PareshGmat wrote:
If we take x = 2 & calculate, we cant get the answers;
seems that x has to be taken 1 to execute all the options
Any random value of x will not help you get the answer. Even if you do not try x = 1, you can use reasoning to solve this question.
A. \(x^5\)
If x is a number with an even power, such as \(x = a^4\) (a is an integer), then \(x^5 = a^{20} = n^2\)
n will be \(a^{10}\), an integer here.
B. \(x^2 - 1\)
\(x^2 - 1 = n^2\)
You need two consecutive perfect squares. Only 0 and 1 are consecutive perfect squares. Thereafter, the distance between perfect squares keeps increasing. x needs to be a positive integers so if x = 1, n = 0 (an integer)
C. \(\sqrt{x^8}\)
\(\sqrt{x^8} = x^4 = n^2\)
n will be \(x^2\), an integer here.
D. \(x^2 + 1\)
x is a positive integer so it must be at least 1. After 1, there are no two consecutive integers. n cannot be an integer.
E. \(\sqrt{x^5}\)
If x is a number with an even power which is a multiple of 4, such as \(x = a^4\) (a is an integer), then \(\sqrt{x^5} = \sqrt{a^{20}} = a^{10} = n^2\)
n will be \(a^5\), an integer here.
Answer (D)
_________________
Karishma
Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >