If |x| = |y|, is x/y = -1?
(1) x < 0
(2) y > 0
OA:C
Source : GMATPrep EP1
If |x| = |y|, is x/y = -1?
This topic has expert replies
- melguy
- Master | Next Rank: 500 Posts
- Posts: 335
- Joined: Mon Mar 21, 2011 11:31 pm
- Location: Australia / India
- Thanked: 37 times
- Followed by:2 members
Rephrasing the question : It is asking is either x or y negative?NandishSS wrote:If |x| = |y|, is x/y = -1?
(1) x < 0
(2) y > 0
OA:C
Source : GMATPrep EP1
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
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Target question: Is x/y = -1?NandishSS wrote:If |x| = |y|, is x/y = -1?
(1) x < 0
(2) y > 0
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
- crackverbal
- Master | Next Rank: 500 Posts
- Posts: 157
- Joined: Mon Aug 16, 2010 7:30 pm
- Location: India
- Thanked: 65 times
- Followed by:3 members
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
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
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
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7247
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We are given that |x| = |y| and need to determine if x/y = -1.NandishSS wrote:If |x| = |y|, is x/y = -1?
(1) x < 0
(2) y > 0
OA:C
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
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
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.NandishSS wrote:If |x| = |y|, is x/y = -1?
(1) x < 0
(2) y > 0
OA:C
Source : GMATPrep EP1
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.
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
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