For how many integer values of x, is |x - 8| + |5 - x| > |x + 7|?
(A) 1
(B) 3
(C) 5
(D) 7
(E) Infinite
OA=E
(A) 1
(B) 3
(C) 5
(D) 7
(E) Infinite
OA=E
It can be dealt swiftly with non-algebraic way.ziyuenlau wrote:For how many integer values of x, is |x - 8| + |5 - x| > |x + 7|?
(A) 1
(B) 3
(C) 5
(D) 7
(E) Infinite
OA=E
We have |x - 8| + |5 - x| > |x + 7|.
One of the possibilities is: (x-8) + (5-x) > (x+7)
=> -3 > x+7
=> -10 > x
We see that at least any integer less than -10 is qualified for the value of x, thus x can take infinitely as many integer values. There is no need to test for the more values.
You may test a large random value for x in case there is any restriction with x.
Say = -100. At x = -100, |x - 8| + |5 - x| > |x + 7|.
The correct answer: E
Hope this helps!
Relevant book: Manhattan Review GMAT Number Properties Guide
-Jay
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