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

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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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88% (02:03) correct 13% (01:18) wrong based on 8 sessions
if x and y are integers and y=|x+3| +|4-x|, does y equal 7?

1) x <4
2) x>-3


What is the fastest way to solve this?
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Re: Powerprep Inequality question [#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: Powerprep Inequality question [#permalink] New post 30 Jan 2010, 12:55
Thanks for the post
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Re: Powerprep Inequality question [#permalink] New post 31 Jan 2010, 11:33
Thanks, I solved this just by plugging in different numbers from the ranges provided.
Re: Powerprep Inequality question   [#permalink] 31 Jan 2010, 11:33
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14 Experts publish their posts in the topic If x and y are integers and y=|x+3| + |4-x|, does y equals 7 thirst4edu 23 26 Sep 2010, 20:26
1 If x and y are integers and y = |x+3|+|4-x| , does y equal 7 mavesum 3 11 Mar 2009, 06:53
If x and y are integers and y=|x+3|+|4-x| , does y=7? (1) lumone 8 07 Aug 2008, 09:38
5 Experts publish their posts in the topic If x and y are integers and y=|x+3|+|4-x| does y=7? Sumithra 15 13 Jan 2007, 11:41
If x and y are integers and y=l x+3 l + l 4-x l, does y=7? pesquadero 5 06 May 2006, 08:27
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if x and y are integers and y=|x+3| +|4-x|, does y equal 7?

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