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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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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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    Post Fri Dec 08, 2017 7:27 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
    We are given that the sum of 4 different odd integers is 64 and need to determine the value of the greatest of these integers.

    Statement One Alone:

    The integers are consecutive odd numbers

    Since we know that the integers are consecutive odd integers, we can denote the integers as x, x + 2, x + 4, and x + 6 (notice that the largest integer is x + 6).

    Since the sum of these integers is 64, we can create the following equation and determine x:

    x + (x + 2) + (x + 4) + (x + 6) = 64

    4x + 12 = 64

    4x = 52

    x = 13

    Thus, the largest integer is 13 + 6 = 19.

    Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

    Statement Two Alone:

    Of these integers, the greatest is 6 more than the least.

    Using the information in statement two, we can determine that the four integers are consecutive odd integers. Let’s further elaborate on this idea. If we take any set of four consecutive odd integers, {1, 3, 5, 7}, {9, 11, 13, 15}, or {19, 21, 23, 25}, notice that in ALL CASES the greatest integer in the set is always 6 more than the least integer. In other words, the only way to fit two odd integers between the odd integers n and n + 6 is if the two added odd integers are n + 2 and n +4, thus making them consecutive odd integers. Since we have determined that we have a set of four consecutive odd integers and that their sum is 64, we can determine the value of all the integers in the set, including the value of the greatest one, in the same way we did in statement one. Thus, statement two is also sufficient to answer the question.

    Answer: D

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