Practice MCQ Questions and Answer on Number System

611.

The sum of all natural numbers from 75 to 97 is -

(A) 1598
(B) 1798
(C) 1958
(D) 1978

Solution: The sum of all natural numbers upto 97 - sum of all natural numbers upto 74 sum of n natural numbers $\begin{aligned} = \frac{n (n + 1)}{2} (Formula) \\ = \frac{97 \times 98}{2} - \frac{74 \times 75}{2} \\ = 4753 - 2775 \\ = 1978 \end{aligned}$

612.

Let x = (633)²⁴ - (277)³⁸ + (266)⁵⁴. What is the units digits of x?

(A) 8
(B) 6
(C) 4
(D) 7

613.

Find the remainder when 67¹⁰⁷ is divided by 7.

(A) 4
(B) 2
(C) 1
(D) 6

Solution: $\begin{aligned} \frac{67^{107}}{7} \\ O r, \frac{{(7 \times 9 + 4)}^{107}}{7} \\ The remainder will be same as \\ \frac{4^{107}}{7} \\ O r, \frac{4^{3}}{7} \\ O r, \frac{64}{7} \\ Required Remainder = 1 \end{aligned}$

614.

A gardener plants his garden with 5550 trees and arranged them so that there is one plant more per row as there are rows then number of trees in a row is:

(A) 56
(B) 74
(C) 76
(D) 75

615.

The number 89715938* is divisible by 4. The unknown non-zero digit marked as * will be :

(A) 2
(B) 3
(C) 4
(D) 6

616.

In a certain series, each number except the first and second is obtained by adding the previous two numbers. If the first no is 2 and sixth no is 26, then the seventh number is:

(A) 52
(B) 46
(C) 40
(D) 42

617.

If sum of two numbers be a and their product be b, then the sum of their reciprocals is :

(A) $\frac{1}{b}$ + $\frac{1}{b}$
(B) $\frac{b}{a}$
(C) $\frac{a}{b}$
(D) $\frac{1}{a b}$

Solution: Let the two number are P and Q P + Q = a PQ = b ⇒ $\frac{1}{P}$ + $\frac{1}{Q}$ ⇒ $\frac{Q + P}{P Q}$ ⇒ $\frac{a}{b}$

618.

Which of the following fraction is the smallest ?
$\frac{7}{6}, \frac{7}{9}, \frac{4}{5}, \frac{5}{7}$

(A) $\frac{7}{6}$
(B) $\frac{7}{9}$
(C) $\frac{4}{5}$
(D) $\frac{5}{7}$

Solution: $\frac{7}{6}, \frac{7}{9}, \frac{4}{5}, \frac{5}{7}$ Step 1 : Compare two fractions $\frac{7}{6}$ ⤩ $\frac{7}{9}$ Cross multiply 63 , 42 ↑ ↑ $\frac{7}{6}$ ⤩ $\frac{7}{9}$ 42 is smaller than 63 So, $\frac{7}{9}$ is smaller than $\frac{7}{6}$ Step 2 : Compare (i) $\frac{7}{9}, \frac{4}{5}$ (ii) $\frac{7}{9}$ ⤩ $\frac{4}{5}$ Cross multiply it 35 , 36 ↑ ↑ $\frac{7}{9}$ ⤩ $\frac{4}{5}$ 35 is smaller than 36 So, $\frac{7}{9}$ is smaller than $\frac{4}{5}$ Step 3 : Compare (i) $\frac{7}{9}, \frac{5}{7}$ (ii) $\frac{7}{9}$ ⤩ $\frac{5}{7}$ Cross multiply it 49 , 45 ↑ ↑ $\frac{7}{9}$ ⤩ $\frac{5}{7}$ 45 is smaller than 49 S0, $\frac{5}{7}$ is the smallest Alternate : $\begin{aligned} \frac{7}{6} = 1.166, \\ \frac{7}{6} = 0.777 \\ \frac{4}{5} = 0.8, \\ \frac{5}{7} = 0.714 \\ Thus \frac{5}{7} is the smallest . \end{aligned}$

619.

Find the least number which will leaves remainder 5 when divided by 8, 12, 16 and 20.

(A) 240
(B) 245
(C) 265
(D) 235

620.

A number divided by 68 gives the quotient 260 and remainder zero. If the same number is divided by 65, the remainder is :

(A) 0
(B) 1
(C) 2
(D) 3

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Practice MCQ Questions and Answer on Number System

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