OG11 - DS 105

Question

is |x| = y - z?
(1) X + Y = Z
(2) X < 0

OA is C, while I thought it was B...

Here's my thought process:

whenever I see an absolute value sign, I think of the negative and the positive possibilities.

if x = positive, then X = y - z
if x = negative, then -X = -(y-z) -> Z + Y

so the question for me was - what's X?

I feel like I'm missing a link in tackling this problem - when I read the explanation in the OG11 book, I don't get why they look to see whether x is negative or positive, given Statement 1 X + Y = Z.

Anurag@Gurome · Answer

gnod wrote:is |x| = y - z?
(1) X + Y = Z
(2) X < 0

OA is C, while I thought it was B...

Here's my thought process:

whenever I see an absolute value sign, I think of the negative and the positive possibilities.

if x = positive, then X = y - z
if x = negative, then -X = -(y-z) -> Z + Y

so the question for me was - what's X?

I feel like I'm missing a link in tackling this problem - when I read the explanation in the OG11 book, I don't get why they look to see whether x is negative or positive, given Statement 1 X + Y = Z.

Solution:
Let us first consider (1) alone.
Or x = z – y.
Now lxl = x if x >= 0 and lxl = -x if x < 0.
So lxl = x = z – y if x >= 0 or if z >= y and lxl = -x = y – z if x < 0 or if z < y.
Since (1) does not tell us whether x is positive or negative, it is not sufficient to answer the question.
Next, consider (2) alone.
It tells us nothing about y or z.
So, (2) alone is not sufficient.
Lastly, combine both the statements together and check.
On combining, we have that lxl = -x = y-z since x < 0.
So, both statements together are sufficient.
The correct answer is (C).

Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
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gnod · Answer

man, i think i just got it.
something wasn't clicking right -

so the question is: is the absolute value of X = y - z? yes/no.

s1) X + Y = Z -> rewrite to get X, to see if X = Y - Z.
X = Z - Y when X is positive
X = Y - Z when X is negative (right?)

since it can be both - insufficient.

s2) X < 0
X may be negative, but doesn't tell us about whether X = Y - Z - insufficient.

S1 + S2 = X < 0 and X = Y - Z when X is negative.

just to confirm... we checked Statement 1 for positive and negative because we were asked if the absolute value of X equaled to something.. correct?

that's why - absolute value of X if positive = Z - Y
and absolute value of X is negative = Y - Z...

ahh i think i got it. writing it down helps..

smackmartine · Answer

Please use spoiler!!

dtweah · Answer

gnod wrote:man, i think i just got it.
something wasn't clicking right -

so the question is: is the absolute value of X = y - z? yes/no.

s1) X + Y = Z -> rewrite to get X, to see if X = Y - Z.
X = Z - Y when X is positive
X = Y - Z when X is negative (right?)

since it can be both - insufficient.

s2) X < 0
X may be negative, but doesn't tell us about whether X = Y - Z - insufficient.

S1 + S2 = X < 0 and X = Y - Z when X is negative.

just to confirm... we checked Statement 1 for positive and negative because we were asked if the absolute value of X equaled to something.. correct?

that's why - absolute value of X if positive = Z - Y
and absolute value of X is negative = Y - Z...

ahh i think i got it. writing it down helps..

Too Long: Here is how to see it.
Transform the question is |x|= y-z ? to is Y=Z?
How? Solve the absolute value equation and cancel out X.
Now 1 cannot answer b/c you get a Yes and No. Yes if X is 0 and No if X is positive.
2 does not have Z and Y. With both, if X is negative then Y = Z-x. Clearly Y has to be bigger than Z. Hope this helps.

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