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30 Aug 2016, 16:29
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
48% (01:14) correct
52%
(01:22)
wrong
based on 368
sessions
History
Date
Time
Result
Not Attempted Yet
How many trailing Zeroes does 53! + 54! have?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Note -> This question is a part of Stone cold's PS and DS question collection -> https://gmatclub.com/forum/stonecold-s- ... l#p1676182
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Note -> This question is a part of Stone cold's PS and DS question collection -> https://gmatclub.com/forum/stonecold-s- ... l#p1676182
30 Aug 2016, 17:58
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53! + 54! = 53! + 54 * 53!
= 53! (1 + 54)
= 53! * 55
Number of trailing 0s in 53! = number of 5s in the expansion of 53!
= 10 + 2 = 12
There is 1 more 5 in 55.
Hence, total number of trailing 0s = 12 + 1 = 13
Answer (B).
In most cases, when we are adding multiple terms, all of which have trailing 0s, the sum will have as many trailing 0s as that in the lowest term. Example: 20 + 2300 + 34210000 = 34212320 -> one 0 because lowest term 20 has one 0.
This case has an exception because of an additional 5 in 55.
= 53! (1 + 54)
= 53! * 55
Number of trailing 0s in 53! = number of 5s in the expansion of 53!
= 10 + 2 = 12
There is 1 more 5 in 55.
Hence, total number of trailing 0s = 12 + 1 = 13
Answer (B).
In most cases, when we are adding multiple terms, all of which have trailing 0s, the sum will have as many trailing 0s as that in the lowest term. Example: 20 + 2300 + 34210000 = 34212320 -> one 0 because lowest term 20 has one 0.
This case has an exception because of an additional 5 in 55.
General Discussion
31 Aug 2016, 07:09
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stonecold
53!+54! = 53! (1+54) = 53!*55
Now No. of zeros in 53!*55 = pairs of 5 and 2 in prime factorization of 53!*55
Power of 5 in 53! = [53/5]+[53/5^2] = 10+2 = 12
i.e. Power of 5 in 53!*55 = 12+1(one power of 5 in 55) = 13
Since power of 2 in 53! will be much greater than power of 5 in 53!*55 so no. of pairs of 5 and 2 = power of 5 in 53!*55 = 13
Answer: Option B
