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Compare (r - s)^4 and r^4 - s^4

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GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4711
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1614 [0], given: 376

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Compare (r - s)^4 and r^4 - s^4 [#permalink] New post 10 May 2016, 07:23
Expert's post
00:00

Question Stats:

75% (00:48) correct 25% (01:13) wrong based on 36 sessions
Quantity A
Quantity B
\((r - s)^4\)
\(r^4 - s^4\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.




Practice Questions
Question: 4
Page: 62
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4711
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1614 [0], given: 376

CAT Tests
Re: Compare (r - s)^4 and r^4 - s^4 [#permalink] New post 10 May 2016, 07:27
Expert's post
Explanation

If you substitute the given numbers into the expressions in Quantities A and B, you can compare them.

Substituting in Quantity A gives \((r - s)^4\) = \((2 - (-7))^4\) = \(9^4\).
Substituting in Quantity B gives \(r^4 - s^4\) = \(2^4 - (-7)^4\) = \(2^4 - 7^4\).
Without further calculation, you see that Quantity A is positive and Quantity B is negative.

Now consider the possibility that r = s. In that case both quantity A ans Quantity B are equal to 0. hence right option is option D.

Thus the correct answer is Choice D.
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Sandy
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Re: Compare (r - s)^4 and r^4 - s^4 [#permalink] New post 14 May 2016, 21:15
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The answer is D. If r and s are equal (r - s)^4 and r^4 - s^4 are equal and zero. If r and s are not equal then we get other relations between (r - s)^4 and r^4 - s^4.
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Re: Compare (r - s)^4 and r^4 - s^4 [#permalink] New post 24 Feb 2018, 19:05
sandy wrote:
Quantity A
Quantity B
\((r - s)^4\)
\(r^4 - s^4\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.




Practice Questions
Question: 4
Page: 62



this is a classic case of substituting and finding out the value. But this can be solved using logic more efficiently

(r-s)^4 = (r2+s2)(r2-s2)
we have a r-s component which can simplify further, but rhs has a r+s. And we know nothing about r or s. Either can be any number of any sign.
Information Underload, so D..... booyah!
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4711
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1614 [0], given: 376

CAT Tests
Re: Compare (r - s)^4 and r^4 - s^4 [#permalink] New post 26 Feb 2018, 04:17
Expert's post
Dev_ben wrote:
sandy wrote:
Quantity A
Quantity B
\((r - s)^4\)
\(r^4 - s^4\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.




Practice Questions
Question: 4
Page: 62



this is a classic case of substituting and finding out the value. But this can be solved using logic more efficiently

(r-s)^4 = (r2+s2)(r2-s2)
we have a r-s component which can simplify further, but rhs has a r+s. And we know nothing about r or s. Either can be any number of any sign.
Information Underload, so D..... booyah!


\((r-s)^4 = (r^2+s^2)(r^2-s^2)\)

This is incorrect.

\((r^2+s^2)(r^2-s^2)=r^4-s^4\)

This is correct.
_________________

Sandy
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Re: Compare (r - s)^4 and r^4 - s^4   [#permalink] 26 Feb 2018, 04:17
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