GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 29 Jan 2020, 09:47

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Is x^2 – y^2 a positive number ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 07 Jan 2008
Posts: 77
Is x^2 – y^2 a positive number ?  [#permalink]

Show Tags

New post 02 Oct 2008, 06:47
1
21
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

64% (01:16) correct 36% (01:25) wrong based on 405 sessions

HideShow timer Statistics

Is x^2 – y^2 a positive number?

(1) x – y is a positive number.
(2) x + y is a positive number.


DS48302.01

I chose (A) for this one. If x - y > 0 then x > y. So x2-y2 will be a +ve number.

the OA is C though x2 - y2 = (x+y)(x-y)
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 60778
Re: Is x^2 – y^2 a positive number ?  [#permalink]

Show Tags

New post 31 Oct 2014, 04:40
6
5
topmbaseeker wrote:
Is x^2 – y^2 a positive number?

(1) x – y is a positive number.
(2) x + y is a positive number.

I chose (A) for this one. If x - y > 0 then x > y. So x2-y2 will be a +ve number.

the OA is C though x2 - y2 = (x+y)(x-y)


Is x^2 – y^2 a positive number?

Is x^2 - y^2 > 0? is x^2 > y^2? --> is |x| > |y|? So, the question asks whether x is further from 0 than y.

(1) x – y is a positive number --> x > y. One number is greater than another. Also, insufficient to say which one is further from 0. For example, if x = 2 and y = 1, then x is further but if x = 2 and y = -3, then y is further. Not sufficient.

(2) x + y is a positive number. The sum of two numbers is greater than 0. Clearly insufficient to say which one is further from 0.

(1)+(2) Is x^2 - y^2 > 0? Can be rephrased as "is (x - y)(x + y) > 0?" (1) says that x - y > 0 and (2) says that x + y > 0, thus their product, the product of two positive values, must be greater than 0. Sufficient.

Answer: C.

Hope it's clear.
_________________
General Discussion
Manager
Manager
avatar
Joined: 22 Sep 2008
Posts: 93
Re: Is x^2 – y^2 a positive number ?  [#permalink]

Show Tags

New post 03 Oct 2008, 07:47
1
x = 2
y = -3

x-y = 2 - -3 = 5 which is positive number now x^2 - y^2 = 4 - 9 = -5 which is not positive number :)

B alone is also not suff.

A + B is sufficient
Manager
Manager
avatar
Joined: 31 Jul 2008
Posts: 163
Re: Is x^2 – y^2 a positive number ?  [#permalink]

Show Tags

New post 05 Oct 2008, 13:27
C

for x+y is +ve , imagine y as 3 and x as -2 :: -> (-2-3)(-2+3)
Intern
Intern
User avatar
Joined: 18 Dec 2013
Posts: 24
Location: Canada
GPA: 2.84
WE: Project Management (Telecommunications)
GMAT ToolKit User
Re: Is x^2 – y^2 a positive number ?  [#permalink]

Show Tags

New post 30 Oct 2014, 18:22
topmbaseeker wrote:
24. Is x2 – y2 a positive number?
(1) x – y is a positive number.
(2) x + y is a positive number.

I chose (A) for this one. If x - y > 0 then x > y. So x2-y2 will be a +ve number.

the OA is C though x2 - y2 = (x+y)(x-y)


Dear Bunuel ... Need help with this question... please... Whats wrong with topmbaseeker's method?
Intern
Intern
User avatar
Joined: 18 Dec 2013
Posts: 24
Location: Canada
GPA: 2.84
WE: Project Management (Telecommunications)
GMAT ToolKit User
Re: Is x^2 – y^2 a positive number ?  [#permalink]

Show Tags

New post 31 Oct 2014, 20:24
1
study wrote:
Does anyone here know how to get access to the 1000 DS questions?


