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Answer: A. Discuss this question HERE.
Example #12 (hard)
and are positive integers. Is the remainder of bigger than the remainder of ?
(1) .
(2) The remainder of is 2
First of all any positive integer can yield only three remainders upon division by 3: 0, 1, or 2.
Since, the sum of the digits of and is always 1 then the remainders of and are
only dependent on the value of the number added to and . There are 3 cases:
If the number added to them is: 0, 3, 6, 9, ... then the remainder will be 1 (as the sum of the digits
of and will be 1 more than a multiple of 3);
If the number added to them is: 1, 4, 7, 10, ... then the remainder will be 2 (as the sum of the digits
of and will be 2 more than a multiple of 3);
If the number added to them is: 2, 5, 8, 11, ... then the remainder will be 0 (as the sum of the digits
of and will be a multiple of 3).
(1) . Not sufficient.
(2) The remainder of is ‐‐> is: 2, 5, 8, 11, ... so we have the third case. Which means that the remainder
of is 0. Now, the question asks whether the remainder of , which is 0, greater than the
reminder of , which is 0, 1, or 2. Obviously it cannot be greater, it can be less than or equal to. So, the
answer to the question is NO. Sufficient.
Answer: B. Discuss this question HERE.
Resources
Check more DS questions on remainders HERE.
Check more PS questions on remainders HERE.
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