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What is w + z? - Number Properties

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LulaBrazilia Really wants to Beat The GMAT! Default Avatar
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What is w + z? - Number Properties Post Tue Feb 25, 2014 8:43 am
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    If the product of the integers w, x, y, and z is 770 and if 1 < w < x < y < z, what is the value of w + z ?

    A) 10

    B) 13

    C) 16

    D) 18

    E) 21

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    Post Tue Feb 25, 2014 8:46 am
    LulaBrazilia wrote:
    If the product of the integers w, x, y, and z is 770 and if 1 < w < x < y < z, what is the value of w + z ?

    A) 10
    B) 13
    C) 16
    D) 18
    E) 21
    This requires us to use prime factorization.
    770 = (2)(5)(7)(11)

    So, if 1 < w < x < y < z then:
    w = 2
    x = 5
    y = 7
    z = 11

    This means that w + z = 2 + 11 = 13 = B


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    Patrick_GMATFix GMAT Instructor
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    Post Tue Feb 25, 2014 8:54 am
    Questions about factors & multiples are usually best handled by breaking numbers into their prime factors, since these primes are the building blocks of all integers. The full solution below is taken from the GMATFix App.



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    Post Tue Feb 25, 2014 9:49 am
    wxyz = 770

    770 = 7 x 11 x 5 x 2

    Since, 1 < w < x < y < z

    w = 2
    z = 11

    w + z = 13


    R A H U L

    Post Tue Feb 25, 2014 2:29 pm
    Hi LulaBrazilia,

    Each of the explanations in this string focused on "prime factorization", which is a MUST to solving this question.

    The reason you KNOW that prime factorization is necessary is in the wording and "design" of the question. Here's why:

    The question asks for THE sum of the biggest and smallest variables, NOT what COULD BE the sum. Since 1<w<x<y<z there must be a fixed value for each of the variables, meaning that they're most likely prime numbers. If they weren't prime, then they'd have factors and it's possible that the variables (especially the z) could change.

    For example, the numbers 2, 6, 8 and 10 would have a product of 960. So do the numbers 2, 3, 8 and 20. In this scenario z could be different values, which would change the answer to the question. But this scenario does not match the wording of the prompt.

    When thinking about how to solve a problem, pay attention to the specific wording of the prompt. GMAT questions are very carefully worded and often provide clues as to how to approach the problem (and sometimes the easiest approach to it).

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