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What is the value of a^4-b^4? 1) a^2 - b^2 = 16 2) a + b = 8

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What is the value of a^4-b^4? 1) a^2 - b^2 = 16 2) a + b = 8 [#permalink] New post 23 Dec 2004, 00:32
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What is the value of a^4-b^4?

1) a^2 - b^2 = 16

2) a + b = 8
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Official answer and my answer [#permalink] New post 23 Dec 2004, 00:38
The OA is C, which I disagree with.


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

While attempting the problem, I tried a few combinations of numbers and figured out that a=5 and b=3.

Possibilities are: 1 * 16, 2*8, 4*4. But only 2*8 would work here for the equation to make sense.

So for the answer, I put A.
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Re: Official answer and my answer [#permalink] New post 23 Dec 2004, 10:01
Questor wrote:
The OA is C, which I disagree with.


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

While attempting the problem, I tried a few combinations of numbers and figured out that a=5 and b=3.

Possibilities are: 1 * 16, 2*8, 4*4. But only 2*8 would work here for the equation to make sense.

So for the answer, I put A.


What about a= -5 and b=-3? I think you need statement 2.
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 [#permalink] New post 23 Dec 2004, 11:33
Exactly!
Same mistake I made when I was solving problem.

My suggestion to you as SOON as you SPOT a EVEN power. KICK yourself and say "I HAVE TO CHECK -VE NUMBERS ALSO"

Thats how I learnt. Otherwise I always forget to check the -ve numbers.

Thanks
Saurabh Malpani
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Re: DS #250 [#permalink] New post 23 Dec 2004, 11:37
Good point, toddmartin! Thanks!

Even though plugging in numbers could be helpful for solving problems like this one, this strategy can very time consuming (and costly if one forgets to plug in a key set of numbers). While going through the OG, I found that ETS prefers to manipulate equations in clever ways instead. I guess we need to put ourselves in ETS's frame of mind.
Re: DS #250   [#permalink] 23 Dec 2004, 11:37
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What is the value of a^4-b^4? 1) a^2 - b^2 = 16 2) a + b = 8

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