Practice MCQ Questions and Answer on Number System
81.
On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ?
(A) 0
(B) 3
(C) 5
(D) 11
Solution:
Let x be the number and y be the quotient. Then, x = 357 × y + 39 = (17 × 21 × y) + (17 × 2) + 5 = 17 × (21y + 2) + 5 ∴ Required remainder = 5
82.
A positive integer when divided by 425 gives a remainder 45. When the same number is divided by 17, the remainder will be :
(A) 7
(B) 8
(C) 11
(D) 10
Solution:
$$\eqalign{ & \frac{{{\text{Remainder of number }}}}{{17}} = \frac{{45}}{{17}} \cr & \Rightarrow {\text{Remainder = 11}} \cr} $$
83.
For any integral value of n, 32n + 9n + 5 when divided by 3 will leave the remainder
(A) 1
(B) 2
(C) 0
(D) 5
Solution:
32n + 9n + 5 Put n = 1 ⇒ 32 × 1 + 9 × 1 + 5 ⇒ 9 + 9 + 5 ⇒ 23 ⇒ $$\frac{{23}}{3}$$ ⇒ remainder = 2 Note: value of n can be 1, 2, 3, 4, . . . . .
84.
A number when divided by 3 leaves a remainder 1. When the quotient is divided by 2, it leaves a remainder 1. What will be the remainder when numbers is divided by 6 ?
(A) 2
(B) 3
(C) 4
(D) 5
Solution:
y = 2 × 1 + 1 = 3 x = 3 × y + 1 = 3 × 3 + 1 = 10 Clearly, 10 when divided by 6, leaves a remainder 4
85.
If 6*43 - 46@9 = 1904, which of the following should come in place of * ?
(A) 4
(B) 6
(C) 9
(D) Cannot be determined
Solution:
Answer & Solution Answer: Option E Solution: Let 6x43 - 46y9 = 1904 Clearly, y = 3 and x = 5 Hence * must be replaced by 5
86.
The unit digit of the expression : $${25^{6251}} \, + $$ ÃÂÃÂ $${36^{528}} \, + $$ ÃÂÃÂ $${73^{54}} = ?$$
(A) 6
(B) 5
(C) 4
(D) 0
Solution:
256251 = 56251 = 5 (because unit digit of 5 is always 5) 36528 = 6528 = 6 (because unit digit of 6 is always 6) 7354 = 354 = 9(unit digit of 354 = 32 ($$\frac{{54}}{4}$$ = 2 remainder) = 9) now add all the unit digit 5 + 6 + 9 = 20 = 0
87.
The numerator of a fraction is multiple of two numbers. One of the numbers is greater than the other by 2. The greater number is smaller than the denominator by 4. If the denominator 7 + C (C > - 7) is a constant, then the minimum value of the fraction is:
(A) 5
(B) 1/5
(C) -5
(D) -1/5
Solution:
According to the given condition Denominator = 7 + C [C > -7] \[\begin{array}{*{20}{c}} {{\text{Denominator}} = }&{{\text{Greator number}}}&{}&{{\text{Smaller number}}} \\ {}&{\left( {7 + C - 4} \right)}& \times &{\left( {7 + C - 4 - 2} \right)} \end{array}\] Equation $$ = \frac{{\left( {3 + C} \right)\left( {1 + C} \right)}}{{7 + C}}$$ By putting value according to option C = -2 for minimum value = -1/5
88.
A number which divided by 192 gives a remainder of 54. What remainder would be obtained on dividing the same number by 16 ?