What is the value of the positive integer n? What is the va

The number n has to be greater than 7, since it leaves a remainder 7.

Now 31/n has remainder 7, so 31 is 7 greater than a multiple of n. => 31-7 = 24 is a multiple of n.
on similar lines 32 is a multiple of n.
The greatest number that can divide 24 and 32 is HCF(24,32) = 8
Hence the maximum possible value of n = 8, also since n > 7 so it is the only value.
therefore n = 8

32 is a multiple of n -> n could be 1,2,4,8,32,16,8,4
31/n has remainder of 7 -> n > 7 -> 8,16
test -> n = 8
-> A

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 Suff.

Statement 2:

Not enough. n can be any even number.

Answer A

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

RELATED VIDEO

From stmnt 1: only n value 8 satisfies the given relation sufficient
Frm stmn2 clearly insufficient
IMOA
[quote="eybrj2"]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.[/quote]

[size=80][b][i]Posted from my mobile device[/i][/b][/size]

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