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The sum of 4 different odd integers is 64.

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jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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Posted:
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The sum of 4 different odd integers is 64.

Post Mon Aug 07, 2017 8:46 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    The sum of 4 different odd integers is 64. What is the value of the greatest of these integers?
    (1) The integers are consecutive odd numbers
    (2) Of these integers, the greatest is 6 more than the least.

    Official Guide question
    Answer: D

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    Post Mon Aug 07, 2017 10:46 am
    jjjinapinch wrote:
    The sum of 4 different odd integers is 64. What is the value of the greatest of these integers?
    (1) The integers are consecutive odd numbers
    (2) Of these integers, the greatest is 6 more than the least.

    Official Guide question
    Answer: D
    Target question: What is the value of the greatest of these integers?

    Given: The 4 numbers are different odd integers, and their sum is 64.

    Statement 1: The integers are consecutive odd numbers
    Let x = the first odd integer
    So, x + 2 = the 2nd odd integer
    So, x + 4 = the 3rd odd integer
    So, x + 6 = the 4th odd integer
    Since we're told the sum is 64, we can write: x + (x+2) + (x+4) + (x+6) = 64
    Since we COULD solve this equation for x, we COULD determine all 4 values, which means we COULD determine the value of the greatest of the 4 odd integers
    Of course, we're not going to waste valuable time solving the equation, since our sole goal is to determine whether the statement provides sufficient information.
    Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

    Statement 2: Of these integers, the greatest is 6 more than the least.
    Notice that the 4 CONSECUTIVE integers (from statement 1) can be written as x, x+2, x+4 and x+6
    Notice that the biggest number (x+6) is 6 more than the smallest number (x).
    Since the 4 odd integers are different, statement 2 is basically telling us that the 4 integers are CONSECUTIVE
    So, for the same reason we found statement 1 to be SUFFICIENT, we can also conclude that statement 2 is SUFFICIENT

    Answer: D

    Cheers,
    Brent

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