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If the sum of the reciprocals of two consecutive

This topic has 2 expert replies and 1 member reply

If the sum of the reciprocals of two consecutive

Post Sun Sep 24, 2017 6:41 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If the sum of the reciprocals of two consecutive odd integers is 12/35 then the greater of the two integers is

    A) 3
    B) 5
    C) 7
    D) 9
    E) 11

    The OA is C.

    Should I solve the equation 1/(2k+1) + 1/(2k+3) = 12/35? Or there is another way to solve it?

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    pannalal Junior | Next Rank: 30 Posts Default Avatar
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    Post Sun Sep 24, 2017 6:58 am
    Let us assume that two consecutive odd integers are a and b where b = a+2. Then, sum of their reciprocal is (a+b)/ab. We have been given that sum of two consecutive odd integers is 12/35.

    As GCD of two consecutive integers is always 1, sum of these two is 12 and multiplication of these two integers is 35.

    Obviously, these two odd integers are 5 and 7.

    Thus, larger integer is 7. So, answer is C.



    Last edited by pannalal on Sun Sep 24, 2017 7:22 am; edited 1 time in total

    Post Sun Sep 24, 2017 7:01 am
    Vincen wrote:
    If the sum of the reciprocals of two consecutive odd integers is 12/35 then the greater of the two integers is

    A) 3
    B) 5
    C) 7
    D) 9
    E) 11
    Since the denominator of the sum is 35, and since 35 equals the product of 5 and 7 (two consecutive odd integers), let's start by testing whether 5 and 7 are the integers in question.

    So, the RECIPROCALS are 1/5 and 1/7
    1/5 + 1/7 = 7/35 + 5/35
    = 12/35
    Voila!!

    So, the odd integers are 5 and 7
    The greater of the two integers is 7
    Answer: C

    Cheers,
    Brent

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    Post Sun Sep 24, 2017 10:34 am
    Hi Vincen,

    We're told that the sum of the reciprocals of two CONSECUTIVE ODD integers is 12/35. We're asked for the GREATER of the two integers. This question can be solved by TESTing THE ANSWERS.

    Let's TEST Answer B: 5
    IF.... the values are 3 and 5....
    then the sum of the reciprocals is 1/3 + 1/5 = 5/15 + 3/15 = 8/15
    This is clearly not the correct answer, but the denominator ends in a '5', so it's likely that 12/35 will ALSO include a 5...

    Let's TEST Answer C: 7
    IF.... the values are 5 and 7....
    then the sum of the reciprocals is 1/5 + 1/7 = 7/35 + 5/35 = 12/35
    This is an exact match for what we were told, so this MUST be the answer.

    Final Answer: C

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