BTGModeratorVI wrote: ↑Sat Jun 13, 2020 5:32 am
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
