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]

29 Jan 2010, 11:55

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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

What is the fastest way to solve this?

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Re: Powerprep Inequality question [#permalink]

29 Jan 2010, 12:24

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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.

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Manager

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Re: Powerprep Inequality question [#permalink]

30 Jan 2010, 13:55

Thanks for the post

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Re: Powerprep Inequality question [#permalink]

31 Jan 2010, 12:33

Thanks, I solved this just by plugging in different numbers from the ranges provided.

Re: Powerprep Inequality question [#permalink] 31 Jan 2010, 12:33

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

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

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

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