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OG Question 105

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OG Question 105

by mdavis » Tue Jan 20, 2009 11:39 am
Hello everyone, I am having trouble understanding question 105 of the yellow OG. Here it is:

Is |x|=y-z?

(1) x+y=z
(2) x<0

So the explanation says to treat |x| as two possible solutions, |x|=x or |x|=-x. Thus, in combination with 2, you can rule out the |x|=x as a possible solution.

My question is more in line with why does the explanation break it down to x or -x? Wouldn't |x| of x always be positive? I thought there were no negative numbers when it comes to the absolute value?

Or when it asks the question does |x|=y-z, is it saying that the y-z part would be inbetween the absolute brackets?

Could someone help clarify this explanation for me? Thanks!
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Source: — Data Sufficiency |
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by DominicanKing » Thu Jan 22, 2009 8:04 pm
hi
|x|=x or |x|=-x

the above is simply stating that x could be positive in the first case, or x could have a negative value in the second case where the absolute value would be equal to minus x since x is negative

now the questions asks
Is |x|=y-z?

Remember this is a Yes or No question
Firstly statement two by itself (x<0) is Insufficient...
looking at the first statement
(1) x+y=z
this can be rewritten as
-x= y-z
if x is positive, the y-z has a negative value and the answer is NO since an absolute value cant equal a negative number, on the other hand if x is negative in equation (1) then -x = |x| = y-z since all these values are positive with the same numberical value and the asnwer is YES...since answer could be yes or no, then (1) insufficient

equation 2 tells us that x is negative or x<0 so the two statements together are sufficient
JIB
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Answer is C

by peddisetty » Fri Jan 23, 2009 1:02 pm
2. States that x<0. and 1. states that x+y = z.
x = z-y => -x = y-z.

So its suff.

take these nos. -2, 4, 2 or 2,2,4 and try. |x| = y-z.

Raj Peddisetty.
Raj Peddisetty
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Answer is C

by peddisetty » Fri Jan 23, 2009 1:03 pm
2. States that x<0. and 1. states that x+y = z.
x = z-y => -x = y-z.

So its suff.

take these nos. -2, 4, 2 or 2,2,4 and try. |x| = y-z.

Raj Peddisetty.
Raj Peddisetty
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