Question 44 Data Sufficiency: Diagnostic GMAT Official Guide
Question 43 (DS34400.02): GMAT Online Question Bank (GMAT Official Guide 2021 and beyond)
Video explanation: If m and n are positive integers, is $(\sqrt{m})^n$ an integer?…
Comments
Parth Patelsays
I think I am getting tripped up on something simple, can you please help me figure out where I am going wrong? For statement 1, if you raise it to a negative power (which is also an integer) then it is possible to end up with a fraction. Doesn’t that mean it’s not sufficient alone?
You are right that there are two square roots of $16$, which are $4$ and $-4$. However, the symbol $\sqrt{}$ is used to denote the nonnegative square root of the nonnegative number $n$. That means $\sqrt{16} = 4$ and $\sqrt{16} \neq -4$.
I think I am getting tripped up on something simple, can you please help me figure out where I am going wrong? For statement 1, if you raise it to a negative power (which is also an integer) then it is possible to end up with a fraction. Doesn’t that mean it’s not sufficient alone?
Nevermind. I get it, it’s restricted to positive integers in the problem.
square root of 4 is 2 and -2, square root of 9 is 3 and -3.
You are right that there are two square roots of $16$, which are $4$ and $-4$. However, the symbol $\sqrt{}$ is used to denote the nonnegative square root of the nonnegative number $n$. That means $\sqrt{16} = 4$ and $\sqrt{16} \neq -4$.