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Which of the following expressions can be written as an inte

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boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
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Which of the following expressions can be written as an inte

Post Wed May 04, 2016 4:35 am
Which of the following expressions can be written as an integer?

I. (sqrt82 + sqrt82)^2
II. (82)(sqrt82)
III. (sqrt82)(sqrt82)/82

A) None
B) I only
C) III only
D) 1 and II
E) I and III

OA: E

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Post Wed Dec 20, 2017 10:53 am
boomgoesthegmat wrote:
Which of the following expressions can be written as an integer?

I. (sqrt82 + sqrt82)^2
II. (82)(sqrt82)
III. (sqrt82)(sqrt82)/82

A) None
B) I only
C) III only
D) 1 and II
E) I and III
Let’s simplify each expression:

1. (√82 + √82)^2

(√82 + √82)^2 = (2√82)^2 = 4 x 82 = 328

We see that this an integer.

2. 82√82

Since √82 is a non-terminating decimal, 82√82 is not an integer.

3. (√82√82)/82

(√82√82)/82 = 82/82 = 1

We see that this is an integer.

Answer: E

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Scott Woodbury-Stewart Founder and CEO

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GMAT/MBA Expert

Post Wed May 04, 2016 12:14 pm
boomgoesthegmat wrote:
Which of the following expressions can be written as an integer?

I. (√82 + √82)²
II. (82)(√82)
III. (√82)(√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

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