Is x^2 – y^2 a positive number ? : GMAT Data Sufficiency (DS)
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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, 05:47
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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.

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

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03 Oct 2008, 06:47
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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05 Oct 2008, 12:27
C

for x+y is +ve , imagine y as 3 and x as -2 :: -> (-2-3)(-2+3)
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30 Oct 2014, 17:17
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Re: Is x^2 – y^2 a positive number ? [#permalink]

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30 Oct 2014, 17:22
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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31 Oct 2014, 03:40
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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.

[Reveal] Spoiler:
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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31 Oct 2014, 19:24
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06 Nov 2015, 04:28
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Re: Is x^2 – y^2 a positive number ? [#permalink]

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09 Apr 2016, 06:19
topmbaseeker wrote:
Is x^2 – y^2 a positive number?

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

[Reveal] Spoiler:
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, 06:41
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.
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Re: Is x^2 – y^2 a positive number ? [#permalink]

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10 Aug 2016, 20:34
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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10 Aug 2016, 23:36
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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.

[Reveal] Spoiler:
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] 10 Aug 2016, 23:36
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