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Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0

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Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink] New post 12 Jul 2010, 16:53
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Is x > y^2?

(1) x > y+5

(2) x^2-y^2 = 0

Hello,

I was wondering if someone can help with providing a detailed explanation as to how they arrived at (c). The explanation on the test (GMAT Club Test m2#19) review is a bit brief. Thanks
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Re: GMAT Club Test 2 #19 [#permalink] New post 12 Jul 2010, 18:39
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tonebeeze wrote:
Hello,

I was wondering if someone can help with providing a detailed explanation as to how they arrived at (c). The explanation on the test review is a bit brief. Thanks


Is x>y^2?

(1) x>y+5

(2) x^2-y^2 = 0


Is x>y^2?

(1) x>y+5 --> x-y>5. Clearly insufficient, for example: if x=1 and y=-10 then the answer is NO, but if x=10 and y=1 then the answer is YES. Two different answers, hence not sufficient.

(2) x^2-y^2=0 --> (x-y)(x+y)=0 --> so either x-y=0 or x+y=0. Also insufficient: if x=1 and y=1, then answer is NO, buy if x=\frac{1}{2} and y=\frac{1}{2}, then the answer is YES. Two different answers, hence not sufficient.

(1)+(2) As from (1) x-y>5\neq{0}, then from (2) must be true that x+y=0 --> so x=-y --> substitute x in (1) --> -y-y>5 --> y<-\frac{5}{2}<0, as x=-y, then x>\frac{5}{2}>0, so y^2 (or which is the same x^2) will always be more than x, thus the answer to the question "Is x>y^2" is NO. Sufficient.

To elaborate more as x=-y>0, the only chance for x>y^2 to hold true (or which is the same for x>x^2 to hold true) would be if x is fraction (0<x<1). For example if x=\frac{1}{2} and y=-\frac{1}{2} then x=\frac{1}{2}>y^2=\frac{1}{4}. But the fact that x>\frac{5}{2}>0 rules out this option.

Answer: C.

Hope it's clear.
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Re: Number properties [#permalink] New post 08 Jan 2012, 21:58
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Hi, there! I'm happy to help with this. :)

The question: is x > y^2

Statement #1: x > y + 5

This doesn't necessarily tell us anything. If y = 1, and x = 7, then x > y^2, but if y = -6 and x = 0, then x < y^2. But itself, Statement #1 is not sufficient.

Statement #2: x^2 - y^2 = 0

This means that x^2 = y^2, which means that x = ±y. Same absolute value, but both could be positive, both could be negative, or either one could be positive and the other negative. We know that y^2 will be positive, but the x can be positive or negative, so by itself, Statement #2 is insufficient.

Combined
Now, we know that x^2 - y^2 = 0 ---> x = ±y, AND we know that x > y + 5. This leads immediate to a few conclusions
(a) x is positive and y is negative --- that's the only way they could have the same absolute value, but with x bigger than y + 5
(b) x and y must have an absolute value greater than 2.5, so that the different between positive x and negative y is more than 5

So we are comparing a positive number x, greater than 2.5, to the square of the negative number with the same absolute value. Of course, x^2 and y^2 are equal, so the question really boils down to: given that x > 2.5, is x > x^2?

For all x greater than one, the square of x is greater than x. That's because, squaring is multiplying a number by itself, and when you multiply anything by a number greater than one, it gets bigger.

Thus, if x > 2.5, when we square it, it will get bigger. Therefore, x^2 = y^2 > x for all values of x > 2.5.

Thus, combined, the statements are sufficient together. Answer = C

Does that make sense? Please let me know if you have any questions.

Mike :)
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Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink] New post 07 Oct 2013, 22:15
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priyankakhosla wrote:
Hi i had a question.

Statement two provides us with equation x^2=y^2

Doesn't that answer our question for x>y^2 as No always ?

For example if x=-2 and y=2 then -2 is not greater than y^2..
Or x=2 and y=2; 2 is not greater than 4 ?

Am i missing something here ? :?:

P.S: Thanks in advance for the help !


If x and y are fractions for eg. x=1/2 and y=1/2
then 1/2 > 1/4 ; i.e. x > y^2 - Hence you get a YES answer here and statement 2 becomes Insufficient.

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Re: GMAT Club Test 2 #19 [#permalink] New post 12 Jul 2010, 19:13
Thanks! That was a much clear explanation.

Last problem of the day:

What is the best approach to solve problems such as this:


"How many times will the digit 7 be written when listing the integers from 1 to 1000?"

Is there any combinationatorics shortcuts? The GMTClub test approached seemed very time consuming.
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Re: GMAT Club Test 2 #19 [#permalink] New post 15 Jul 2010, 07:33
tonebeeze wrote:
Thanks! That was a much clear explanation.

Last problem of the day:

What is the best approach to solve problems such as this:


"How many times will the digit 7 be written when listing the integers from 1 to 1000?"

Is there any combinationatorics shortcuts? The GMTClub test approached seemed very time consuming.


digits-problem-difficulty-in-gmat-club-test-97153.html
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Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink] New post 16 Jul 2013, 23:22
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Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink] New post 18 Jul 2013, 18:33
Bunnel, can you please provide a graphical solution to this particular problem?
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Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink] New post 18 Jul 2013, 21:41
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Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0 [#permalink] New post 07 Oct 2013, 11:06
Hi i had a question.

Statement two provides us with equation x^2=y^2

Doesn't that answer our question for x>y^2 as No always ?

For example if x=-2 and y=2 then -2 is not greater than y^2..
Or x=2 and y=2; 2 is not greater than 4 ?

Am i missing something here ? :?:

P.S: Thanks in advance for the help !
Re: Is x > y^2? (1) x > y+5 (2) x^2-y^2 = 0   [#permalink] 07 Oct 2013, 11:06
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