## What is the value of |x + 5| + |x - 3|? Exam pack 2

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### What is the value of |x + 5| + |x - 3|? Exam pack 2

by prata » Sat Aug 27, 2016 9:31 pm
What is the value of |x + 5| + |x - 3|?

1. x^2 < 25

2. x^2 > 9

[spoiler]OA: E[/spoiler]

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by [email protected] » Sun Aug 28, 2016 9:27 am
Hi prata,

This question can be solved by TESTing VALUES.

We're asked for the value of |X + 5| + |X - 3|.

1) X^2 < 25

IF...
X = 4
then the answer to the question is |9| + |1| = 10

IF...
X = 3
then the answer to the question is |8| + |0| = 8
Fact 1 is INSUFFICIENT

2) X^2 > 9

IF...
X = 4
then the answer to the question is |9| + |1| = 10

IF...
X = 5
then the answer to the question is |10| + |2| = 12
Fact 2 is INSUFFICIENT

Combined, we know that....
X^2 < 25
X^2 > 9

At first glance, you might think that X=4 is the only possibility. HOWEVER, we were never told that X had to be an integer (so it could be 3.5 or 4.9999, for example). TESTing any of those possibilities will prove that the answer to the question changes...

IF...
X = 4
then the answer to the question is |9| + |1| = 10

IF...
X = 3.5
then the answer to the question is |8.5| + |.5| = 9
Combined, INSUFFICIENT

Final Answer: E

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by Mo2men » Mon Aug 29, 2016 7:22 am
[email protected] wrote:Hi prata,

This question can be solved by TESTing VALUES.

We're asked for the value of |X + 5| + |X - 3|.

1) X^2 < 25

IF...
X = 4
then the answer to the question is |9| + |1| = 10

IF...
X = 3
then the answer to the question is |8| + |0| = 8
Fact 1 is INSUFFICIENT

2) X^2 > 9

IF...
X = 4
then the answer to the question is |9| + |1| = 10

IF...
X = 5
then the answer to the question is |10| + |2| = 12
Fact 2 is INSUFFICIENT

Combined, we know that....
X^2 < 25
X^2 > 9

GMAT assassins aren't born, they're made,
Rich
Hi Rich,

I believe I can use x=4 and x=-4

fact 1)
x=4.........|9| + |1| = 10
x=-4........|1| + |-7| = 8 Insuff

fact 2) I can use same examples above .....Insuff

combining 1 &2 with same examples above in so Insuff

Answer E

Is my examples correct? can I use x=-4???

Thanks

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by GMATGuruNY » Mon Aug 29, 2016 8:55 am
prata wrote:What is the value of |x + 5| + |x - 3|?

1. x^2 < 25

2. x^2 > 9
What is the value of |x + 5| + |x - 3|?
The critical points are the values that make the absolute values equal to 0.
Here, the critical points are -5 and 3.

The distance between the critical points is the LEAST POSSIBLE VALUE for the expression in blue.
The distance between -5 and 3 is 8.
Thus, the least possible value for the expression in blue is 8.

If x is between the critical points of -5 and 3, inclusive, then the expression in blue will be equal to the LEAST POSSIBLE VALUE (8):
If x=0, then |x + 5| + |x - 3| = |0+5| + |0-3| = 8.
If x=-2, then |x + 5| + |x - 3| = |-2+5| + |-2-3| = 8.
If x=3, then |x + 5| + |x - 3| = |3+5| + |3-3| = 8.

If x is NOT between the critical points of -5 and 3, inclusive, then the expression in blue will be equal to a VALUE GREATER THAN 8:
If x=4, then |x + 5| + |x - 3| = |4+5| + |4-3| = 10.
If x=10, then |x + 5| + |x - 3| = |10+5| + |10-3| = 22.
If x=-7, then |x + 5| + |x - 3| = |-7+5| + |-7-3| = 12.

Both statements are satisfied by x=-4.
In this case, x is between -5 and 3, inclusive, so the expression in blue will be equal to the least possible value (8).
Both statements are satisfied by x=4.
In this case, x is NOT between -5 and 3, inclusive, so expression in blue will equal to a value greater than 8.
Since the expression in blue can be different values, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by [email protected] » Mon Aug 29, 2016 9:15 am
Hi Mo2men,

Yes - very good!; you can absolutely use negative values when TESTing VALUES in this prompt. One of my default 'rules' for dealing with DS questions is that if there's an inconsistent result to be found (in this case, the answer to the 'value' question changes), then I have to find it (and that might involve TESTing negatives, 0, fractions, etc.).

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