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

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07 May 2013, 23:13
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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08 May 2013, 01:48
Expert's post
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]

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08 May 2013, 13:22
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.
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Re: If x and y are integers and y=|x+3| + |4-x|, does y equals 7 [#permalink]

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23 Sep 2014, 19:28
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Re: If x and y are integers and y=|x+3| + |4-x|, does y equals 7 [#permalink]

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06 Jan 2015, 08:02
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

I dont think this should be solved, as in dont waste time on it trying to solve it.
We need the signs of both modulus expressions to know the answer to the question

Both statements together do that for us
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Re: If x and y are integers and y=|x+3| + |4-x|, does y equals 7 [#permalink]

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25 Jan 2016, 03:14
Hello from the GMAT Club BumpBot!

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Re: If x and y are integers and y=|x+3| + |4-x|, does y equals 7 [#permalink]

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08 Jun 2016, 05:29
Bunuel wrote:
thirst4edu wrote:
If x & 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

$$y=|x+3|+|4-x|$$ two check points: $$x=-3$$ and $$x=4$$ (check point: the value of $$x$$ when expression in || equals to zero), hence three ranges to consider:

A. $$x<{-3}$$ --> $$y=| x + 3| +|4-x| =-x-3+4-x=-2x+1$$, which means that when $$x$$ is in the range {-infinity,-3} the value of $$y$$ is defined by $$x$$ (we would have multiple choices of $$y$$ depending on $$x$$ from the given range);

B. $$-3\leq{x}\leq{4}$$ --> $$y=|x+3|+|4-x|=x+3+4-x=7$$, which means that when $$x$$ is in the range {-3,4} the value of $$y$$ is $$7$$ (value of y does not depend on value of $$x$$, when $$x$$ is from the given range);

C. $$x>{4}$$ --> $$y=|x+3|+|4-x|=x+3-4+x=2x-1$$, which means that when $$x$$ is in the range {4, +infinity} the value of $$y$$ is defined by $$x$$ (we would have multiple choices of $$y$$ depending on $$x$$ from the given range).

Hence we can definitely conclude that $$y=7$$ if $$x$$ is in the range {-3,4}

(1) $$x<4$$ --> not sufficient ($$x<4$$ but we don't know if it's $$\geq{-3}$$);
(2) $$x>-3$$ --> not sufficient ($$x>-3$$ but we don't know if it's $$\leq{4}$$);

(1)+(2) $$-3<x<4$$ exactly the range we needed, so $$y=7$$. Sufficient.

OR: looking at $$y=|x+3|+|4-x|$$ you can notice that $$y=7$$ ($$y$$ doesn't depend on the value of $$x$$) when $$x+3$$ and $$4-x$$ are both positive, in this case $$x-es$$ cancel out each other and we would have $$y=|x+3|+|4-x|=x+3+4-x=7$$. Both $$x+3$$ and $$4-x$$ are positive in the range $$-3<{x}<4$$ ($$x+3>0$$ --> $$x>-3$$ and $$4-x>0$$ --> $$x<4$$).

Hope it's clear.

Sorry I have a question. I understand that because of two check points, there are three possible ranges. But how |x+3| + |4-x| have different results in each scenario?

Thank you
Re: If x and y are integers and y=|x+3| + |4-x|, does y equals 7   [#permalink] 08 Jun 2016, 05:29

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