If N is product of even numbers from 2 to 100 and N is divisibly by 4725^n,find the largest possibility value of n.
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GMAT Club Forum Index Problem Solving (PS)
If n is a positive integer and n^2 is divisible by 72, then : Problem Solving (PS)
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amitvmane
Mar 31, 2012
00:00ABCDE
DIFFICULTY: 55% (hard) QUESTION STATS: based on 2845 sessions
60% (01:24) correct
40% (01:43) wrong
If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is
A. 6
B. 12
C. 24
D. 36
E. 48
Spoiler: OA
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Most Helpful Expert Reply
Bunuel
EXPERT'S
POST
Mar 31, 2012
If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is
A. 6
B. 12
C. 24
D. 36
E. 48
The largest positive integer that must divide , means for the least value of which satisfies the given statement in the question. The lowest square of an integer, which is multiple of is --> --> . Largest factor of is .
OR:
Given: , where is an integer (as is positive).
--> , as is an integer , also must be an integer. The lowest value of , for which is an integer is when --> -->
Answer:
If we can use log,
log4721 100＝n