# Number System Aptitude Questions and Answers:

#### Overview:

 Questions and Answers Type: MCQ (Multiple Choice Questions). Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Number System Aptitude Questions and Answers. Number of Questions: 10 Questions with Solutions.

1. If the difference between a positive proper fraction and its reciprocal is $$\frac{16}{15}$$ then find the fraction?

1. $$\frac{6}{5}$$
2. $$\frac{3}{5}$$
3. $$\frac{5}{6}$$
4. $$\frac{5}{3}$$

Answer: (b) $$\frac{3}{5}$$

Solution: Let the fraction is $$x$$ then. $$\frac{1}{x} - x = \frac{16}{15}$$ $$\frac{1 - x^2}{x} = \frac{16}{15}$$ $$15 - 15 \ x^2 = 16 \ x$$ $$15 \ x^2 + 16 \ x - 15 = 0$$ $$15 \ x^2 + 25 \ x - 9 \ x - 15 = 0$$ $$5x \ (3x + 5) - 3 \ (3x + 5) = 0$$ $$(3x + 5) \ (5x - 3) = 0$$ According to the question fraction is positive, hence $$x = \frac{3}{5}$$

1. The difference between the two numbers is 945. On dividing the larger number by the smaller, we get 4 as quotient and 15 as the remainder. Find the smaller number?

1. 260
2. 290
3. 310
4. 322

Solution: Let the smaller number is $$x$$ then the larger number should be $$x + 945$$. $$dividend = divisor \times quotient \\ + remainder$$ $$x + 945 = 4 \times x + 15$$ $$3 \ x = 930$$ $$x = \frac{930}{3}$$ $$x = 310$$ Hence the smaller number is 310.

1. Find the sum of all two-digit numbers divisible by 5?

1. 900
2. 910
3. 925
4. 945

Solution: Two-digit numbers divisible by 5 are 10, 15, 20, 25,.....95.

These numbers are making an arithmetic progression series, hence $$a = 10$$ $$d = 5$$ $$l = T_n = 95$$ Let the number of terms in the series are "n" then. $$T_n = a + (n - 1) \ d$$ $$95 = 10 + (n - 1) \ 5$$ $$85 = (n - 1) \ 5$$ $$n - 1 = \frac{85}{5}$$ $$n - 1 = 17$$ $$n = 18$$ Hence the sum of all two-digit numbers divisible by 5. $$S = \frac{n}{2} \ (a + l)$$ $$= \frac{18}{2} \ (10 + 95)$$ $$= 9 \times 105$$ $$S = 945$$ Learn Arithmetic Progression Click Here

1. Find the sum of all three-digit numbers divisible by 5?

1. 98,550
2. 98,390
3. 98,320
4. 98,000

Solution: Three-digit numbers divisible by 5 are 100, 105, 110, 115,.....995.

These numbers are making an arithmetic progression series, hence $$a = 100$$ $$d = 5$$ $$l = T_n = 995$$ Let the number of terms in the series are "n" then. $$T_n = a + (n - 1) \ d$$ $$995 = 100 + (n - 1) \ 5$$ $$895 = (n - 1) \ 5$$ $$n - 1 = \frac{895}{5}$$ $$n - 1 = 179$$ $$n = 180$$ Hence the sum of all three-digit numbers divisible by 5. $$S = \frac{n}{2} \ (a + l)$$ $$= \frac{180}{2} \ (100 + 995)$$ $$= 90 \times 1095$$ $$S = 98,550$$ Learn Arithmetic Progression Click Here

1. What number should be divided by $$\sqrt{0.36}$$ to give the result as 36?

1. 22.3
2. 21.6
3. 20.5
4. 18.2

Solution: Let the number is $$x$$ then. $$\frac{x}{\sqrt{0.36}} = 36$$ $$\frac{x}{0.6} = 36$$ $$x = 36 \times 0.6$$ $$x = 21.6$$