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GMAT Problem of the Week. Issue#35


<img 70-446 class=”aligncenter size-thumbnail wp-image-698″ src=”http://blog.mbastrategy.ua/wp-content/uploads/2013/09/numbers1-150×150.jpg” alt=”" width=”150″ height=”150″ />

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If n is a positive integer, and its greatest divisor different from n 70-447 itself equals to 91, casinos how many possible values are there for n?

(A) 3

(B) 4

(C) 37

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(D) 90

(E) Infinitely many

9 thoughts on “GMAT Problem of the Week. Issue#35

  1. Roman, could you please add some details to your comment? =)
    By the way, here we do not deal with the greatest COMMON divisor, just the greatest divisor of a number.

  2. N – positive integer
    D – greatest divisor

    So,
    N*D-D=91, hence
    (1) D(N-1)=13*7 or
    (2) D(N-1)=91*1

    ->(1) D=7, N=14 (N-1=13)
    D=13, N=8 (N-1=7) – is not suitable, 1 – is not greatest divisor
    ->(2) D=1, N=92 (N-1=91) – is not suitable, 1 – is not greatest divisor
    D=91, N=0 (N-1=1) – is not suitable, 0 – is not positive integer

    Answer: N=14 D=7
    Only ONE solution, another thought?

  3. It seems, that we are solving different problems indeed. The 1st sentence reads, that n’s greatest divisor different from n itself equals to 91. So, 91 is the divisor of n.
    And how do you explain, that N*D-D=91?

  4. :( I thought, that the difference between number and greatest divisor is equal 91.

    If N- positive integer
    D = 91 – is the greatest divisor of N (D<N)
    Hence,
    N=91*prime number – from 2 to 91 (2.3.5.7.11.13.17.19.23.29.31.37.41.43.47.53.59.61.67.71.73.79.83.89) – 24 possible values for N

    Because if we use 91*4 we can provide the same as 91*2*2=182*2… so greatest divisor will be 182

    But no answers. – 24.
    Of all the calculations I tend to only answer D.
    confused …

  5. N = 91 * 91 = 1729
    I think that if we choose two numbers 91 and 19, then 91 – the greatest :) ,
    But, if we divide into prime factors and combine = 91*19 = (7*13)*19 = 7* (13*19) = 7*247=1729 – not suitable, 247>91

    So,
    1) 91*2=(7*13)*2 – ok, the greatest 91
    2) 91*3=(7*13)*3 – ok, the greatest 91
    3) 91*5=(7*13)*5 – ok, the greatest 91
    4) 91*7=(7*13)*7=7*(13*7) – ok, the greatest 91
    5) 91*11=(7*13)*11=7*(13*11)=143 – not suitable, 143>91, hence all prime numbers >7 not suitable.

    Correct answer В=4?

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