Here you go, in the attachment, however, the attachment contains all - DS, PS, RC, SC, CR! :drunk Go nuts!! :P
Attachments

File comment: 1000 Series - ALL ( Quant & Verbal)
1000 Series.zip [1.27 MiB]
Downloaded 537 times

To download please login or register as a user

Retired Moderator
avatar
V
Joined: 22 Jun 2014
Posts: 1087
Location: India
Concentration: General Management, Technology
GMAT 1: 540 Q45 V20
GPA: 2.49
WE: Information Technology (Computer Software)
GMAT ToolKit User
Re: Is x^2 – y^2 a positive number ?  [#permalink]

Show Tags

New post 09 Apr 2016, 07:19
1
topmbaseeker wrote:
Is x^2 – y^2 a positive number?

(1) x – y is a positive number.
(2) x + y is a positive number.

I chose (A) for this one. If x - y > 0 then x > y. So x2-y2 will be a +ve number.

the OA is C though x2 - y2 = (x+y)(x-y)


is (x+y) * (x-y) +ve?

stmt -1:

x-y is positive but x+y may not be

stmt2

x+y is positive but x-y may not be

combining both means +ve*+ve = +ve -- sufficient.
_________________
Current Student
avatar
Joined: 17 Mar 2015
Posts: 17
Location: United States (UT)
Concentration: Entrepreneurship, Finance
GMAT 1: 700 Q48 V38
GPA: 3.55
Re: Is x^2 – y^2 a positive number ?  [#permalink]

Show Tags

New post 09 Apr 2016, 07:41
1
1
Almost all data sufficiency questions (and generally most problem solving questions) benefit from the "dumb" approach. I'll elaborate on that in a second but first, as a trigger, you should ALWAYS attempt to rearrange the question they give you especially when you see exponents. When you see x^2 – y^2 you should immediately realize that it equals (x + y)(x - y).

Now for the dumb approach:
The question asks is (x + y)(x - y) > 0. The dumb approach says that you take this problem and translate it to the simplest terms possible. "Is a number times a number positive?" For this to be true, both numbers must either be positive or negative. That's why you need to both statements. And knowing number properties such as "a positive times a positive is a positive" or "an odd number to any power is odd" will save you the hassle of plugging and chugging.
Retired Moderator
User avatar
G
Joined: 18 Sep 2014
Posts: 1096
Location: India
GMAT ToolKit User Reviews Badge
Re: Is x^2 – y^2 a positive number ?  [#permalink]

Show Tags

New post 10 Aug 2016, 21:34
Is \(x^2 – y^2\) a positive number?

(1) \(x – y\) is a positive number.

We can take two values which say \(x – y\) is a positive number.
a. x=10, y=5
by plugging these values we get \(10^2 – 5^2\)=100-25=75

i.e., \(x^2 – y^2\) a positive number

b. x=-5, y=-10
by plugging these values we get \((-5)^2 – (-10)^2\)=25-100=-75 a negative number

i.e., \(x^2 – y^2\) is a negative number.

Hence result is uncertain and statement 1 is not sufficient on its own.




(2) \(x + y\) is a positive number.

We can take two values which say \(x + y\) is a positive number.
a. x=10, y=-5
by plugging these values we get \(10^2 – (-5)^2\)=100-25=75

i.e., \(x^2 – y^2\) a positive number

b. x=-5, y=10
by plugging these values we get \((-5)^2 – (10)^2\)=25-100=-75 a negative number

i.e., \(x^2 – y^2\) is a negative number.

Hence result is uncertain and statement 2 is not sufficient on its own.



Now combine both of them and multiplication of tw positive numbers is always a positive number.

And \(x-y>0\) indicates that x is greater than y(both positive and negative)
Whereas \(x+y>0\) indicates that x,y are either both positive or only one is negative
thus eliminating both of them to be negative.
Director
Director
User avatar
B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 518
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)
Re: Is x^2 – y^2 a positive number ?  [#permalink]

Show Tags

New post 11 Aug 2016, 00:36
Top Contributor
topmbaseeker wrote:
Is x^2 – y^2 a positive number?

(1) x – y is a positive number.
(2) x + y is a positive number.

