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x denotes the decimal fraction part of

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by Max@Math Revolution » Mon Mar 09, 2020 8:30 am

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[GMAT math practice question]

x denotes the decimal fraction part of \(\sqrt{57}\) . What is x(x + 14)?

A. 6
B. 7
C. 8
D. 9
E. 10
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Re: x denotes the decimal fraction part of

by Max@Math Revolution » Thu Mar 12, 2020 12:13 am
=>


7 = √49 < √57 < √64 = 8
We have x = √57 – 7 since x denotes the decimal fraction part of √57.

Then
x(x + 14) = (√57 – 7)(√57 + 14 - 7)
x(x + 14) = (√57 – 7)(√57 + 7) (adding like terms)
x(x + 14) = 57 + 7√57 - 7√57 – 49 (foiling the right side)
x(x + 14) = 57 – 49 (cancelling terms)
x(x + 14) = 8 (adding like terms)

Therefore, C is the answer.
Answer: C
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