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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. _________________

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]

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23 Sep 2014, 19:28

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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

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!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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