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

Expert replies

Previous Topic Next Topic

NandishSS: Master | Next Rank: 500 Posts; Posts: 366; Joined: Fri Jun 05, 2015 3:35 amFollowed by: 2 members; Thanked: 3 times

by NandishSS » Tue Nov 08, 2016 7:05 am

If |x| = |y|, is x/y = -1?
(1) x < 0
(2) y > 0

OA:C

Source : GMATPrep EP1

Like this post

Source: Beat The GMAT — Data Sufficiency | Tue Nov 08, 2016 7:05 am

melguy: Master | Next Rank: 500 Posts; Posts: 335; Joined: Mon Mar 21, 2011 11:31 pmFollowed by: 2 members; Location: Australia / India; Thanked: 37 times

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

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

crackverbal: Master | Next Rank: 500 Posts; Posts: 157; Joined: Mon Aug 16, 2010 7:30 pmFollowed by: 3 members; Location: India; Thanked: 65 times

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.

CrackVerbal Academics Team

Join Free 4 part MBA Through GMAT Video Training Series here -
https://gmat.crackverbal.com/mba-throug ... video-2018

Enroll for our GMAT Trial Course here -
https://gmatonline.crackverbal.com/

For more info on GMAT and MBA, follow us on @AskCrackVerbal

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8142; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

GMAT/MBA Expert

Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

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
_________________
Manhattan Review GMAT Prep

Locations: New York | Jakarta | Nanjing | Berlin | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

_________________
Manhattan Review GMAT Prep

Locations: New York | Jakarta | Nanjing | Berlin | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

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

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review