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Re: The integer n is greater than or equal to 40. When the integ [#permalink]
linder wrote:
If n = 28k + 12, where k is some positive integer, then 2n = 56k + 24 and 3n = 84k + 36 (just multiply through by 2 and 3).

Divide 2n by 14 and you get 56k/14 + 24/14, simplify it to 4k + 1 + 10/14. (4k + 1) represents the whole part of the answer and 10 is the remainder.

Divide 3n by 14 and you get 84k/14 + 36/14, simplify it to 6k + 2 + 8/14. (6k + 2) represents the whole part of the answer and 8 is the remainder.

The remainder of 2n/14 is 10, which is greater than 8, the remainder of 3n/14. The answer is A.


Here the remainder in the 2nd case should be 6; not 8. Anyway, the result remains the same-- 10 > 6, so ans is A
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Re: The integer n is greater than or equal to 40. When the integ [#permalink]
Just pick 40.

40/28 = R12

A: 80/14 = R10 (5x14 = 70)

B: 120/14 = R8 (8x14 = 112)

A > B
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