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Is a an integer?

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Is a an integer?

by BTGmoderatorDC » Mon Aug 26, 2019 10:06 pm

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Is a an integer?

(1) a^3 is an integer.
(2) The cube root of a is an integer.

OA B

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by Ian Stewart » Tue Aug 27, 2019 9:03 am

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Statement 1 tells us that a is the cube root of some integer. Sometimes cube roots of integers are themselves integers, and sometimes not, so Statement 1 is not sufficient.

Statement 2 tells us that the cube root of a is an integer, so a itself will be the cube of an integer, and must therefore be an integer. So Statement 2 is sufficient and the answer is B.
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by swerve » Thu Aug 29, 2019 2:44 pm

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BTGmoderatorDC wrote:Is a an integer?

(1) a^3 is an integer.
(2) The cube root of a is an integer.

OA B

Source: Veritas Prep
From 1:
We don't know the orientation of a, what if it was

\(a = 3^{1/3}\), we satisfy 1, but answer to the question will be a No
\(a = 3\), we satisfy 1, and answer the question a Yes

From 2:
The cube root of a is an integer.

This will always be true, \(a^{1/3} = 3^{3\cdot 1/3} =\) Yes

Therefore, __B__