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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
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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 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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