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# What is the value of a^4 – b^4 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 49430
What is the value of a^4 – b^4 ?  [#permalink]

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25 Sep 2017, 00:03
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Difficulty:

55% (hard)

Question Stats:

50% (01:53) correct 50% (01:59) wrong based on 32 sessions

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What is the value of $$a^4 – b^4$$ ?

(1) $$(a – b)(a + b)^3 = 10$$

(2) $$ab(a^2 – b^2) = 5$$

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Joined: 27 Feb 2015
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Re: What is the value of a^4 – b^4 ?  [#permalink]

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Updated on: 25 Sep 2017, 03:12
a^4 - b^4 =( a^2- b^2) (a^2 + b^2)
a^2- b^2 = (a -b)(a+b)
so a^4 - b^4 = (a -b)(a+b)(a^2 + b^2) Stat 1 NS

Stat 2. NS

Ans C

Sent from my SM-G935F using GMAT Club Forum mobile app

Originally posted by Ejiroghene on 25 Sep 2017, 00:14.
Last edited by Ejiroghene on 25 Sep 2017, 03:12, edited 1 time in total.
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Re: What is the value of a^4 – b^4 ?  [#permalink]

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25 Sep 2017, 01:32
Ejiroghene wrote:
a^4 - b^4 =( a^2- b^2) (a^2 + b^2)
a^2- b^2 = (a -b)(a+b)
so a^4 - b^4 = (a -b)(a+b)(a^2 + b^2) which is = (a -b)(a+b)^3 = 10. Stat 1 Suff

Stat 2. NS

Ans A

Sent from my SM-G935F using GMAT Club Forum mobile app

Mistake : $$a^4 - b^4 = (a -b)(a+b)(a^2 + b^2)$$ is "Not" equal to $$(a -b)(a+b)^3$$

=> $$a^4 - b^4 = (a-b)(a+b)(a^2+b^2) = (a-b)(a+b)(a^2+b^2+2ab-2ab) = (a-b)(a+b)[(a+b)^2 -2ab] = (a-b)(a+b)^3 - 2ab(a-b)(a+b)$$

$$= (a-b)(a+b)^3 - 2ab(a^2-b^2)$$

Statement 1 and statement 2 alone are not sufficient to solve it.
By combining 1 and 2 we can calculate value of $$a^4-b^4$$ by putting values from 1 and 2 in above mentioned equation

Re: What is the value of a^4 – b^4 ? &nbs [#permalink] 25 Sep 2017, 01:32
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# What is the value of a^4 – b^4 ?

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