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Is |x| = Y-Z

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Is |x| = Y-Z

by monusangeeta » Tue Aug 03, 2010 8:53 pm
Dear Experts,

Please help me with this question.

IS |X| = Y-Z?

1. X+Y = Z
2. X<0

My Approach:

|X| = Y-Z => X = Y-Z OR X = -(Y-Z)

Statement 1 : X +Y = Z => X = Z-Y = > X = -(Y-Z) => |X| = Y-Z = > SUFF
Statement 2 : X<0 => Only informs that X is -ve no. => InSuff

So as per my opinion Option A is correct, which is obviously not the correct one. :( Please suggest me where I am wrong. Image
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Source: — Data Sufficiency |

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by Rahul@gurome » Tue Aug 03, 2010 9:30 pm
IS |X| = Y-Z?

1. X+Y = Z
2. X<0

(1)If X = 3, Y = 2, Z = 5, then Y - Z = -3, which is not equal to |X| = 3.
If X = -3, Y = 2, Z = -1, then Y - Z = 3, |X| = |-3| = 3.
We don't get a unique answer.
So, (1) is NOT SUFFICIENT to answer the question.

(2) X < 0 implies |X| will always be positive but Y and Z are not given so Y - Z can either be positive or negative. Again, we don't get a unique answer.
So, (2) is NOT SUFFICIENT to answer the question.

Combining (1) and (2), X = (Z - Y) and X is negative implies Z - Y will also be negative. So, -(Z - Y) will be positive. Hence, |X| = Y - Z. So, the answer to the main question is yes.

The correct answer is [spoiler](C)[/spoiler].
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by sindhu b » Tue Aug 03, 2010 9:31 pm
The Ans is C

from A X=Y-Z or Z-Y depending on whethr X is negative or postive...

from B u know that X is Negative
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by dinesh19aug » Tue Aug 03, 2010 10:08 pm
|X| = Y - Z

When x>=0
X = Y-Z

When X<0
(- X) = Y -Z

STMT 1: X + Y = Z ===> -X = Y - Z This wil be true when X<0 but we do not know if X is less than 0. Hence INSUFF.

STMT 2: X<0 , INSUFF No info about Y and Z

BOTH: We know x<0 hence -X = Y-Z ==> X+Y = Z Hence Suff

ANS C
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