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

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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: — Data Sufficiency |
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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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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.
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by abhinav85 » Thu Jul 16, 2009 5:56 am
Nice Explanation Gmat coach

IMO C.
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