45% of the questions correctly. Find the least number of correct answers needed to pass. 1. 62.5%, 18 2. 63.5%, 16 3. 64.5%, 20 4. 61.0%, 21 5. 60.0%, 22 $$x \text{% of } 40 = 25$$ $$x \text{% } × 40 = 25$$ $$x = {25 \over 40} × 100$$ x = 62.5 $$x = 45 \text{% of } 40$$ $$x = 0.45 × 40$$ x = 18 5. 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 6. 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 $$\frac{6𝑥^2 + 4𝑥}{2𝑥} = 3𝑥 + 2$$ 7. A bank increased the rate of interest which it paid to depositors from 3.5% to 4% per annum. Find how much more interest a man would receive if he deposited$ 64000 in the bank for 6 months at the new interest rate

1. $160 2.$ 180
3. $200 4.$ 220
5. $150 If the interest rate is 3.5% then interest amount is 3.5% of 6400 = 0.035 × 6400 =$ 2240
If the interest rate is 4% then interest amount is
4% of 6400 = 0.04 × 6400 = $2560 Now the difference of both interests = 2560 - 2240 =$ 320 per annum
Interest for half year (6 months) = $$320 \over 2$$ = $160 8. A bank exchanges British currency for Singapore currency at the rate of S$ 3.20 to pond 1. Calculate, in Pond, the amount exchanged for S$1,600 by a customer who also had to pay an extra 3% commission for this transaction. 1. Pond 475 2. Pond 485 3. Pond 495 4. Pond 505 5. Pond 510 As commission is 3% of 1600 = 0.03 × 1600 = S$ 48
the rest amount = 1600 - 48 = S$1552 S$ 1 = $$1 \over 3.20$$ = Pond 0.3125
Now S$1552 = 1552 × 0.3125 = Pond 485 9. $${63.84 \over ?}$$ = 21 1. 3.04 2. 3.4 3. 30.4 4. 300.4 5. 0.304 ? = $$63.84 \over 21$$ = 3.04 10. 8 : ? :: 1 : 4 1. 24 2. 16 3. 0 4. 32 5. 20 ? × 1 = 8 × 4 ? = 32 11. A man pays 10% of his income for his income tax. If his income tax amounts to$ 1500, what is his income?

1. $13000 2.$ 15000
3. $17000 4.$ 19000
5. $11000 Let x = income 10% of x =$ 1500
0.1x = $1500 x = $$1500 \over 0.1$$ =$ 15000
12. 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
13. 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.
14. 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)%
$60 (reduced price) gives profit = (50/75 x 60)% = 40% 15. A shopkeeper sold two articles for$ 48 each. He made a 25% profit on one article and a loss of 20% on the other. What was his net gain or loss on the sale of the two articles?

1. loss of $1.40 2. gain of$ 2.40
3. loss of $2.40 4. gain of$ 1.40
5. gain of $2.60 25% profit at selling price$ 48 = 48 x .25 = $12 20% loss at selling price$ 48 = 48 x 0.2 = $9.6 gain = profit - loss = 12 - 9.6 =$ 2.4
16. 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 – ($$ab \over 100$$ + $$bc \over 100$$ + $$ca \over 100$$ – $$abc \over 10000$$)
a = 20, b = 10, c = 25, solving we get, 46%.
17. 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
18. 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 = 2400 + 3000 + 1500 = 6900 A's profit = $$2400 \over 6900$$ × 966 =$ 336
B's profit = $$3000 \over 6900$$ × 966 = $420 C's profit = $$1500 \over 6900$$ × 966 =$ 210
19. After spending 88% of his income, a man had $2160 left. Find his income. 1.$ 18000
2. $19000 3.$ 20000
4. $22000 5.$ 17000
Let income = x
x = 88% of x + 2160
x - 0.88x = 2160
0.12x = 2160
x = $$216000 \over 12$$ = 18000
20. 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,
$$\frac{𝑥^2 + 3x + 1}{x + 1} = \frac{𝑥^2 + 3x + 2}{x + 1} - \frac{1}{x + 1} = (𝑥 + 2) - \frac{1}{x + 1}$$