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# What is the value of a^4 - b^4 ?

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What is the value of a^4 - b^4 ? [#permalink]  25 Nov 2005, 08:43
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What is the value of a^4 - b^4 ?

(1) a^2 - b^2 = 16
(2) a + b = 8

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-a-4-b-83520.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Jul 2013, 07:41, edited 1 time in total.
Edited the question and added the OA
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Re: PS - Number properties [#permalink]  25 Nov 2005, 14:28
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tobiastt wrote:
What is the value of a^4 - b^4 ?

I - a^2 - b^2 = 16
II - a + b = 8

Looks obvious at the first look but....

It should be C

i) a^2 - b^2=16
=> (a - b) (a + b)=16 --> insuff

ii) a+b =8 --> insuff

from i and ii => a - b = 2
so a=5 & b=3

so the ans should be C
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Re: What is the value of a^4 - b^4 ? I - a^2 - b^2 = 16 II [#permalink]  02 Jul 2013, 05:38
tobiastt wrote:
What is the value of a^4 - b^4 ?

I a^2 - b^2 = 16
II a + b = 8

Looks obvious at the first look but....

The question can be simplified $$a^4 - b^4 = (a^2)^2 - (b^2)^2 = (a^2 - b^2) ( a^2 + b^2)$$

From statement 1

$$(a^2 - b^2) ( a^2 + b^2)$$

we know the info in blue but can't solve the other part

Statement 2 clearly insufficient

(a+b) (a-b) = 16

and we know a+b = 8

test some numbers (1,7)(2,6),(5,3)

It satisfies both equation. Hence sufficient!
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Re: What is the value of a^4 - b^4 ? [#permalink]  02 Jul 2013, 07:42
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What is the value of a^4 - b^4 ?

$$a^4 - b^4 =(a^2-b^2)(a^2+b^2)$$

(1) a^2 - b^2 = 16 --> clearly not sufficient.
(2) a + b = 8 --> clearly not sufficient.

(1)+(2) As from (2) $$a + b = 8$$ then $$a^2 - b^2 =(a-b)(a+b)=(a-b)*8 =16$$ --> $$a-b=2$$. Sum $$a-b=2$$ and $$a + b = 8$$ --> $$2a=10$$ --> $$a=5$$ --> $$b=3$$ --> $$a^4 - b^4 =(a^2-b^2)(a^2+b^2)=16*34$$. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: what-is-the-value-of-a-4-b-83520.html
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Re: What is the value of a^4 - b^4 ?   [#permalink] 02 Jul 2013, 07:42
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