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Is n the square of an integer?

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GMATinsight
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Is n the square of an integer? [#permalink] New post   19 Jan 2016, 09:38
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Question Stats:

22% (02:04) correct 78% (01:52) wrong based on 105 sessions
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Is n the square of an integer?

Statement 1: 4n is the square of an integer
Statement 2: n^3 is the square of an integer
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C
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Re: Is n the square of an integer? [#permalink] New post   19 Jan 2016, 09:39
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GMATinsight wrote:
Is n the square of an integer?

Statement 1: 4n is the square of an integer
Statement 2: n^3 is the square of an integer



Question : Is n the square of an integer?

Statement 1: 4n is the square of an integer
for n = 1/4, 4n = 1 which is square of Integer but n is not square of an Integer (NO)
for n = 1, 4n = 4 which is square of Integer and n also is square of an Integer (YES)
NOT SUFFICIENT

Statement 2: n^3 is the square of an integer
for n^3 = 4, n = cube root of 4 which not square of an Integer (NO)
for n^3 = 1, n = 1 which is square of Integer(YES)
NOT SUFFICIENT

Combining the two statements
4n is square of an Integer and n^3 also is square of an Integer which is possible only when n is an Integer and also a perfect square
e.g. n=4, n^3=64, 4n=16 all Squares of Integers
e.g. n=1, n^3=1, 4n=4 all Squares of Integers
SUFFICIENT

Answer: option
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C
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Re: Is n the square of an integer? [#permalink] New post   08 Dec 2016, 01:39
Given,
Statement 1: 4n is the square of an integer. there are many to satisfy this statement.
n=1, 4n=4
n=4, 4n=16
n=9, 4n=36........... Not Sufficient
Statement 2: n^3 is the square of an integer
n=4, n^3 = 4^3 = 64 (square of 8)
n=9, n^3 = 9^3 = 729 (square of 27)............. Not sufficient

Taking both the options, we can prove that values of n = 4 and 9 satisfy both the equations and both are square of integers.
Answer C.
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Re: Is n the square of an integer? [#permalink] New post   24 Mar 2017, 23:59
GMATinsight wrote:
GMATinsight wrote:
Is n the square of an integer?

Statement 1: 4n is the square of an integer
Statement 2: n^3 is the square of an integer



Question : Is n the square of an integer?

Statement 1: 4n is the square of an integer
for n = 1/4, 4n = 1 which is square of Integer but n is not square of an Integer (NO)
for n = 1, 4n = 4 which is square of Integer and n also is square of an Integer (YES)
NOT SUFFICIENT

Statement 2: n^3 is the square of an integer
for n^3 = 4, n = cube root of 4 which not square of an Integer (NO)
for n^3 = 1, n = 1 which is square of Integer(YES)
NOT SUFFICIENT

Combining the two statements
4n is square of an Integer and n^3 also is square of an Integer which is possible only when n is an Integer and also a perfect square
e.g. n=4, n^3=64, 4n=16 all Squares of Integers
e.g. n=1, n^3=1, 4n=4 all Squares of Integers
SUFFICIENT

Answer: option
Show Spoiler
C


Dear GMATinsight,

First, +1 for the question. I eventually chose (C) and that turned out to be correct. But I am not very convinced with it. I need help from you. Please explain using an algebraic approach that when both the statements are together true,

n necessarily has to be an integer.

This will really clear things up for me and improve my understanding of numbers.
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Probus
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Re: Is n the square of an integer? [#permalink] New post   15 Apr 2019, 16:12
hi chetan2u,

Just Curious to know
if we were told that n is integer, would the correct answer for this question be D
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Re: Is n the square of an integer? [#permalink] New post   22 Sep 2021, 22:32
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Re: Is n the square of an integer? [#permalink]
22 Sep 2021, 22:32
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