remainder

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buoyant Master | Next Rank: 500 Posts Default Avatar
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remainder

Post Thu Dec 25, 2014 8:02 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If k is an even integer, what is the remainder when k is divided
    by 10 ?
    (1) The remainder when k is divided by 5 is equal to the
    remainder when k is divided by 10.
    (2) The remainder is greater than 3.

    OA:C

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    Post Thu Dec 25, 2014 8:17 pm
    Hi buoyant,

    This question is perfect for TESTing VALUES, but there are a few Number Properties that are worth noting (and taking advantage of).

    We're told that K is an EVEN integer. We're asked for the REMAINDER when K is divided by 10.

    Fact 1: K/5 has the same remainder as K/10

    Since K has to be EVEN the possible remainders for K/5 are severely limited...

    If
    K = 12...
    12/5 = 2r2
    12/10 = 1r2
    The answer to the question is 2

    K = 14
    14/5 = 2r4
    14/10 = 1r4
    The answer to the question is 4

    **Note that K is EVEN, so K/5 means that the remainder MUST be 0, 2 or 4**
    Fact 1 is INSUFFICIENT

    Fact 2: The remainder is greater than 3

    If
    K = 14
    14/10 = 1r4

    K = 16
    16/10 = 1r6
    Fact 2 is INSUFFICIENT

    Combined, we know...
    The remainder is either 0, 2 or 4
    The remainder is greater than 3
    The ONLY value that fits both is 4
    Combined, SUFFICIENT

    Final Answer: C

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Thanked by: buoyant
    Post Fri Dec 26, 2014 12:56 pm
    buoyant wrote:
    If k is an even integer, what is the remainder when k is divided by 10?

    (1) The remainder when k is divided by 5 is equal to the remainder when k is divided by 10.
    (2) The remainder is greater than 3.

    OA:C
    Target question: What is the remainder when k is divided by 10?
    This question is a good candidate for REPHRASING the target question.
    Aside: We have a free video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

    Let's make a few observations:
    24 divided by 10 equals 2 with remainder 4
    70 divided by 10 equals 7 with remainder 0
    86 divided by 10 equals 8 with remainder 6
    2 divided by 10 equals 0 with remainder 2

    As you can see, the remainder (when we divide by 10) will always be the same as the UNITS digit of k. So, we can write....
    REPHRASED target question: What is the units digit of k?

    Given: k is an EVEN integer
    Since k is an EVEN integer, then we know that, the UNITS digit of k will be 0, 2, 4, 6, or 8.

    Statement 1: The remainder when k is divided by 5 is equal to the remainder when k is divided by 10.
    Let's examine all possible cases:
    case a: units digit of k is 0: When k is divided by 5, the remainder is 0. When k is divided by 10, the remainder is also 0. So, the units digit of k COULD be 0
    case b: units digit of k is 2: When k is divided by 5, the remainder is 2. When k is divided by 10, the remainder is also 2. So, the units digit of k COULD be 2
    case c: units digit of k is 4: When k is divided by 5, the remainder is 4. When k is divided by 10, the remainder is also 4. So, the units digit of k COULD be 4
    case d: units digit of k is 6: When k is divided by 5, the remainder is 1. When k is divided by 10, the remainder is 6. So, the units digit of k CANNOT be 6
    case e: units digit of k is 8: When k is divided by 5, the remainder is 3. When k is divided by 10, the remainder is 8. So, the units digit of k CANNOT be 8
    Since the units digit of k COULD be 0, 2 or 4, statement 1 is NOT SUFFICIENT

    Statement 2: The remainder [when k is divided by 10] is greater than 3.
    In other words, the units digit of k COULD be 4, 6 or 8
    Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

    Statements 1 and 2 combined
    Statement 1 tells us that the units digit of k COULD be 0, 2 or 4
    Statement 2 tells us that the units digit of k COULD be 4, 6 or 8
    The ONLY possible scenario that satisfies BOTH statements is that the units digit of k MUST be 4
    Since we can answer the target question with certainty, the combined statements are SUFFICIENT

    Answer = C

    Cheers,
    Brent

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    Thanked by: buoyant
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    Gurpreet singh Senior | Next Rank: 100 Posts Default Avatar
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    Post Sat Jun 18, 2016 10:49 pm
    Divisibility rule 0<r<10-where r is reminder and 10 is the divisor.

    now k is even so k can be 2, 4, 6 or 8

    statement 1 Reminder r is same when k is divided by 5. so reminder could be 2 or 4. -Insufficient
    Statement 2 Reminder is greater than 3-could be 2,4,6 or 8.

    Combining both the statements reminder is 4

    Answer c.

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