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Is n the square of an integer?

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Is n the square of an integer?  [#permalink]

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New post 19 Jan 2016, 09:38
1
4
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A
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C
D
E

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  95% (hard)

Question Stats:

24% (01:46) correct 76% (01:45) wrong based on 81 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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Re: Is n the square of an integer?  [#permalink]

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New post 19 Jan 2016, 09:39
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1
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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Re: Is n the square of an integer?  [#permalink]

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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]

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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


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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Re: Is n the square of an integer? &nbs [#permalink] 24 Mar 2017, 23:59
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