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by MartyMurray » Mon Dec 07, 2015 3:30 am
rajan_agarwal wrote:Q. A number when divided by a divisor, the remainder is 25. When 3 times the number is divided by the same divisor, the remainder is 4. Find the divisor.
If the remainder of x/y is 25, then x = ky + 25. So 3x = 3ky + 75.

We know that 3ky is divisible by y, so the remainder of 75/y = 4. So 71 is a multiple of y.

71 is prime. So y = 71.

Rajan, including the answer choices would be helpful.
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by Brent@GMATPrepNow » Mon Dec 07, 2015 8:58 am
rajan_agarwal wrote:Q. A number when divided by a divisor, the remainder is 25. When 3 times the number is divided by the same divisor, the remainder is 4. Find the divisor.
Another approach:

A number when divided by a divisor, the remainder is 25
So, it's possible that the number is 25 and the divisor is GREATER THAN 25
For example, 25 divided by 26 = 0 with remainder 25
Likewise, 25 divided by 58 = 0 with remainder 25
And so on.

When 3 times the number is divided by the same divisor, the remainder is 4
3 times 25 is 75
So, when 75 is divided by the same divisor, the remainder is 4
What is the divisor?
The divisor is 71
That is, 75 divided by 71 = 1 with remainder 4
Also, 25 divided by 71 = 0 with remainder 25

Perfect!

Answer: 71

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