Data Sufficiency

What is the value of |x + 5| + |x - 3|?

1. x^2 < 25

2. x^2 > 9

[spoiler]OA: E[/spoiler]

[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

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.