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If x and y are negative numbers,

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by fiza gupta » Mon Jan 02, 2017 10:39 pm
If x and y are negative numbers, what is the value of (x^2)/x − (y∗|y|)^.5?
A) 1+y
B) 1−y
C) −1−y
D) y−1
E) x-y

OA:D
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by GMATGuruNY » Tue Jan 03, 2017 8:38 am
The problem has been transcribed incorrectly.
It should read as follows:
If x and y are negative numbers, what is the value of (√x²)/x − √(-y|y|)?

A) 1+y
B) 1−y
C) −1−y
D) y−1
E) x-y
Let x=-3 and y=-2.
Plugging these values into (√x²)/x − √(-y|y|), we get:
(√9)/(-3) − √(2|-2|) = 3/-3 - √4 = -1 - 2 = -3.

The target value is -3.
Now y=-2 into the answers to see which yields -3.
Only D works:
y-1 = -2-1 = -3.

The correct answer is D.
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by Jay@ManhattanReview » Sun Jan 08, 2017 9:53 pm
fiza gupta wrote:If x and y are negative numbers, what is the value of (√x²)/x - √(-y|y|)?

A) 1+y
B) 1-y
C) -1-y
D) y-1
E) x-y

OA:D
We have to find out the value of (√x²)/x - √(-y|y|).

Since x and y are negatives, we can write (√x²)/x as |x| / (-|x|) = 1/(-1) = -1

Similarly, we can write √(-y|y|) as √(|y|.|y|) = √(|y|^2) = |y|

Thus, (√x²)/x - √(-y|y|) = -1 - |y|

Since y is negative, we can write -1 - |y| as -1 + y.

Answer: D

Hope this helps!

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by [email protected] » Mon Jan 09, 2017 11:06 am
Hi fiza gupta,

TESTing VALUES is really useful in these types of situations; Mitch showcased that approach perfectly, so I won't rehash any of that work here. Instead, I want to point out that it's important to remember that math functions are based on a finite set of rules, so when you see a question that includes squares, square roots, absolute values, etc. you should not get overly emotional about it. Instead, think about what the rules 'mean' - and jotting down a few simple examples on the pad can help. In that way, you can focus on the patterns and Tactics that can be used to answer the question, and not be bogged down trying to decipher how all of these functions will interact with one another.

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