SOLUTION: When a whole number N is divided by 2, the remainder is 0. When N is divided by 3, the remainder is 2. Which is a possible value of N? (A) 17 (B) 30 (C) 49 (D) 53 (E) 74

Question 845303: When a whole number N is divided by 2, the remainder is 0. When N is divided by 3, the remainder is 2. Which is a possible value of N?
(A) 17
(B) 30
(C) 49
(D) 53
(E) 74
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"When a whole number N is divided by 2, the remainder is 0" so the number is even.

"When N is divided by 3, the remainder is 2" which means that the digits must add to some number p, that when divided by 3, gives you a remainder of 2 again.

Notice how 1+7 = 8 and 8/3 = 2 remainder 2...but...17 is NOT even. So A is out

30 is even and 3+0=3 but 3/3 = 1 remainder 0, and we want remainder 2. So B is out.

49 is odd, so C is out

53 is odd, so D is out

74 is even and 7+4 = 11 ---> 11: 1+1 = 2, this means that 74/3, 11/3 both give remainders of 2.

So (E) 74 is the answer.
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!
Or you can look at it like this:
`
It's divisible by 2, so it's even, so that narrows it down to
30 and 74. When divided by 3 it leaves a remainder of 2 so
it's 2 more than a multiple of 3. 30 is 2 more than 28, but
that's not a multiple of 3, but 74 is 2 more than 72, which
is a multiple of 3, so the answer is 74.

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