What is the value of a^4 - b^4? (1) a^2 - b^2 = 16 (2) a + b : DS Archive
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# What is the value of a^4 - b^4? (1) a^2 - b^2 = 16 (2) a + b

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What is the value of a^4 - b^4? (1) a^2 - b^2 = 16 (2) a + b [#permalink]

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23 Aug 2007, 16:55
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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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23 Aug 2007, 18:35
Ans. is C:

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

I. Ins: we know only one part
II. Ins: But we can fugure out what is the value of a-b

Together: Suff
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23 Aug 2007, 19:34
What is the answer for this one-

I come up with A as the answer

from one ...
a ^2 - b ^ 2 = ( a+b) ( a-b) = 16

The only values that satify this are 8 and 2 ...

you can solve for a nad b...
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23 Aug 2007, 23:17
Sumithra Sen wrote:
What is the answer for this one-

I come up with A as the answer

from one ...
a ^2 - b ^ 2 = ( a+b) ( a-b) = 16

The only values that satify this are 8 and 2 ...

you can solve for a nad b...

I don't agree with this.
We cannot assume that the respective values will be a-b= 2
and a+b= 8.

a and b can be any values here. one of them could be negative, or a fraction or any combination.
Also if b is negative it will result in a-b actually greater than a+ b, impacting the values of a and B and thus the values of a^4-b^4.

So I go with C.
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27 Aug 2007, 13:05
Sumithra Sen wrote:
What is the answer for this one-

I come up with A as the answer

from one ...
a ^2 - b ^ 2 = ( a+b) ( a-b) = 16

The only values that satify this are 8 and 2 ...

you can solve for a nad b...

Incorrect assumption.

a= 8, b=2 is one solution. So is a=4, b=0. In both cases, a^4-b^4 will give differerent results. St1 is insuff.

S2 - a+b =8. Insuff.

S1+S2: a+b = 8 and a-b=2. Suff.
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27 Aug 2007, 13:23
this is C..

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

1) a^2-b^2=16

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

insuff

2) a+b=8...insuff

1+2

(a-b)(8)=16

then a-b=2

you get 2 simeltaneous equations

a-b=2
a+b=8

2a=10

a=5

5+3=8
5-3=2

now we can soleve 5^4-3^4
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Re: Algebra - Arithmetic (DS) [#permalink]

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27 Aug 2007, 13:42
above720 wrote:
What is the value of a^4 - b^4?

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

(2) a + b = 8

C for me

You know that a^4 - b^4 = (a^2 - b^2) * (a^2 + b^2)
(1) only tell a^2-b^2
Insufficient

(2) Doesn't tell anything.

Together:
(a+b)*(a-b) = 16
Plug in
a-b = 2
a+b = 8
Solve for a and b, get a=5, b=3
SUFFICIENT.
Re: Algebra - Arithmetic (DS)   [#permalink] 27 Aug 2007, 13:42
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# What is the value of a^4 - b^4? (1) a^2 - b^2 = 16 (2) a + b

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