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What is the difference between x and y?

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What is the difference between x and y?

by Max@Math Revolution » Thu Nov 21, 2019 12:33 am
[GMAT math practice question]

What is the difference between x and y?

1) |x - y| is the first odd prime number
2) x and y are positive integers such that 3x + 5y = 23
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun Nov 24, 2019 5:54 pm
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.
The question asks the value of |x - y|.

Condition 1)
Since the first odd prime number is 3, we have |x - y| = 3.
Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
3x = 23 - 5y
If y = 1, then we have 3x = 23 - 5 = 18 or x = 6 and |x - y| = 5.
If y = 2, then we have 3x = 23 - 10 = 13 and we don't have an integer solution.
If y = 3, then we have 3x = 23 - 15 = 8 and we don't have an integer solution.
If y = 4, then we have 3x = 23 - 20 = 3 or x = 1 and |x - y| = 3
If y = 5, then we have 3x = 23 - 25 = -2 and we start to have negative numbers and we can stop this substitution process.

Since condition 2) does not yield a unique solution, it is not sufficient.

Therefore, A is the answer.
Answer: A
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