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Remainder

This topic has 2 expert replies and 0 member replies

Remainder

Post Sat Sep 30, 2017 7:45 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    A number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34. Such a least possible number is

    A. 74
    B. 75
    C. 175
    D. 680
    E. 690
    Please help me out on how you solve this.
    qa is b

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Sat Oct 07, 2017 3:29 pm
    Hi Roland. This an interesting question.

    To start, let x be the number we are looking for. It says that x/5 gives a number which is 8 more than the remainder... As the remainder is an integer number, then x/5 is an integer. It implies that x is divisible by 5. So, option A is out.

    Now, let's try with option B.

    We have that 75/5 = 15.
    Now, when we divide 75 by 34, the remainder is 7.
    If we add 7 + 8 we will get 15 which is the result of dividing 75 by 5.

    So, B is the correct option.

    I hope it helps you.

    I'm available if you'd like any follow up.

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    GMAT/MBA Expert

    Post Thu Oct 12, 2017 9:28 pm
    Let's call our number n. We're told that

    n/5 = 8 + (remainder of n/34)

    To find that remainder, we can say that n = 34*something + r, or n = 34z + r, or r = n - 34z. Once we've got that, we can replace (remainder of n/34) with r, or with n - 34z:

    n/5 = 8 + n - 34z

    34z = 8 + (4/5)n

    170z = 40 + 4n

    To solve this, we need n and z both to be integers. We want the smallest possible solutions, so let's start with z = 1. That gives n = 32.5 - not an integer!

    If we try z = 2, however, we get n = 75, which is an integer, and our smallest solution.

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