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

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

by dollydevashryee » Sat Sep 05, 2020 2:59 pm
I. $$ \left(\sqrt{82}+\sqrt{82}\right)^2 = \left(2\sqrt{82}\right)^2 =\ 4\cdot 82 = integer $$
II. \(\sqrt{82}\) not an integer so \(82\sqrt{82}\) can't be an integer.
III. $$\frac{\sqrt{82}\cdot \sqrt{82}}{82} = \frac{82}{82}= 1 = integer$$

Therefore the answer is E -> I and III.
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Re: Which of the following expressions can be written as an integer?

by Brent@GMATPrepNow » Mon Sep 07, 2020 2:21 pm
AAPL wrote: ↑
Sat Sep 05, 2020 12:48 pm
 Official Guide

I. \(\left(\sqrt{82} + \sqrt{82}\right)^2\)
II. \(82\sqrt{82}\)
III. \(\dfrac{\sqrt{82}\cdot \sqrt{82}}{82}\)

A. None
B. I only
C. III only
D. I and II
E. I and III

OA E
We'll use the fact that (√82)(√82) = 82

I. (√82 + √82)² = (2√82)² = (2√82)(2√82) = (2)(2)(√82)(√82) = (4)(82) = some integer
III. (√82)(√82)/82 = 82/82 = 1

NOTE: As we're checking expressions, we should also be checking the answer choices.
Since I and III both work, the correct answer must be E, since there's no option for all 3 to be true.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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