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

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Re: Algebra->Inequalities (Absolute Value) [#permalink] New post 07 May 2013, 22:13
The answer is C as per above justification by manishuol.

I just wan to add, that care has to be taken not to break down the expression. For example, lx+3l is not equal to lxl + 3.
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Re: Algebra->Inequalities (Absolute Value) [#permalink] New post 08 May 2013, 00:48
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mario1987 wrote:
Hi guys,
I would like to deeply understand how to deal with absolute value questions like the one attached.
Thank you very much


For the given question, note that you can get y=7 when both the values inside the mod, i.e. (x+3) & (4-x)>0 .It is so, because the variable(x) will get cancelled and you will get a constant value for y = 7, irrespective of the value of x.
Thus, x>-3 AND x<4.
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Re: If x and y are integers and y=|x+3| + |4-x|, does y equals 7 [#permalink] New post 08 May 2013, 12:22
thirst4edu wrote:
If x and y are integers and y=|x+3| + |4-x|, does y equals 7?

(1) x < 4
(2) x > -3

Had a hard time solving this, would like to know how to solve this using number picking approach as well as algebraic approach. Thanks.

OA is
[Reveal] Spoiler:
C


At first i tried to apply the approach given in the gmatclub math guide regarding dealing with absolute value questions. But than i remembered that approach is for finding the solutions of an equation.
After further thought i looked at the question and than at
1) x < 4. Their can be infinite values of x less than 4. Some of which gives y= 4(3,2..etc) and some don't x = -10. INSUFFICIENT.
2)x > -3. Same as above. Some values give y=7(-2,-1..etc). Some don't x= 10. INSUFFICIENT.

Combining 1 and 2, we can see that all values -2,-1,0,1,2,3 given y=7. Hence SUFFICIENT.
Re: If x and y are integers and y=|x+3| + |4-x|, does y equals 7   [#permalink] 08 May 2013, 12:22
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1 Experts publish their posts in the topic if x and y are integers and y=|x+3| +|4-x|, does y equal 7? zaarathelab 3 29 Jan 2010, 10:55
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If x and y are integers and y=|x+3|+|4-x| , does y=7? (1) lumone 8 07 Aug 2008, 09:38
4 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
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