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If |x| = |y|, is x/y = -1?

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by melguy » Tue Nov 08, 2016 7:54 am
NandishSS wrote:If |x| = |y|, is x/y = -1?
(1) x < 0
(2) y > 0

OA:C

Source : GMATPrep EP1
Rephrasing the question : It is asking is either x or y negative?

Statement 1

x = -1 y = 1 | Is x/y = -1 ? Yes
x = -1 y = -1 | Is x/y = -1 ? No

Statement 2

x = 1 y = 1 | Is x/y = -1 ? No
x = -1 y = 1 | Is x/y = -1 ? Yes

Combine

x = -1 y = 1 | Is x/y = -1 ?

One sign is negative and one is positive. So we know for certain that the result will be negative.

Answer C
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by Brent@GMATPrepNow » Tue Nov 08, 2016 8:05 am
NandishSS wrote:If |x| = |y|, is x/y = -1?

(1) x < 0
(2) y > 0
Target question: Is x/y = -1?

Given: |x| = |y|
First of all, this tells us that x and y have the same magnitude.
So, EITHER x and y are equal, OR one is negative and one is positive

Statement 1: x < 0
There's no information about y, so this statement probably isn't sufficient. let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = -2 and y = 2. Notice that |x| = |y|. In this case x/y = (-2)/2 = -1
Case b: x = -2 and y = -2. Notice that |x| = |y|. In this case x/y = (-2)/(-2) = 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: y > 0
There's no information about x, so this statement probably isn't sufficient. let's TEST some values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = -2 and y = 2. Notice that |x| = |y|. In this case x/y = (-2)/2 = -1
Case b: x = 2 and y = 2. Notice that |x| = |y|. In this case x/y = 2/2 = 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x is negative
Statement 2 tells us that y is positive
The given information tells us that x and y must have the same magnitude.
So, we can conclude that x/y = -1
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

RELATED VIDEO
- Solving equations with absolute value: https://www.gmatprepnow.com/module/gmat ... /video/972
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by crackverbal » Wed Nov 09, 2016 9:31 am
Hi NandishSS,

One approach to solve such problems is by plugging in values to get a YES and a NO. This approach is the safest but not necessarily the fastest as it requires you to be flexible with the types of numbers you choose. One strategy you can think of employing while dealing with DS questions based on Algebra and Word Problems is to 'Deconstruct and rephrase the question'.

While dealing with questions where you have a modulus on both sides of an equality/inequality for eg. |x| = |y| or |x| < |y|, the blanket rule that you can follow to deconstruct the question is to square both sides and remove the modulus. Now the reason we do this is because of an important relationship that |x| = root(x^2).

The question here says that |x| = |y|. Squaring both sides we get x^2 = y^2
x^2 - y^2 = 0 -----> (x - y)(x + y) = 0 -----> x = y and x = -y -----> x/y = 1 and x/y = -1.

Now this is a YES/NO DS where we need to answer the question 'Is x/y = -1' i.e. x and y have to be of different signs.

Looking at both the statements the answer here has to be C as the statements individually do not give any information about x AND y.

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by Scott@TargetTestPrep » Fri Nov 11, 2016 7:20 am
NandishSS wrote:If |x| = |y|, is x/y = -1?
(1) x < 0
(2) y > 0

OA:C
We are given that |x| = |y| and need to determine if x/y = -1.

Statement One Alone:

x < 0

Knowing that x is less than zero is not enough information to determine whether x/y = -1.

For instance, if x = -1 and y = -1, then x/y does not equal -1; however if x = -1 and y = 1, then x/y does equal -1. Statement one alone is not sufficient. We can eliminate answer choices A and D.

Statement Two Alone:

y > 0

Knowing that y is greater than zero is not enough information to determine whether x/y = -1.

For instance, if y = 1 and x = 1, then x/y does not equal -1; however if y = 1 and x = -1, then x/y does equal -1. Statement two alone is not sufficient. We can eliminate answer choice B.

Statements One and Two Together:

Using the information from statements one and two, we see that x is less than zero and that y is greater than zero. Thus, x and y must have opposite signs. From the given information, we also know that |x| = |y|. In that case, x and y must be opposites (e.g.. -2 and 2, -10 and 10, -1 and 1) and x/y will always equal -1.

Answer: C

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by Jay@ManhattanReview » Sun Jan 08, 2017 10:05 pm
NandishSS wrote:If |x| = |y|, is x/y = -1?
(1) x < 0
(2) y > 0

OA:C

Source : GMATPrep EP1
The meaning of |x| = |y| is that x and y have the same value, but they may or may not have the same direction, i.e., they may be at the opposite sides on a number line.

1. If x and y have the same direction, or we can say that x = y, then x/y = 1. The answer is NO.
2. However, if x = -y, the x/y = -1, The answer is YES. No unique answer.

S1: x < 0

If x < 0 and y < 0, the answer is NO. However, if x < 0 and y > 0, the answer is YES. No unique answer.

S2: y > 0

Its fate is as the same as S1. Not sufficient.

S1 and S2:

Since x < 0 and y > 0, we see that x = -y, thus x/y = -1. Answer is YES. Sufficient.

Answer: C

Hope this helps!

-Jay
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by [email protected] » Mon Jan 09, 2017 11:13 am
Hi All,

This is a great 'concept' question, meaning that you don't have to do a lot of math to get to the correct answer as long as you understand the concepts involved.

To start, we're told that |X| = |Y|. This means that X and Y are either the SAME number or that they're OPPOSITES. For example....

X and Y could be...
0 and 0
1 and 1
1 and -1
-2 and 2
1.5 and -1.5
Etc.

We're asked if X/Y = -1. This is a YES/NO question; it can also be 'rewritten' as "Are X and Y exact opposites of one another?"

1) X < 0

This tells us that X is NEGATIVE, but it doesn't tell us whether Y is positive or negative.
IF....
Y is positive, then the answer to the question is YES.
Y is negative, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) Y > 0

This tells us that Y is POSITIVE, but it doesn't tell us whether X is positive or negative.
IF....
X is positive, then the answer to the question is NO.
X is negative, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we know that X is negative and Y is positive. With the information from the prompt, we can tell that X and Y are clearly opposites of one another, so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT.

Final Answer: C

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