Problem solving

[BTGmoderatorRO]

If X = -|Y| and X-Y =-10, what is Y?

A. -5 or +5
B. -10
C. 0
D. -5
E. 5

QA is e.
I have been struggling since on how to get Y=-5.

[Jay@ManhattanReview]

If X = -|Y| and X-Y =-10, what is Y?

A. -5 or +5
B. -10
C. 0
D. -5
E. 5

QA is e.
I have been struggling since on how to get Y=-5.

From x = -|y|, we know that |y| is positive, thus, x is a negative number. Also, the absolute values of x and y are equal. For example, if x = -2, then y is either +2 or -2.

Given, x - y = -10

=> -|x| - y = -10; we already deduced that x is negative.

=> |x| + y = 10; multiplying the equation by '-'.

Case 1: Say x = -a, and y = +a

Thus, |-a| + a = 10 => a + a = 10 => a = 5 => y = 5.

Case 2: Say x = -a, and y = -a

Thus, |-a| - a = 10 => a - a = 10. This is not possible, thus y must be positive.

Thus, y = 5.

The correct answer: E

Hope this helps!

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-Jay
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[Scott@TargetTestPrep]

If X = -|Y| and X-Y =-10, what is Y?

A. -5 or +5
B. -10
C. 0
D. -5
E. 5

QA is e.
I have been struggling since on how to get Y=-5.

Since X = -|Y|, we have either X = Y or X = -Y. If X = Y, then X - Y = 0. However, we are given that X - Y = -10, so we can’t have X = Y. Thus, X = -Y and substitute -Y for X in X - Y = -10, we get:

-Y - Y = -10

-2Y = -10

Y = 5

Answer: E