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Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE PS
Solution:
We are given that x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200. We need to determine which answer choice MUST be a multiple of x.
Because y is a multiple of 5, we can represent y as 5k, in which k is an integer, and we have:
3x + 4(5k) = 200
3x + 20k = 200
Since the sum of 3x and 20k is 200 (or a number that has a units digit of zero), and since 20k has a units digit of zero, 3x must also contain a units digit of zero. The only way for 3x to contain a units digit of zero is if it’s multiplied by a multiple of 10. Thus, x must be a multiple of 10.
Answer: E
