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

SOLUTION

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

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

The answer to this question is E. Notice that we don't know relative positioning of the points on the number line:Answer: E.
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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.

Solution:

Question Stem Analysis:

We need to determine the distance between S and V, given that they are points on the number line along with J.

Statement One Alone:

Since we don’t know anything about point V, statement one alone is not sufficient.

Statement Two Alone:

Since we don’t know anything about point S, statement two alone is not sufficient.

Statements One and Two Together:

Both statements together are still not sufficient. For example, if J is between S and V, then the distance between S and V is 20 + 25 = 45. However, if J is to the right (or to the left) of both S and V, then the distance between S and V is 25 - 20 = 5.

Answer: E

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