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absolute value question prob??

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by willbeatthegmat » Wed Sep 24, 2008 7:02 am
Q1- If y= |x+7| + |2-x|, Is y=9?
1)x<2
2)x>-7
Ans: C

Q-2 Find k if the given system of equation has infinite no. of solutions.
4x+ky=2+10y
kx+24y=8

a)-10 b)16 c)-16 d)cannot b determined
Ans: b)16

Can someone help solvin these quest
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by anniev2 » Wed Sep 24, 2008 1:18 pm
Q1- If y= |x+7| + |2-x|, Is y=9?
1)x<2
2)x>-7
Ans: C

Statement 1 alone is not sufficient b/c x can be any number less than 2 and some of those values do not hold true to y equaling 9.

Statement 2 alone is not sufficient b/c x can be any number greater than -7 and some of those numbers do not hold true to y equaling 9.

However, when combining the statements x is contained to numbers between -6 and 1. Those numbers are -6, -5, -4, -3, -2, -1, 0, 1. When we plug in all of those numbers into the equation in the question stem...y is always equal to 9 so together the statements make it possible to determine the answer but alone the answer is not determinable or C.
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by andreasonlinegr » Thu Sep 25, 2008 3:55 am
Anniev2,

Statement 1 - for which values below 2, y is not equal to 9
Statement 2 - for which values greater than -7, y is not equal to 9

I've tried values outside this range and y always equals to 9.
thanks,
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by anniev2 » Thu Sep 25, 2008 5:56 pm
Andreas -

Great observation...being that its DS I didn't bother going that far. Do you agree with the explanation I set forth?
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by Ian Stewart » Thu Sep 25, 2008 7:28 pm
anniev2 wrote:Q1- If y= |x+7| + |2-x|, Is y=9?
1)x<2
2)x>-7
Ans: C
While you can certainly get the correct answer by picking numbers here, you can be certain of the answer without much work if you understand that absolute value measures distance. In particular |a-b| is just the distance between a and b on the number line. Rewriting the given equation to get minus signs:

|x-(-7)| + |2-x| = y

So y is just the distance between x and -7 plus the distance between x and 2. If you draw the number line, draw the points 2 and -7, and place x somewhere between them, it's easy to see that y will be 9 (because the distance from x to 2 plus the distance from x to -7 will then just be the distance from 2 to -7). And if x is to the left of -7 or to the right of 2, you can see that y will certainly be greater than 9. Much easier to see if you draw the number line of course.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by welett » Fri Sep 26, 2008 2:41 pm
4x+ky=2+10y
kx+24y=8

since there are infinite solutions, we need to have exact same equations in each row

4x+(k-10)y=2 (to make right hand side equal to 8 we multiply both sides with 4)
kx+24y=8

16x+(4k-40)y=8
kx+24y=8

from multipliers of y:
4k-40=24
k=16

from multipliers of x:
k=16

both match each other.
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by dally_gmat » Sat Sep 27, 2008 7:13 am
Thanks Ian..Useful insight.
Ian Stewart wrote:
anniev2 wrote:Q1- If y= |x+7| + |2-x|, Is y=9?
1)x<2
2)x>-7
Ans: C
While you can certainly get the correct answer by picking numbers here, you can be certain of the answer without much work if you understand that absolute value measures distance. In particular |a-b| is just the distance between a and b on the number line. Rewriting the given equation to get minus signs:

|x-(-7)| + |2-x| = y

So y is just the distance between x and -7 plus the distance between x and 2. If you draw the number line, draw the points 2 and -7, and place x somewhere between them, it's easy to see that y will be 9 (because the distance from x to 2 plus the distance from x to -7 will then just be the distance from 2 to -7). And if x is to the left of -7 or to the right of 2, you can see that y will certainly be greater than 9. Much easier to see if you draw the number line of course.
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by willbeatthegmat » Sun Sep 28, 2008 10:51 am
thanks Ian..the explanation is just perfect...n thank u all for ur response
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by ravikirancheni » Fri Oct 24, 2008 8:09 am
As per the Given question

X --> 9 only when (x+7) and (2-x) , both being positive.

1. x<2 implies (2-x)>0 i.e it is positive
2. x>-7 implies (x+7)>0 i.e it is positive...

Both requirements necessary for X to be 9 ...is provided when 1,2 both taken into consideration.

So ans is C
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Thanks

by saabidi » Wed Oct 29, 2008 4:08 pm
Thanks Ian. Explaination was just perfect. Do you have any post/suggestion/tip for work related problems.
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by maihuna » Tue Apr 14, 2009 8:08 am
Ian,
I will prefer the number line algebra here:

-------|---------------|----------
-7 2

I will pick a number in the three region and find my eqn:

for less than -7: y = -(x+7) + 2 -x = -2x - 5
-7<x<2 : x + 7 + 2 -x = 9
2<x : x + 7 - 2 + x = 2x + 5

SO if we see the two option we need both to have the region -7 to 2 and so C:
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