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GMAT.QR.0300 Book Question: 300

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GMAT.QR.0300 Book Question: 300 [#permalink]

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New post 19 Nov 2017, 05:54
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 :

C -You Answered Incorrectly.
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

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Re: GMAT.QR.0300 Book Question: 300 [#permalink]

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New post 20 Nov 2017, 22:06
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 :

C -You Answered Incorrectly.
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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Kudos [?]: 3172 [0], given: 0

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avatar
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Joined: 16 May 2017
Posts: 13

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Re: GMAT.QR.0300 Book Question: 300 [#permalink]

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New post 03 Dec 2017, 01:45
Hey math revolution

Thanks for your reply.

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.

Kudos [?]: 1 [0], given: 89

Re: GMAT.QR.0300 Book Question: 300   [#permalink] 03 Dec 2017, 01:45
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