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21 Apr 2021, 05:45
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A
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Difficulty:
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Question Stats:
92% (00:59) correct
8%
(02:12)
wrong
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A positive integer when divided by 296 gives a remainder 75. What will be the remainder when the same number is divided by 37?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 7
(A) 1
(B) 3
(C) 5
(D) 6
(E) 7
21 Apr 2021, 06:02
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Bunuel
Let the number be n and quotient be q.
n=296q+75=8*37q+75=8*37q+2*37+1=37(8q+2)+1
When you divide n, that is 37(8q+2)+1, by 37, the remainder will be 1.
A
16 May 2021, 07:41
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Bunuel
Solution:
The positive integer could be 296 + 75 = 371 (notice that 371/296 = 1 R 75). Therefore, the remainder when 371 is divided by 37 is 1 (notice that 371/37 = 10 R 1).
Alternate Solution:
Let n be the number. We are told that the remainder when n is divided by 296 is 75, thus:
n = 296k + 75
where k is some positive integer. Notice that 296 = 37 * 8. Let’s rewrite the equality as follows:
n = 296k + 75 = 37 * 8 * k + 74 + 1 = 37(8k) + 37(2) + 1 = 37(8k + 1) + 1
Thus, when n is divided by 37, the remainder is 1 (and the quotient is 8k + 1).
Answer: A
