The Official Guide For GMAT® Quantitative Review, 2ND Edition

If J, S, and V are points on the number line, what is the distance between S and V?

(1) The distance between J and S is 20.
(2) The distance between J and V is 25.




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If J, 5, and V are points on the number line, what is the distance between 5 and V?

(1) The distance between J and 5 is 20.
(2) The distance between J and V is 25.


Sol:

We need to find the distance between 5 and V ie. l 5-V l

From St 1 we have the distance between J and 5. We can J anywhere to the left or right of 5 and the distance between them can be 20. So Possible values of J will be 25 or -15 . Not Sufficient

From St 2 we have the distance b/w J and V is 25. Not sufficient as we do not know the position relative to 5 on the number line

Combining we get there are the 2 values of J ie. -15 or 25 and thus value of V can be -40 or 10 (25 to the left or right of -15(J value)) or 50 or 0 (25 to the left or right of 25 (J value))

Hence 5- V can have multiple values.

Ans E
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This is a good question to understand the concept of absolute value.
Prompt: |S-V| = ?

1) |J-S| = 20
Picking some numbers... Say J is 0, so S is either -20 or 20. No info about V, NS

2) |J-V| = 25
Say J is 0 again, so V is either -25 or 25. No info about S, NS

3) Combining we could say:
|S-V| = |±20 - ±25|

20±25 = -5 or 45 and -20±25 = 5 or -45

Since we're looking for |S-V|, or the distance between the two points, it has two possible values, 5 and 45. So Both are still NS.