What is the value of the positive integer n?

[BTGModeratorVI]

What is the value of the positive integer n?

1) If 31, 32, and 33 are each divided by n, the reminders are 7, 0, and 1, respectively.
2) n is an even number.

Answer: A
Source: GMAT paper tests

[Brent@GMATPrepNow]

What is the value of the positive integer n?

1) If 31, 32, and 33 are each divided by n, the reminders are 7, 0, and 1, respectively.
2) n is an even number.

Answer: A
Source: GMAT paper tests

Target question: What is the value of the positive integer n?

Statement 1: If 31, 32, and 33 are each divided by n, the reminders are 7, 0, and 1, respectively.

----ASIDE----------------
When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0
-----------------------------

If 31 divided by n leaves a reminder of 7, then (according to the above property), n > 7

If 32 divided by n leaves a reminder of 0, then n is a divisor of 32.
The divisors of 32 are: 1, 2, 4, 8, 16 and 32
Since we already know that n > 7, n must be 8 or 16 or 32. Let's test these three possible n-values

If n = 8, then 31, 32, and 33 divided by n leaves reminders 7, 0, and 1, respectively. PERFECT.
If n = 16, then 31 divided by n leaves a reminder of 15, when we're hold the remainder is 7. So, n can't be 16.
If n = 32, then 31 divided by n leaves a reminder of 31, when we're hold the remainder is 7. So, n can't be 32.

The process of elimination, n must be 8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n is an even number.
Clearly not sufficient.

Answer: A

Cheers,
Brent

[swerve]

What is the value of the positive integer n?

1) If 31, 32, and 33 are each divided by n, the reminders are 7, 0, and 1, respectively.
2) n is an even number.

Answer: A
Source: GMAT paper tests

Let's analyse Statement 1:

32 divided by \(n\) gives remainder as \(0\). That means \(n\) can be 1, 2, 4, 8, 16, 32. Now 33 will give remainder as 1 with all those values of \(n\) except 1. But 31/8 gives remainder as 7 and no other value of \(n\) will give remainder as 7.

Hence Sufficient \(\Large{\color{green}\checkmark}\)

Statement 2:

Not enough. \(n\) can be any even number. \(\Large{\color{red}\chi}\)

Therefore, the correct answer is A