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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
67% (01:29) correct
33%
(01:37)
wrong
based on 748
sessions
History
Date
Time
Result
Not Attempted Yet
If n is a prime number and n ≠ 3, which of the following could be the remainder when 100! + n is divided by 3?
I. 0
II. 1
III. 2
A. II only
B. III only
C. I and II only
D. II and III only
E. I, II and III
Bunuel - I checked out reminders concepts in the math book https://gmatclub.com/forum/compilation- ... 86714.html
but the below idea wasn't mentioned
You can add and subtract remainders directly, as long as you correct excess or negative remainders. "
if x leaves a remainder of 4 after division by 7, and y leaves a remainder of 2 after division by 7, then x +y leaves a remainder of 4 + 2 = 6 after division by 7.
Similarly 100! leaves a remainder 0 on division by 3 so we are only interested in the remainder when N divided by 3,which will be actual remainders of 100! + n is divided by 3
if n =1 remainder 1 so overall remainder is 1
if n = 2 remainder 2 so overall remainder is 2
if n = 6 remainder = 0 so overall remainder is 0
All 3 are possible right then why Princeton says D?
Cheers.
I. 0
II. 1
III. 2
A. II only
B. III only
C. I and II only
D. II and III only
E. I, II and III
Bunuel - I checked out reminders concepts in the math book https://gmatclub.com/forum/compilation- ... 86714.html
but the below idea wasn't mentioned
You can add and subtract remainders directly, as long as you correct excess or negative remainders. "
if x leaves a remainder of 4 after division by 7, and y leaves a remainder of 2 after division by 7, then x +y leaves a remainder of 4 + 2 = 6 after division by 7.
Similarly 100! leaves a remainder 0 on division by 3 so we are only interested in the remainder when N divided by 3,which will be actual remainders of 100! + n is divided by 3
if n =1 remainder 1 so overall remainder is 1
if n = 2 remainder 2 so overall remainder is 2
if n = 6 remainder = 0 so overall remainder is 0
All 3 are possible right then why Princeton says D?
Cheers.
13 Aug 2014, 02:45
Kudos
Bookmarks
\(\frac{100! + n}{3} = \frac{100!}{3} + \frac{n}{3}\)
\(\frac{100!}{3}\) is a perfect division
\(\frac{n}{3}\) may give remainder either 1 or 2 as n is prime
Answer = D
\(\frac{100!}{3}\) is a perfect division
\(\frac{n}{3}\) may give remainder either 1 or 2 as n is prime
Answer = D
General Discussion
03 Nov 2012, 01:59
Kudos
Bookmarks
Jp27
Notice that we are told that n is a prime number and n ≠ 3. Thus, n cannot be 1.
n also cannot be 6 or any other multiple of 3, thus the remainder cannot be 0.
It can be 1 for n=7 and 2 for n=5.
Answer: D.
Hope it's clear.
