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If N is a positive integer, what is the tens digit of N?

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Source: — Data Sufficiency |
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by Jay@ManhattanReview » Mon Aug 19, 2019 8:52 pm

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BTGmoderatorDC wrote:If N is a positive integer, what is the tens digit of N?

(1) N is divisible by 25.

(2) N is divisible by 16.

OA C

Source: Veritas Prep
Let's take each statement one by one.

(1) N is divisible by 25.

1. Say N = 25, tens digit of N = 2.
2. Say N = 50, tens digit of N = 5.

No unique answer. Insufficient.

(2) N is divisible by 16.

1. Say N = 16, tens digit of N = 1.
2. Say N = 32, tens digit of N = 3.

No unique answer. Insufficient.

(1) and (2) together

Since 25 and 16 are co-prime, we conclude that N is divisible by 25*16 = 400.

Say N = 400k, where k is any positive integer

Whatever be the value of k, the tens digit of 400k would be 0. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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by swerve » Tue Aug 20, 2019 2:37 pm

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Given: \(N > 0\) and integer
Required: Tens digit of \(N\)?

Statement 1: \(N\) is divisible by 25
\(N = 25\) or \(50\)
Hence we cannot tell the tens digit.
INSUFFICIENT \(\color{red}{\large{\times}}\)

Statement 2: \(N\) is divisible by 16
\(N = 16\) or \(32\)
We cannot tell the tens digit
INSUFFICIENT \(\color{red}{\large{\times}}\)

Combining Statement 1 and Statement 2:
\(N\) is a multiple of both 16 and 25
Hence \(N\) is a multiple of 400
\(N = 400, 800, \cdots \)
In all the cases, the tens digit will be 0
SUFFICIENT \(\color{green}{\large{\checkmark}}\)

Therefore, __C__
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