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If x and y are integers and y = |x + 3| + |4 - x|, does y equal 7?

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Manager
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If x and y are integers and y = |x + 3| + |4 - x|, does y equal 7? [#permalink] New post 29 Jan 2010, 10:55
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If x and y are integers and y = |x + 3| + |4 - x|, does y equal 7?

(1) x < 4
(2) x > -3
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Jul 2015, 13:57, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: If x and y are integers and y = |x + 3| + |4 - x|, does y equal 7? [#permalink] New post 29 Jan 2010, 11:24
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if x and y are integers and y=|x+3| +|4-x|, does y equal 7

If we carefully look at the question we can see that "does y equal 7" actually means that y doesn't depend on x and then you can see that if we open two moduli with same signs (++ or --), x and -x disappear and 3+4 is 7. So, let's see when we can open moduli ++ or --:

++) x>-3 and x<4 or x e (-3,4)
--) x<-3 and x>4 - it can't be.

So, if x between -3 and 4, y =7. Now, look at our statements: it is obvious that we need two statements.

C.
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Re: If x and y are integers and y = |x + 3| + |4 - x|, does y equal 7? [#permalink] New post 30 Jan 2010, 12:55
Thanks for the post
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Re: If x and y are integers and y = |x + 3| + |4 - x|, does y equal 7? [#permalink] New post 31 Jan 2010, 11:33
Thanks, I solved this just by plugging in different numbers from the ranges provided.
Re: If x and y are integers and y = |x + 3| + |4 - x|, does y equal 7?   [#permalink] 31 Jan 2010, 11:33
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If x and y are integers and y = |x + 3| + |4 - x|, does y equal 7?

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