I chose (A) for this one. If x - y > 0 then x > y. So x2-y2 will be a +ve number.

the OA is C though x2 - y2 = (x+y)(x-y)


Number plugging method worked for me

Question: Is \(x^2-y^2\)>0? ,or Is (x+y)(x-y)>0 ?

(1)x-y>o;
    when x=5,y=2 then (x+y)(x-y)>0
    when x=2,y=-5 then (x+y)(x-y)<0, Not Sufficient

(2)x+y>0;
    when x=5,y=2 then (x+y)(x-y)>0
    when x=2,y=5 then (x+y)(x-y)<0,Not Sufficient

(1)+(2) Clearly x-y>0 and x+y>0 ensured (x+y)(x-y)>0 ,or \(x^2-y^2\) is positive number.Sufficient

Correct Answer C
IIMA, IIMC School Moderator
User avatar
V
Joined: 04 Sep 2016
Posts: 1382
Location: India
WE: Engineering (Other)
CAT Tests
Re: Is x^2 – y^2 a positive number ?  [#permalink]

Show Tags

New post 21 Dec 2018, 03:33

Project DS Butler: Day 46: Data Sufficiency (DS92)


For DS butler Questions Click Here


Bumping for DS Butler project.
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4236
Location: Canada
Re: Is x^2 – y^2 a positive number ?  [#permalink]

Show Tags

New post 15 Dec 2019, 07:40
Top Contributor
topmbaseeker wrote:
Is x² – y² a positive number?

(1) x – y is a positive number.
(2) x + y is a positive number.


The key to answering this question is the first recognize that x² – y² = (x + y)(x - y)
This allows us to rephrase our target question as follows:

Target question: Is (x + y)(x - y) a positive number?

Statement 1: x – y is a positive number
Here we know that (x - y) is positive, but we know nothing about (x + y)
To see what I mean, consider these two possible cases that satisfy statement 1:

Case a: x = 2 and y = 1. In this case, (x + y)(x - y) = (2 + 1)(2 - 1) = 3. So, the answer to the target question is YES, (x + y)(x - y) IS a positive number
Case b: x = 1 and y = -2. In this case, (x + y)(x - y) = (1 + (-2))(1 - (-2)) = -3. So, the answer to the target question is NO, (x + y)(x - y) is NOT a positive number
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x + y is a positive number.
Here we know that (x + y) is positive, but we know nothing about (x - y)
Consider these two possible cases that satisfy statement 2:

Case a: x = 2 and y = 1. In this case, (x + y)(x - y) = (2 + 1)(2 - 1) = 3. So, the answer to the target question is YES, x² – y² IS a positive number
Case b: x = -1 and y = 2. In this case, (x + y)(x - y) = ((-1) + 2)((-1) - 2) = -3. So, the answer to the target question is NO, x² – y² is NOT a positive number
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 - y) is POSITIVE
Statement 2 tells us that (x + y) is POSITIVE
So, (x + y)(x - y) = (POSITIVE)(POSITIVE) = POSITIVE
The answer to the target question is YES, x² – y² IS a positive number
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Rice (Jones) School Moderator
User avatar
P
Joined: 18 Jun 2018
Posts: 332
Location: United States (AZ)
Concentration: Finance, Healthcare
GMAT 1: 620 Q45 V31
GPA: 3.36
CAT Tests
Is x^2 – y^2 a positive number ?  [#permalink]

Show Tags

New post 15 Dec 2019, 08:12
Question: \(x^{2}\) - \(y^{2}\) > 0? ==> (x - y)(x+y) > 0? ==> Does x - y and x + y have the same sign?

St 1: x - y > 0 ==> x - y is positive ==> insufficient since we don't know the sign of x + y

St 2: x + y > 0 ==> x + y is positive ==> insufficient since we don't know the sign of x - y

Sts 1 & 2 ==> x - y and x + y are positive ==> (x-y)(x+y) = positive > 0 ==> sufficient (the answer is C)
GMAT Club Bot
Is x^2 – y^2 a positive number ?   [#permalink] 15 Dec 2019, 08:12
Display posts from previous: Sort by

Is x^2 – y^2 a positive number ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne