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GMAT - Problem Solving - Arithmetic

Which of the following expressions can be written as an integer?

Which of the following expressions can be written as an integer?

{ I.\quad \left( \sqrt { 82 }  \sqrt { 82 } \right) }^{ 2 }\\ \\ II.\quad 82\sqrt { 82 } \\ \\ III.\quad \frac { \sqrt { 82 } \sqrt { 82 } }{ 82 }

(A) None
(B) I only
(C) III only
(D) I and II
(E) I and III

Statement I

{ \left( \sqrt { 82 } +\sqrt { 82 } \right) }^{ 2 }\\ =\quad { \left( 2\sqrt { 82 } \right) }^{ 2 }\\ =\quad 4*82\quad =\quad 328

Yes

Statement II

\\ \\ 82\sqrt { 82 }

No further simplification possible. Can't be written as an integer

Statement III

\\ \\ \frac { \sqrt { 82 } \sqrt { 82 } }{ 82 } \\ \\ =\frac { 82 }{ 82 } =1

Can be written as an integer

Correct option E.