Number System Questions and Answers with Solution
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Number System Questions
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Number System Questions and Answers with Solution
Q : Which of the following fraction is the smallest? $$7\over 6 $$,$$7\over 9$$,$$4\over 5$$,$$5\over 7$$
(A) $$7\over 6 $$
(B) $$7\over 9$$
(C) $$4\over 5$$
(D) $$5\over 7$$
Correct Answer : D
Explanation :
The cube of 997 is
(A) 991026973
(B) 991029673
(C) 991029773
(D) 991027273
Correct Answer : A
Explanation :
A number when divided by 899 gives a remainder 63. If the same number is divided by 29, the remainder will be
(A) 10
(B) 5
(C) 4
(D) 2
Correct Answer : B
Explanation :
Solution: $${Remainder\over 29}={7\over 9}$$
=> remainder (शेषफल)=5
96-11 when divided by 8 would leave a remainder of :
(A) 6
(B) 16
(C) 1
(D) 2
Correct Answer : A
Explanation :
(49)15 – 1 is exactly divisible by:
(A) 29
(B) 8
(C) 50
(D) 51
Correct Answer : B
Explanation :
if 5432*7 is divisible by 9, then the digit in place of * is :
(A) 0
(B) 1
(C) 6
(D) 9
Correct Answer : C
Explanation :
Two positive numbers differ by 1280. When the greater number is divided by the smaller number, the quotient is 7 and the remainder is 50. The greater number is:
(A) 1558
(B) 1458
(C) 1585
(D) 1485
Correct Answer : D
Explanation :
Given :- Two positive numbers differ by 1280
When the greater number is divided by the smaller number The quotient is 7 and the remainder is 50
Concept :- Dividend = Quotient × divisor + remainder
Calculation :- Let greater number = a and Smaller number = b From question, ⇒ a - b = 1280 ....(1) Again from question, ⇒ a = 7b + 50 ....(2)
Put the value of a from equation (2) into equation (1) ⇒ 7b + 50 - b = 1280 ⇒ 6b = 1280 - 50 ⇒ 6b = 1230 ⇒ b = (1230/6) ⇒ b = 205
Put the value of b in equation (1) ⇒ a - 205 = 1280 ⇒ a = 1280 + 205 ⇒ a = 1485 ⇒ Greater number = 1485 ∴ Greater number is 1485
When 1062, 1134 and 1182 are divided by the greatest number .x, the remainder in each case is y. What is the value of (x − y)?
(A) 17
(B) 18
(C) 16
(D) 19
Correct Answer : B
Explanation :
The value of (x-y) will be 18
A number when divided by 296 gives a remainder 75. When the same number is divided by 37 the remainder will be:
(A) 8
(B) 1
(C) 2
(D) 11
Correct Answer : B
Explanation :
Let number (dividend) be X.
∴ X = 296 × Q + 75 where Q is the quotient and can have the values 1, 2, 3 etc.
= 37 × 8 × Q + 37 × 2 + 1
= 37 (8Q + 2) + 1
Thus we see that the remainder is 1.
[Remark : When the second divisor is a factor of the first divisor, the second remainder is obtained by dividing the first remainder by the second divisor.
Hence, divide 75 by 37, the remainder is 1].
A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively. When it is successively divided by 5 and 4 the respective remainders will be
(A) 2, 3
(B) 1, 2
(C) 4, 1
(D) 3, 2
Correct Answer : A
Explanation :
The least number X in this case will be determined as follows:
Y = 5 × 1 + 4 = 9
X = 4 × Y + 1 = 4 × 9 + 1 = 37 Now,
Hence, the respective remainders are 2, 3.
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