naaga
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
What is the remainder when the positive integer n is divided by 2?
Question basically asks whether n is odd or even: if it's odd then the remainder will be 1 and if it's even then the remainder will be zero.
(1) When n is divided by 5, the remainder is an odd integer --> n=5q+odd, so
n could be odd (1, 3, 11, 13, 21, 23, ...) as well as even (6, 8, 16, 18, ... ). Not sufficient.
(2) When n is divided by 10, the remainder is an odd integer --> n=10p+odd=even+odd=odd. Sufficient.
Answer: B.
P. S. naaga please always tag your questions.how can the remainder of n/5 be 11 or 6 and so on? Isn't it always between 1 and 4? e.g. 9/ 5 = 1+4 or 23 / 5 = 1+3.