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

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by M7MBA » Sat May 30, 2020 4:09 pm

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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

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Source: Beat The GMAT — Data Sufficiency | Sat May 30, 2020 4:09 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

Re: If $N$ is a positive three-digit number that is greater than 200, and each digit of $N$ is a factor of $N$ its

by Jay@ManhattanReview » Mon Jun 01, 2020 11:39 pm

M7MBA wrote: ↑
Sat May 30, 2020 4:09 pm
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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