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# Is x^2 – y^2 a positive number ?

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Is x^2 – y^2 a positive number ?  [#permalink]

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02 Oct 2008, 06:47
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35% (medium)

Question Stats:

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

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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)
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Re: Is x^2 – y^2 a positive number ?  [#permalink]

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31 Oct 2014, 04:40
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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.

Hope it's clear.
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Re: Is x^2 – y^2 a positive number ?  [#permalink]

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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
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Re: Is x^2 – y^2 a positive number ?  [#permalink]

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05 Oct 2008, 13:27
C

for x+y is +ve , imagine y as 3 and x as -2 :: -> (-2-3)(-2+3)
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Re: Is x^2 – y^2 a positive number ?  [#permalink]

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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?
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Re: Is x^2 – y^2 a positive number ?  [#permalink]

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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! Go nuts!!
Attachments

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

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Re: Is x^2 – y^2 a positive number ?  [#permalink]

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09 Apr 2016, 07:19
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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.
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Re: Is x^2 – y^2 a positive number ?  [#permalink]

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09 Apr 2016, 07:41
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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.
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Re: Is x^2 – y^2 a positive number ?  [#permalink]

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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.
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Re: Is x^2 – y^2 a positive number ?  [#permalink]

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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

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Re: Is x^2 – y^2 a positive number ?  [#permalink]

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21 Dec 2018, 03:33

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

Bumping for DS Butler project.
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Re: Is x^2 – y^2 a positive number ?  [#permalink]

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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

Cheers,
Brent
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Is x^2 – y^2 a positive number ?  [#permalink]

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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)
Is x^2 – y^2 a positive number ?   [#permalink] 15 Dec 2019, 08:12
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