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

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

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## Your Answer

**A**

**B**

**C**

**D**

**E**

## Global Stats

**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