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Using the formula a^2–b^2 =(a+b)(a-b), find the value of (

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Using the formula a^2–b^2 =(a+b)(a-b), find the value of (

by Max@Math Revolution » Tue Sep 10, 2019 5:39 am
[GMAT math practice question]

Using the formula a^2-b^2 =(a+b)(a-b), find the value of (1+ 1/2 )(1+ 1/4)(1+1/16).

A. 255/128
B. 255/256
C. 257/128
D. 127/128
E. 555/128
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by Max@Math Revolution » Fri Sep 13, 2019 6:40 am
=>

Let X = (1+1/2)(1+1/4)(1+1/16).
Then
(1-1/2)X = (1-1/2)(1+1/2)(1+1/4)(1+1/16)
=(1-1/4)(1+1/4)(1+1/16)
=(1-1/16)(1+1/16)
=1-1/256
=255/256.
So, (1/2)X = 255/256, and X = 255/128

Therefore, A is the answer.
Answer: A
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