Official Guide Quantitative Review 2nd Ed. DS #110
Following is the question with explanation given in OG.
110. If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?
(1) n is even.
(2) The cube root of n is an integer.
OG Explanation:
[Arithmetic Properties of numbers]
(1) If n is even, there are several possible even values of n that are squares of integers and
are between 2 and 100, namely, 4, 16, 36, and 64; NOT sufficient.
(2) If the cube root of n is an integer, it means that n must not only be the square of an
integer but also the cube of an integer. There is only one such value of n between 2 and
100, which is 64; SUFFICIENT.
The correct answer is B; statement 2 alone is sufficient.
However, I think the answer should be "C".
According to the second statement, 27 also qualifies to be a valid value of n, in addition to 64. As we cannot definitely say what is n, statement 2 is not sufficient. But if we consider statements 1 and 2 together then we can exclude 27 from valid number list of n and definitely find value of n to be 64.
Is anything wrong in my observation?
Following is the question with explanation given in OG.
110. If n is an integer between 2 and 100 and if n is also the square of an integer, what is the value of n?
(1) n is even.
(2) The cube root of n is an integer.
OG Explanation:
[Arithmetic Properties of numbers]
(1) If n is even, there are several possible even values of n that are squares of integers and
are between 2 and 100, namely, 4, 16, 36, and 64; NOT sufficient.
(2) If the cube root of n is an integer, it means that n must not only be the square of an
integer but also the cube of an integer. There is only one such value of n between 2 and
100, which is 64; SUFFICIENT.
The correct answer is B; statement 2 alone is sufficient.
However, I think the answer should be "C".
According to the second statement, 27 also qualifies to be a valid value of n, in addition to 64. As we cannot definitely say what is n, statement 2 is not sufficient. But if we consider statements 1 and 2 together then we can exclude 27 from valid number list of n and definitely find value of n to be 64.
Is anything wrong in my observation?
