Practice MCQ Questions and Answer on Number System

671.

Which one of the following is a prime number ?

(A) 161
(B) 221
(C) 373
(D) 437

672.

Let x be the least number which when divided by 15,18, 20 and 27, the remainder in each case is 10 and x is a multiple of 31. What least number should be added to x to make it a perfect square?

(A) 39
(B) 37
(C) 43
(D) 36

673.

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

Solution: Let the numbers are 7x and 9x According to the question, $\begin{aligned} \Rightarrow 7 x \times 9 x = 1575 \\ \Rightarrow 63 x^{2} = 1575 \\ \Rightarrow x^{2} = 25 \\ \Rightarrow x = 5 \end{aligned}$ Then greater number = 9x= 9 × 5= 45

674.

Arrangement of the fractions $\frac{4}{3}, - \frac{2}{9}, - \frac{7}{8}, \frac{5}{12}$ ÃÂÃÂ ÃÂÃÂ into ascending order:

(A) $- \frac{2}{9}, - \frac{7}{8}, \frac{4}{3}, \frac{5}{12}$
(B) $- \frac{7}{8}, - \frac{2}{9}, \frac{5}{12}, \frac{4}{3}$
(C) $- \frac{7}{8}, - \frac{2}{9}, \frac{4}{3}, \frac{5}{12}$
(D) $- \frac{2}{9}, - \frac{7}{8}, \frac{5}{12}, \frac{4}{3}$

Solution: $\begin{aligned} \frac{4}{3}, \frac{- 2}{9}, \frac{- 7}{8}, \frac{5}{12} \\ \frac{4}{3} = 1.33 \\ \frac{- 2}{9} = - 0.22 \\ \frac{- 7}{8} = - 0.875 \\ \frac{5}{12} = 0.416 \\ So, \frac{- 7}{8}, \frac{- 2}{9}, \frac{5}{12}, \frac{4}{3} \end{aligned}$

675.

The product of two number is 48. If one number equals "The number of wings of a bird plus 2 times the number of figure on your hand divided by the number of wheels of a Tricycle." Then the other number is?

(A) 9
(B) 10
(C) 12
(D) 18

Solution: $\begin{aligned} Let number are x and y \\ According to the question, \\ x \times y = 48 \\ and x = \frac{2 + \overset{total fingers in one hand}{\overset{↑}{5}} \times 2}{3} = \frac{12}{3} = 4 \\ y = \frac{48}{4} = 12 \end{aligned}$

676.

The real number to be added to 13851 to get a number which is divisible by 87 is :

(A) 18
(B) 43
(C) 54
(D) 69

677.

How many number are there between 1 to 200 which are divisible by 3 but not by 7?

(A) 38
(B) 45
(C) 57
(D) 66

Solution: Number from 1 to 200 which is divisible by 3 3, 6, . . . . . . . . ., 198 $\begin{aligned} = \frac{198 - 3}{3} + 1 \\ = 66 \end{aligned}$ Total number which divisible by 3 & 7 $\begin{aligned} = \frac{189 - 21}{21} + 1 \\ = \frac{168}{21} + 1 \\ = 9 \end{aligned}$ Total number which is divisible by 3 but not 7 = 66 - 9 = 57 Alternate solution Total number which is divisible by 3 & 7 both from 1 to 200 LCM (3 & 7) $\to \frac{1}{21} - \frac{200}{21} = 0 - 9 = 9$ Total number which is divisible by only 3, from 1 to 200 $\frac{1}{3} - \frac{200}{3} = 0 - 66 = 66$ ∴ Total number which is divisible by 3 but not 7 = 66 - 9 = 57

678.

Find the HCF of (3¹²⁵-1) and (3³⁵-1).

(A) 34 - 1
(B) 35 - 1
(C) 312 - 1
(D) None of these

679.

A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be

(A) 1, 2
(B) 2, 3
(C) 3, 2
(D) 4, 1

680.

A number when divided by 14 leaves reminder of 8, but when the same number is divided by 7, it will leave the remainder :

(A) 3
(B) 2
(C) 1
(D) 4

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Practice MCQ Questions and Answer on Number System

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