santham wrote:What is the remainder when the positive integer n is divided by 2?
(1) When n is divided by 5, the remainder is an odd integer.
(2) When n is divided by 10, the remainder is an odd integer.
Please help
IMOE
When an even integer is divided by 2, the remainder is 0.
When an odd integer is divided by 2, the remainder is 1.
Thus, to determine the remainder when n is divided by 2, we need to know whether n is even or odd.
Question rephrased: Is n even?
Statement 1: When n is divided by 5, the remainder is an odd integer.
n=6 works, because 6/5 = 1 R1.
n=11 works, because 11/5 = 2 R1.
Since n can be even or odd, insufficient.
Statement 2: When n is divided by 10, the remainder is an odd integer.
Thus, n = (multiple of 10) + (odd integer), so that when n is divided by 10, the remainder is an odd integer.
A multiple of 10 is even.
Thus, n = even + odd = odd.
Sufficient.
The correct answer is
B.
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