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# GMAT.QR.0300 Book Question: 300

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Intern
Joined: 16 May 2017
Posts: 33
Location: India

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19 Nov 2017, 06:54
GMAT.QR.0300
Book Question: 300

If a and b are positive integers, is a b 3 an integer?

a is an integer.
b = a
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements (1) and (2) TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are not sufficient.

Explanation in Wiley's website :

Arithmetic Properties of numbers

Given that a is an integer, then a = 4 is possible. If, in addition b = 1, then a b 3 = 4 3 is not an integer. However, if, in addition b = 2, then a b 3 = 8 3 = 2 is an integer; NOT sufficient.
Given that b = a , then a b 3 = a a 3 = a 3 3 = a 3 3 = a = b is an integer; SUFFICIENT.
Statement 2 alone is sufficient.

Hi can someone explain to me, what is the logic? I did not get this one!

thanks
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5848
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: GMAT.QR.0300 Book Question: 300 [#permalink]

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20 Nov 2017, 23:06
bapism07 wrote:
GMAT.QR.0300
Book Question: 300

If a and b are positive integers, is a b 3 an integer?

a is an integer.
b = a
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements (1) and (2) TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are not sufficient.

Explanation in Wiley's website :

Arithmetic Properties of numbers

Given that a is an integer, then a = 4 is possible. If, in addition b = 1, then a b 3 = 4 3 is not an integer. However, if, in addition b = 2, then a b 3 = 8 3 = 2 is an integer; NOT sufficient.
Given that b = a , then a b 3 = a a 3 = a 3 3 = a 3 3 = a = b is an integer; SUFFICIENT.
Statement 2 alone is sufficient.

Hi can someone explain to me, what is the logic? I did not get this one!

thanks

The original question is found as follows.

If a and b are positive integers, is $$\sqrt[3]{ab}$$ an an integer?

(1) $$\sqrt{a}$$ is an integer
(2) $$b=\sqrt{a}$$

Your solution for the condition 1) is correct.
Solution for the condition 2) is as follows.

Since $$b=\sqrt{a}$$, we have $$a = b^2$$.
$$\sqrt[3]{ab} = \sqrt[3]{b^2 \cdot b} = \sqrt[3]{b^3} = b$$
Thus this is sufficient.
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Intern
Joined: 16 May 2017
Posts: 33
Location: India
Re: GMAT.QR.0300 Book Question: 300 [#permalink]

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03 Dec 2017, 02:45
Hey math revolution

Actually, i was practicing the OG questions through the website gmat.wiley.com. There few of the special characters (like boldface characters for RC & CR questions, square root, fractions and few decimals were not viewed or viewed in a collapsed manner for DS and PS questions. I had informed them through message and they replied that they are working on it.
Re: GMAT.QR.0300 Book Question: 300   [#permalink] 03 Dec 2017, 02:45
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