What is the distance between \(x\) and \(y\) on the number line?

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What is the distance between \(x\) and \(y\) on the number line?

(1) \(|x| - |y| = 5\)
(2) \(|x| + |y| = 11\)

Answer: E

Source: Manhattan GMAT

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Vincen wrote:
Wed Nov 10, 2021 2:22 am
What is the distance between \(x\) and \(y\) on the number line?

(1) \(|x| - |y| = 5\)
(2) \(|x| + |y| = 11\)

Answer: E

Source: Manhattan GMAT
Target question: What is the distance between x and y on the number line?

When I scan the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the target question. So, I’m going to head straight to……

Statements 1 and 2 combined
Statement 1 tells us that |x| – |y| = 5
Statement 2 tells us that |x| + |y| = 11
If we ADD the two given equations, we get: 2|x| = 16, which means |x| = 8
Similarly, if we SUBTRACT but the bottom equation from the top equation we get: -2|y| = -6, which means |y| = 3

At this point, we can see that there are several possible pairs of values for x & y
Consider these two conflicting cases:
Case a: x = 8 and y = 3. In this case, the answer to the target question is the distance between x and y is 5
Case b: x = 8 and y = -3. In this case, the answer to the target question is the distance between x and y is 11
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E
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