Number System Questions and Answers with Solution
A number when divided by 6 leaves remainder 3. When the square of the same number is divided by 6, the remainder is :
(A) 0
(B) 1
(C) 2
(D) 3
Correct Answer : D
Explanation :
The remainder will be same.
On dividing 9 by 6, remainder = 3
On dividing 81 by 6, remainder = 3
When a number is divided by 893, the remainder is 193. What will be the remainder when it is divided by 47?
(A) 3
(B) 5
(C) 25
(D) 33
Correct Answer : B
Explanation :
Here, 893 is exactly divisible by 47.
Hence, the required remainder is obtained on dividing 193 by 47.
∴ Remainder = 5
A number divided by 13 leaves a remainder 1 and if the quotient, thus obtained, is divided by 5, we get a remainder of 3. What will be the remainder if the number is divided by 65?
(A) 28
(B) 16
(C) 18
(D) 40
Correct Answer : D
Explanation :
Let the least number be x
y = 5 × 1 + 3 = 8
x = 13 × 8 + 1 = 105
On dividing 105 by 65, remainder = 40
Which of the following number is NOT divisible by 18?
(A) 54036
(B) 50436
(C) 34056
(D) 65043
Correct Answer : D
Explanation :
A number will be exactly divisible by 18 if it is divisible by 2 and 9 both.
Clearly 65043 is not divisible by 2.
∴ Required number = 65043
64329 is divided by a certain number, 175, 114 and 213 appear as three successive remainders. The devisor is
(A) 184
(B) 224
(C) 234
(D) 296
Correct Answer : C
Explanation :
Number at (i) = 643 – 175 = 468
Number at (ii) = 1752 – 114 = 1638
Number at (iii) = 1149 – 213 = 936
Clearly, 468, 1638 and 936 are multiples of 234 and 234 > 213.
Divisor = 234
In a question on division, the divisor is 7 times the quotient and 3 times the remainder. If the remainder is 28, then the dividend is
(A) 588
(B) 784
(C) 823
(D) 1036
Correct Answer : D
Explanation :
Let the quotient be Q and the remainder be R. Then
Divisor = 7 Q = 3 R
∴ Divisor = 7 Q = 7 × 12 = 84
Dividend = Divisor × Quotient + Remainder = 84 × 12 + 28 = 1008 + 28 = 1036
If two numbers are each divided by the same divisor, the remainders are respectively 3 and 4. If the sum of the two numbers be divided by the same divisor, the remainder is 2. The divisor is
(A) 9
(B) 7
(C) 5
(D) 3
Correct Answer : C
Explanation :
Required divisor = 3 + 4 – 2 = 5
A number consists of two digits. If the number formed by interchanging the digits is added to the original number, the resulting number (i.e. the sum) must be divisible by
(A) 11
(B) 9
(C) 5
(D) 3
Correct Answer : A
Explanation :
Let the number be 10x + y
After interchanging the digits,
the number obtained = 10y + x
According to the question,
Resulting number
= 10x + y + 10y + x
= 11x + 11y
= 11 (x + y)
which is exactly divisible by 11.
A number when divided by 5 leaves a remainder 3. What is the remainder when the square of the same number is divided by 5 ?
(A) 1
(B) 2
(C) 3
(D) 4
Correct Answer : D
A number when divided by 192 gives a remainder of 54. What remainder would be obtained on dividing the same number by 16 ?
(A) 2
(B) 4
(C) 6
(D) 8
Correct Answer : C
Explanation :
Here, the first divisor 192 is a multiple of second divisor 16.
∴ Required remainder
= remainder obtained by dividing 54 by 16 = 6
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Vikram Singh
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