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 integerfor 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 statements4n 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
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,
.
This will really clear things up for me and improve my understanding of numbers.