Multiple choice

[CAT 2000] The integers 34041 and 32506, when divided by a three-digit integer n, leave the same remainder. What is the value of n?

  1. 289

  2. 367

  3. 453

  4. 307
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D Correct answer
Explanation

If two numbers leave the same remainder when divided by n, their difference must be divisible by n. The difference is 34041 - 32506 = 1535. The factors of 1535 are 1, 5, 307, 1535. Since n is a three-digit integer, n = 307.

AI explanation

Since the numbers leave the same remainder, their difference must be perfectly divisible by the divisor. Calculate the difference as 34041 minus 32506, which equals 1535. We factorize 1535 into 5 multiplied by 307. Checking the options, only 307 is a factor of 1535, so the value of the three-digit integer is 307.

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