The decimal representation of the number is given above,

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by Jay@ManhattanReview » Thu Nov 28, 2019 10:53 pm
AAPL wrote:e-GMAT

\(\frac{\sqrt{z}}{4}=a.bc\)

The decimal representation of the number is given above, where \(z\) is a positive number and \(a, b\) and \(c\) are single-digit non-negative integers. Is \(a=0\)?

1) \(\frac{z^2}{4} > 64\)

2) \(\frac{z^{0.25}}{4} > 2\)

OA D
For a = 0, a.bc must be less than 1; thus, \(0<\frac{\sqrt{z}}{4}<1\). Thus, 0 < z < 16.

Let's take each statement one by one.

1) \(\frac{z^2}{4} > 64\)

\(\frac{z}{2} > 8\)
\(z > 16\)
\(\sqrt{z} > 4\)

\(z > 16\). The answer is no. Sufficient.


2) \(\frac{z^{0.25}}{4} > 2\)

\(z^{0.25} > 8\)
\(z > 8^4\). The answer is no. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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