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For the positive integers q, r, s, and t,

This topic has 2 expert replies and 0 member replies

For the positive integers q, r, s, and t,

Post Thu Sep 14, 2017 1:39 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:

    A. 32
    B. 38
    C. 44
    D. 52
    E. 63

    OA is B.

    I am a little confuse. Can any expert help me?

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Thu Sep 14, 2017 2:07 pm
    Vincen wrote:
    For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:

    A. 32
    B. 38
    C. 44
    D. 52
    E. 63
    Great question!!

    USEFUL PROPERTY:
    When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D
    For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0
    Conversely, if I know that, when k is divided by w, the remainder is 5, then I know that w must be greater than 5

    The remainder when q is divided by r is 7
    This tells us that r is greater than 7

    s is divided by t is 3
    This tells us that t is greater than 3

    Now check the answer choices...

    A) 32
    Is it POSSIBLE for rt to equal 32?
    Yes, if r = 8 and t = 4, then rt = 32
    ELIMINATE A

    B) 38
    Is it POSSIBLE for rt to equal 38?
    NO.
    There are only two ways to write 38 as the product of POSITIVE INTEGERS:
    i) (2)(19) = 38
    ii) (1)(38) = 38
    If r is greater than 7 and t is greater than 3, there's no way that one of the values (r or t) can equal 1 or 2.

    Answer: B

    Cheers,
    Brent

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    Post Tue Sep 19, 2017 2:50 pm
    Vincen wrote:
    For the positive integers q, r, s, and t, the remainder when q is divided by r is 7 and the remainder when s is divided by t is 3. All of the following are possible values for the product rt EXCEPT:

    A. 32
    B. 38
    C. 44
    D. 52
    E. 63

    OA is B.
    To solve this problem, we need a clear insight on division between integers. Recall that in any division, the divisor must be greater than the remainder. Thus, we know that r > 7 and t > 3. In the other words, r ≥ 8 and t ≥ 4. Thus, rt is at least 8(4) = 32. Looking at the answer choices, all of them are at least 32. Therefore, we need further analysis. One thing we can do is to factor each answer choice:

    32 = 1(32) = 2(16) = 4(8)

    38 = 1(38) = 2(19)

    44 = 1(44) = 2(22) = 4(11)

    52 = 1(52) = 4(13)

    63 = 1(63) = 3(21) = 7(9)

    We see that all the answer choices except 38 can be expressed as a product of two factors where one factor is greater than 7 and the other is greater than 3. For example, rt could be 44 since r could be 11 and t could be 4. The only answer choice that doesn’t have this property is 38. Thus, 38 is the correct answer.

    Answer: B

    _________________
    Jeffrey Miller Head of GMAT Instruction

    Thanked by: Vincen

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