Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss! Oct 26 07:00 AM PDT  09:00 AM PDT Want to score 90 percentile or higher on GMAT CR? Attend this free webinar to learn how to prethink assumptions and solve the most challenging questions in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 07 Jan 2008
Posts: 78

Is x^2 – y^2 a positive number ?
[#permalink]
Show Tags
02 Oct 2008, 06:47
Question Stats:
64% (01:11) correct 36% (01:29) wrong based on 289 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 x2y2 will be a +ve number.
the OA is C though x2  y2 = (x+y)(xy)
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 58445

Re: Is x^2 – y^2 a positive number ?
[#permalink]
Show Tags
31 Oct 2014, 04:40
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 x2y2 will be a +ve number.
the OA is C though x2  y2 = (x+y)(xy) 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.
_________________




Manager
Joined: 22 Sep 2008
Posts: 100

Re: Is x^2 – y^2 a positive number ?
[#permalink]
Show Tags
03 Oct 2008, 07:47
x = 2 y = 3 xy = 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
Joined: 31 Jul 2008
Posts: 202

Re: Is x^2 – y^2 a positive number ?
[#permalink]
Show Tags
05 Oct 2008, 13:27
C
for x+y is +ve , imagine y as 3 and x as 2 :: > (23)(2+3)



Intern
Joined: 18 Dec 2013
Posts: 24
Location: Canada
GPA: 2.84
WE: Project Management (Telecommunications)

Re: Is x^2 – y^2 a positive number ?
[#permalink]
Show Tags
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 x2y2 will be a +ve number.
the OA is C though x2  y2 = (x+y)(xy) Dear Bunuel ... Need help with this question... please... Whats wrong with topmbaseeker's method?



Intern
Joined: 18 Dec 2013
Posts: 24
Location: Canada
GPA: 2.84
WE: Project Management (Telecommunications)

Re: Is x^2 – y^2 a positive number ?
[#permalink]
Show Tags
31 Oct 2014, 20:24
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! Go nuts!!
Attachments
File comment: 1000 Series  ALL ( Quant & Verbal)
1000 Series.zip [1.27 MiB]
Downloaded 518 times



Retired Moderator
Joined: 22 Jun 2014
Posts: 1093
Location: India
Concentration: General Management, Technology
GPA: 2.49
WE: Information Technology (Computer Software)

Re: Is x^2 – y^2 a positive number ?
[#permalink]
Show Tags
09 Apr 2016, 07:19
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 x2y2 will be a +ve number.
the OA is C though x2  y2 = (x+y)(xy) is (x+y) * (xy) +ve? stmt 1: xy is positive but x+y may not be stmt2 x+y is positive but xy may not be combining both means +ve*+ve = +ve  sufficient.
_________________



Current Student
Joined: 17 Mar 2015
Posts: 17
Location: United States (UT)
Concentration: Entrepreneurship, Finance
GPA: 3.55

Re: Is x^2 – y^2 a positive number ?
[#permalink]
Show Tags
09 Apr 2016, 07:41
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
Joined: 18 Sep 2014
Posts: 1093
Location: India

Re: Is x^2 – y^2 a positive number ?
[#permalink]
Show Tags
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 \(10^2 – 5^2\)=10025=75
i.e., \(x^2 – y^2\) a positive number
b. x=5, y=10 by plugging these values we get \((5)^2 – (10)^2\)=25100=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 \(10^2 – (5)^2\)=10025=75
i.e., \(x^2 – y^2\) a positive number
b. x=5, y=10 by plugging these values we get \((5)^2 – (10)^2\)=25100=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 \(xy>0\) 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
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 525
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
11 Aug 2016, 00:36
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 x2y2 will be a +ve number.
the OA is C though x2  y2 = (x+y)(xy) Number plugging method worked for me Question: Is \(x^2y^2\)>0? ,or Is (x+y)(xy)>0 ? (1)xy>o; when x=5,y=2 then (x+y)(xy)>0 when x=2,y=5 then (x+y)(xy)<0, Not Sufficient (2)x+y>0; when x=5,y=2 then (x+y)(xy)>0 when x=2,y=5 then (x+y)(xy)<0,Not Sufficient (1)+(2) Clearly xy>0 and x+y>0 ensured (x+y)(xy)>0 ,or \(x^2y^2\) is positive number. SufficientCorrect Answer C
_________________



IIMA, IIMC School Moderator
Joined: 04 Sep 2016
Posts: 1366
Location: India
WE: Engineering (Other)

Re: Is x^2 – y^2 a positive number ?
[#permalink]
Show Tags
21 Dec 2018, 03:33
Project DS Butler: Day 46: Data Sufficiency (DS92) For DS butler Questions Click HereBumping for DS Butler project.
_________________
It's the journey that brings us happiness not the destination. Feeling stressed, you are not alone!!




Re: Is x^2 – y^2 a positive number ?
[#permalink]
21 Dec 2018, 03:33






