Number System - Aptitude MCQ Questions and Solutions with Explanations

11

The sum of three numbers is 2, the 1^st number is $$\frac{1}{2}$$ times the 2^nd and the 3^rd number is $$\frac{1}{4}$$ times the 2^nd number. The 2^nd number is :

A) $$\frac{7}{6}$$ B) $$\frac{8}{7}$$ C) $$\frac{9}{8}$$ D) $$\frac{10}{9}$$

Discuss

Answer & Solution

Answer: Option B

Solution:

Let the number is a, b, c
a + b + c = 2
a = $$\frac{1}{2}$$ b.....(i)
c = $$\frac{1}{4}$$ b.....(ii)
$$\frac{a}{b}$$ = $$\frac{1}{2}$$
$$\frac{b}{c}$$ = $$\frac{4}{1}$$

a	:	b	:	c
1	:	2	↘
↘		4	:	1
4	:	8	:	2

a : b : c = 2 : 4 : 1
(2 + 4 + 1) = 7
7 units → 2
1 unit → $$\frac{2}{7}$$
4 units → $$\frac{2}{7}$$ × 4 = $$\frac{8}{7}$$
So, 2^nd number is $$\frac{8}{7}$$

12

If the product of two positive numbers be 1575 and their ration is 7 : 9, then the greatest number is :

A) 45 B) 135 C) 35 D) 63

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the numbers are 7x and 9x
According to the question,
$$\eqalign{ & \Rightarrow 7x \times 9x = 1575 \cr & \Rightarrow 63{x^2} = 1575 \cr & \Rightarrow {x^2} = 25 \cr & \Rightarrow x = 5 \cr} $$
Then greater number
= 9x
= 9 × 5
= 45

13

A number when divided by 729 given a remainder of 56. What will we get as remainder if the same number is divided by 27 ?

A) 4 B) 2 C) 0 D) 1

Discuss

Answer & Solution

Answer: Option B

Solution:

If first number (729) is completely divide by second number (27) then we divide remainder from second number then remaining remainder will be answer.
$$\frac{729}{27}$$ = 27 times
Now, $$\frac{56}{27}$$ = 2 × 27 + 2 → Remainder

14

Sum of two numbers is thrice their difference. Their ratio is :

A) 1 : 2 B) 2 : 1 C) 3 : 1 D) 1 : 3

Discuss

Answer & Solution

Answer: Option B

Solution:

Let the numbers = a, b
According to the question,
a + b = 3 (a - b)
$$\frac{a + b}{a - b}$$ = $$\frac{3}{1}$$
By componendo and dividendo
$$\frac{2a}{2b}$$ = $$\frac{4}{2}$$
$$\frac{a}{b}$$ = $$\frac{2}{1}$$
a : b = 2 : 1

15

A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder. The number is -

A) 220030 B) 22030 C) 1220 D) 1250

Discuss

Answer & Solution

Answer: Option A

Solution:

Let number is N
N is divided by the sum of 555 and 445, the quotient is 2 times difference
Quotient = 2 (555 - 445) = 220
Remainder = 30 (given)
N = 1000 × 220 + 30
= 220030

16

When simplified the product : $$\left( {2 - \frac{1}{3}} \right)$$ $$\left( {2 - \frac{3}{5}} \right)$$ $$\left( {2 - \frac{5}{7}} \right)$$ .....$$\left( {2 - \frac{{997}}{{999}}} \right)$$

A) $$\frac{1001}{3}$$ B) $$\frac{5}{3}$$ C) $$\frac{5}{999}$$ D) $$\frac{1001}{999}$$

Discuss

Answer & Solution

Answer: Option A

Solution:

According to the question,
$$ \Rightarrow \left( {2 - \frac{1}{3}} \right)\left( {2 - \frac{3}{5}} \right)\left( {2 - \frac{5}{7}} \right).....$$ $$\left( {2 - \frac{{997}}{{999}}} \right)$$
$$\eqalign{ & \Rightarrow \frac{5}{3} \times \frac{7}{5} \times \frac{9}{7}.....\frac{{1001}}{{999}} \cr & \Rightarrow \frac{1}{3} \times 1001 \cr & \Rightarrow \frac{{1001}}{3} \cr} $$

17

The smallest possible three placed decimal is-

A) 0.012 B) 0.123 C) 0.111 D) None of these

Discuss

Answer & Solution

Answer: Option D

Solution:

Smallest number in case of decimal = 0.001

18

The divisor is 25 times of the quotient and 5 times the remainder. If the quotient is 16, the dividend is-

A) 6400 B) 6480 C) 400 D) 480

Discuss

Answer & Solution

Answer: Option B

Solution:

Dividend = (divisor × quotient) + remainder
According to the question
$$\eqalign{ & {\text{Divisor :}} \cr & \Rightarrow {\text{16}} \times {\text{25 = 5}} \times {\text{remainder}} \cr & \Rightarrow {\text{R = }}\frac{1}{5} \times 16 \times 25 \cr & {\text{Dividend :}} \cr & {\text{ = }}\left[ {\left( {{\text{16}} \times {\text{25}}} \right) \times 16} \right] + \frac{1}{5} \times 16 \times 25 \cr & = \left[ {16 \times 25 \times 16} \right] + 80 \cr & = 6480 \cr} $$

19

A runner runs $$1\frac{1}{4}$$ laps of a 5 laps race. What laps of the race remains to be run ?

A) $$\frac{15}{4}$$ B) $$\frac{4}{5}$$ C) $$\frac{5}{6}$$ D) $$\frac{2}{3}$$

Discuss

Answer & Solution

Answer: Option A

Solution:

Remaining distance to be run
$$\eqalign{ & = 5 - \frac{5}{4} \cr & = \frac{{20 - 5}}{4} \cr & = \frac{{15}}{4}\,{\text{laps}} \cr} $$

20

$$\frac{1}{{10}}$$ of a rod is coloured red, $$\frac{1}{{20}}$$ orange, $$\frac{1}{{30}}$$ yellow, $$\frac{1}{{40}}$$ green, $$\frac{1}{{50}}$$ blue, $$\frac{1}{{60}}$$ black and the rest is violet. If the length of the violet part of the rod is 12.08 mtr, then the length of the rod is -

A) 16 m B) 18 m C) 20 m D) 30 m

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the total length of rod is 1 unit
According to question,
$$ \Rightarrow 1 - \frac{1}{{10}} - \frac{1}{{20}} - \frac{1}{{30}} - \frac{1}{{40}} - \frac{1}{{50}}$$ $$ - \frac{1}{{60}}$$

$$ \Rightarrow \frac{{600 - 60 - 30 - 20 - 15 - 12 - 10}}{{600}}$$
$$\eqalign{ & \Rightarrow \frac{{453 \leftarrow {\text{ Violet part}}}}{{600 \leftarrow {\text{ Total part}}}} \cr & 453{\text{ part }} \to {\text{ 12}}{\text{.08 mtr}} \cr & {\text{1 part }} \to \,\,\,\,\,\,\,\,\frac{{12.08}}{{453}} \cr & 600{\text{ part }} \to \frac{{12.08}}{{453}} \times 600 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 16{\text{mtr}} \cr} $$
So total length of rod is 16 metres.