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a4 - b4

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a4 - b4

by ronsom » Thu May 20, 2010 1:53 am
What is the value of a^4 - b^4?

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


Source: GMATPrep
Answer: C
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Source: — Data Sufficiency |
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by kstv » Thu May 20, 2010 2:21 am
1) a²-b²= 16
(a+b) (a-b) = 16 = 2*2*2*2 = 8*2 or 4*4
(a+b) = 8 and (a-b) = 2
a = 5 b = 3
Sufficient
But it is not given that a and b are integers
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by indiantiger » Thu May 20, 2010 3:43 am
a^4 - b^4= ?

This can be written as (a^2-b^2)(a^2+b^2) ----1

Statement(1) a^2 - b^2 = 16
this gives us (a-b)(a+b)=16 or we got one part of equation 1
Not sufficient

Statement(2) a + b = 8 ----3

not sufficient does not give us any information

combine both st1 and st2
plug in value of a+b = 8 in (a-b)(a+b)=16
we get a-b = 2 --- 4

add eq 3 and eq 4

a+b+a-b = 8+2
2a = 10
a = 5
and b=3
so we can get a^4-b^4
hence (C)
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