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Is the product of two positive integers x

This topic has 1 expert reply and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
Joined
24 Jul 2017
Posted:
83 messages

Is the product of two positive integers x

Post Wed Aug 02, 2017 11:14 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Is the product of two positive integers x and y divisible by the sum of x and of y ?
    (1) x = y
    (2) x = 2

    Official Guide question
    Answer: C

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    Post Wed Aug 02, 2017 11:31 am
    For a DS question that gives you few constraints in the question stem, the best strategy is to TEST NUMBERS.

    Start by testing easy numbers that fit the statement, and see if you get a "yes" or "no" answer to the question. Then test another case to try to get the opposite answer.

    Is the product of two positive integers x and y divisible by the sum of x and of y ?

    (1) x = y


    Case 1:
    x = 1
    y = 1
    xy = 1
    x + y = 2
    No, the product xy is not divisible by (x + y). Let's see if we can think of a case that would give us a "yes" answer.

    Case 2:
    x = 2
    y = 2
    xy = 4
    x + y = 4
    Yes, the product xy is divisible by the sum x + y. If one case gives us a "no" and the other gives us a "yes," it's insufficient.

    (2) x = 2

    Case 1:
    x = 2
    y = 2
    We can recycle a test we used above - we know that this gives us a "yes" answer. Now try another case to see if we can get a "no."

    Case 2:
    x = 2
    y = 3
    xy = 6
    x + y = 5
    Since 6 is not divisible by 5, then answer is "no." Insufficient.

    (1) & (2) together:
    If x = 2 and x = y, then y = 2. We know that xy = 4 and x+ y = 4, so we have sufficient information.

    The answer is C.

    _________________


    Ceilidh Erickson
    Manhattan Prep GMAT & GRE instructor
    EdM in Mind, Brain, and Education
    Harvard Graduate School of Education


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