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# If y = /x + 7/ + /2 - x/, is y = 9? (1)x < 2 (2) x >

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If y = /x + 7/ + /2 - x/, is y = 9? (1)x < 2 (2) x > [#permalink]  06 Aug 2007, 21:50
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If y = /x + 7/ + /2 - x/, is y = 9?
(1)x < 2
(2) x > -7
Senior Manager
Joined: 24 Nov 2006
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Re: DS absolute value [#permalink]  06 Aug 2007, 22:01
Balvinder wrote:
If y = /x + 7/ + /2 - x/, is y = 9?
(1)x < 2
(2) x > -7

y = |x+7| + |x-2|. This function has a graphic that is flat between its critical points (x=-7, x=2). We can notice that, putting together (1) n (2) yields -7<x<2, just the range described above. Therefore, C.
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y will always be 9 unless x is 2 or -7. if you plug in other values you always get 9. so you need both - because if x is ever 2 of 7 it won't be 9.
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St1:
If x = -3, then y = 9
If x = -10, then y = 15.
Insufficient.

St2:
If x = -6, then y = 9
If x = 10, then y = 25.
Insufficient.

Using St1 and St2:
-7 < x < 2. All values of x in this range will result in y = 9. Sufficient.

Ans C
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