Is n the square of an integer?

Question

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

GMATinsight · Answer

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  C

prashantrchawla · Answer

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.

ShashankDave · Answer

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.

Probus · Answer

hi  chetan2u ,

Just Curious to know 
 if we were told that n is integer, would the correct answer for this question be D

bumpbot · Answer

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Is n the square of an integer?

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