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If x and y are integers and y = |x + 3| + |4 – x |, does y

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sanjib: Master | Next Rank: 500 Posts; Posts: 109; Joined: Sun May 10, 2009 7:53 am

If x and y are integers and y = |x + 3| + |4 – x |, does y

by sanjib » Sat Jul 11, 2009 11:31 am

If x and y are integers and y = |x + 3| + |4 – x |, does y equal 7?
(1) x < 4
(2) x > -3
OA is C
However if we consider the both statements together it sufficient but if we consider second statemet and it satisfy with x=(-3) also. Then it should be E.
Am I missing something?

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Source: Beat The GMAT — Data Sufficiency | Sat Jul 11, 2009 11:31 am

shibal: Master | Next Rank: 500 Posts; Posts: 345; Joined: Wed Mar 18, 2009 6:53 pm; Location: Sao Paulo-Brazil; Thanked: 12 times; GMAT Score:660

by shibal » Sat Jul 11, 2009 11:41 am

try x=50 in both cases.... i'll see only combining both of them we get the answer....

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GMATQuantCoach: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sun Jun 28, 2009 8:58 am; Location: Online; Thanked: 13 times; GMAT Score:51

by GMATQuantCoach » Sat Jul 11, 2009 1:57 pm

(1) if x < 4 then x - 4 < 0. Then |x - 4| = -(x - 4) = 4 - x
But you don't know if |x + 3| = x + 3 or |x + 3| = -(x + 3).
Insufficient.

(2) if x > -3, then x + 3 > 0. Therefore |x + 3| = x + 3.
But you don't know if |x - 4| = x - 4 or |x - 4| = 4 -x

When combined,
|x - 4| = 4 - x
|x + 3| = x + 3

y = 4 - x + x + 3 = 7
Sufficient

The answer is C.