If \(N\) is a positive three-digit number that is greater than 200, and each digit of \(N\) is a factor of \(N\) itself,

[M7MBA]

If \(N\) is a positive three-digit number that is greater than 200, and each digit of \(N\) is a factor of \(N\) itself, what is the value of \(N?\)

(1) The tens digit of \(N\) is 5.

(2) The units digit of \(N\) is 5.

[spoiler]OA=A[/spoiler]

Source: Manhattan GMAT

[Jay@ManhattanReview]

If \(N\) is a positive three-digit number that is greater than 200, and each digit of \(N\) is a factor of \(N\) itself, what is the value of \(N?\)

(1) The tens digit of \(N\) is 5.

(2) The units digit of \(N\) is 5.

[spoiler]OA=A[/spoiler]

Source: Manhattan GMAT

So, we have \(N > 200\) and each digit of \(N\) is a factor of \(N\) itself. We have to find the value of \(N\).

Let's take each statement one by one.

(1) The tens digit of \(N\) is 5.

So, we have N = a5c

Note that a and c cannot be 0 for 0 is not a factor any number.

Also, the number a5c is divisible by 5 if c is 0 or 5. Since know that c cannot be 0, we have c = 5

So, the no. is N = a55. Since N > 200, a can be one among 2, 3, 4, 5, 6, 7, 8, and 9.

The only possible value of a could be 5; for other values, N would not be divisible by 5.

So, N = 555.

(2) The units digit of \(N\) is 5.

N can be 555 or 315; there can be many values for N. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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