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Is a^2 + b^2 > c^2

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Is a^2 + b^2 > c^2 [#permalink] New post 19 Jun 2012, 11:18
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Is a^2 + b^2 > c^2?

(1) a^3 + b^3 > c^3
(2) a + b > c

Source: http://www.gmathacks.com
[Reveal] Spoiler: OA

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Re: Is a^2 + b^2 > c^2 [#permalink] New post 19 Jun 2012, 18:22
Take two cases,
(a,b,c) = (1,1,1) and (a,b,c) = (1,1,-2)

Both the statements are not sufficient even when taken together.

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Re: Is a^2 + b^2 > c^2 [#permalink] New post 20 Jun 2012, 00:13
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metallicafan wrote:
Is a^2 + b^2 > c^2?

(1) a^3 + b^3 > c^3
(2) a + b > c

Source: http://www.gmathacks.com


The best way to deal with this problem is to plug numbers. Remember on DS questions when plugging numbers, your goal is to prove that the statement is not sufficient. So you should try to get a YES answer with one chosen number(s) and a NO with another.

Is a^2 + b^2 > c^2 ?

(1) a^3 + b^3 > c^3, both YES and NO answers are easy to get:

If a and b are any positive numbers (for example a=b=1) and c is zero then the answer will be YES: 1^3+1^3>0^3 and 1^2+1^2>0^2;

If a and b are some positive numbers (for example a=b=1) and c is large enough negative number (for example c=-10) then the answer will be NO: 1^3+1^3>(-10)^3 and 1^2+1^2<(-10)^2;
Not sufficient.

(2) a + b > c. The same set of numbers will work for this statement as well:

If a and b are any positive numbers (for example a=b=1) and c is zero then the answer will be YES: 1^3+1^3>0^3 and 1^2+1^2>0^2;

If a and b are some positive numbers (for example a=b=1) and c is large enough negative number (for example c=-10) then the answer will be NO: 1^3+1^3>(-10)^3 and 1^2+1^2<(-10)^2;
Not sufficient.

(1)+(2) We have one set of numbers which gives the answer YES for both statements and another set of numbers which gives the answer NO for both statements. Not sufficient.

Answer: E.

Similar question: gmat-prep-exponent-101358.html

Hope it helps.
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Re: Is a^2 + b^2 > c^2   [#permalink] 20 Jun 2012, 00:13
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