What is the value of

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What is the value of

by Max@Math Revolution » Tue Apr 28, 2020 1:33 am

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[GMAT math practice question]

What is the value of
\(32\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)\left(1-\frac{1}{4^2}\right)\left(1-\frac{1}{5^2}\right)\left(1-\frac{1}{6^2}\right)\left(1-\frac{1}{7^2}\right)\left(1-\frac{1}{8^2}\right)\) ?

A.14
B.18
C. 20
D. 22
E.24
Source: — Problem Solving |

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Re: What is the value of

by Max@Math Revolution » Thu Apr 30, 2020 6:20 am
=>

32(1-1/2^2)(1-1/3^2)(1-1/4^2)(1-1/5^2)(1-1/6^2)(1-1/7^2)(1-1/8^2)
= 32(1-1/2)(1+1/2)(1-1/3)(1+1/3)(1-1/4)(1+1/4)...(1-1/8)(1+1/8)
= 32(1-1/2)(1-1/3)(1-1/4)...(1-1/8)(1+1/2)(1+1/3)(1+1/4)...(1+1/8)
= 32(1/2)(2/3)(3/4)...(7/8)(3/2)(4/3)(5/4)...(9/8)
= 32*1/8*9/2 = 18.

Therefore, B is the answer.
Answer: B