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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, 00:48

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.
_________________

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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30 Sep 2017, 10:35

Bunuel and other experts: Can't we solve absolute value questions by the simple strategy of plugging in numbers? That's how I solved this question. I understand that it takes slightly longer by plugging in numbers. But honestly, the properties of absolute values makes me go nuts. They are so confusing and it doesn't come to me naturally. Do you get absolute value questions a lot on the GMAT that I absolutely need to learn the properties or can I get away by solving these questions through the plug in numbers strategy?
_________________

"The fool didn't know it was impossible, so he did it."

Little confused here could you explain by picking numbers for statement 1 and 2.

Hi...

y=|x+3|+|4-x|

Without solving you can say for all values between -3 and 4, y will be 7 as any increase in x in one mod will be negated with decrease in other mod..

Let's see the statements 1) x<4... Take x as 0.. y=|0+3|+|4-0|=3+4=7 Take x as -5 y=|-5+3|+|4-(-5)|=|-2|+|9|=2+9=11 So different answers Insufficient 2) x>-3 Take x as -2 y=|-2+3|+|4-(-2)|=|1|+|4+2|=1+6=7 Take x as 7 y=|3+7|+|4-7|=10+3=13 Different answers Insufficient