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

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1737 [0], given: 397

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

Question Stats:

76% (00:50) correct 23% (01:02) wrong based on 52 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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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1737 [0], given: 397

Re: Compare (r - s)^4 and r^4 - s^4 [#permalink]  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.
_________________

Sandy
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Manager
Joined: 23 Jan 2016
Posts: 137
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Kudos [?]: 110 [1] , given: 15

Re: Compare (r - s)^4 and r^4 - s^4 [#permalink]  14 May 2016, 21:15
1
KUDOS
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.
Intern
Joined: 24 Feb 2018
Posts: 5
Followers: 0

Kudos [?]: 2 [0], given: 2

Re: Compare (r - s)^4 and r^4 - s^4 [#permalink]  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.
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1737 [0], given: 397

Re: Compare (r - s)^4 and r^4 - s^4 [#permalink]  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.

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

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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