a number when divided by 296 gives a remainder 75 when the same number | Examsbook

867

Q:
A number when divided by 296 gives a remainder 75. When the same number is divided by 37 the remainder will be:

1
8
2
1
3
2
4
11

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Answer : 2. "1 "
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].

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