What is the remainder when a positive integer w is divided by 2?

If w is odd, remainder would be 1 and if w is even, remainder would be 0. All we need to know is whether w is odd or even.

(1) w is multiple of an odd integer, but is it an odd multiple of that integer or is it even multiple of that integer - thats not given so we cant say. Eg, take an odd integer say 5. Both 15 and 20 are multiples of 5 (thus both 15/20 classify as multiples of an odd integer) but one of them is odd and other is even. So we cant say. Insufficient.

(2) w is a multiple of 5, again we cant say whether its an odd multiple of 5 (like 15) or an even multiple of 5 (like 20). So Insufficient.

Even after combining the two statements, we cant figure out whether w is an odd multiple of 5 or an even multiple of 5 (as already explained). Data is thus insufficient.

Hence E answer

The remainder of a positive integer w when it is divided by 2 is?

(1) w is a multiple of an odd integer.

(2) w is a multiple of 5.

Remainder when an integer is divided by 2 can be 1 (for odd divisor) and 0 for even divisor

Question: Is w even?

Statement 1: (1) w is a multiple of an odd integer.

w can be 3 or 6 leading to diffeent remainders when divided by 2 hence

NOT SUFFICIENT

statement 2: w is a multiple of 5

w can be 5 or 10 leading to diffeent remainders when divided by 2 hence

NOT SUFFICIENT

COmbining the statements

w can be 5 or 10 leading to diffeent remainders when divided by 2 hence

NOT SUFFICIENT

Answer: Option E


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