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25 Dec 2012, 10:05
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
88% (00:45) correct
12%
(01:17)
wrong
based on 1450
sessions
History
Date
Time
Result
Not Attempted Yet
If n is the greatest positive integer for which 2^n is a factor of 10!, then n =?
A. 2
B. 4
C. 6
D. 8
E. 10
Is any one can provide a solution for this question?It's from GWD. Thanks!
A. 2
B. 4
C. 6
D. 8
E. 10
Is any one can provide a solution for this question?It's from GWD. Thanks!
14 May 2015, 23:06
Kudos
Bookmarks
Hi All,
Many Test Takers get these types of questions wrong because they move too quickly through the work and don't do enough work on their pads. It's a relatively straight-forward prompt though...
We're essentially asked to find all the "2"s inside 10!
The 'key' to this question is to realize that some values have MORE THAN ONE 2 in them....
10! = (10)(9)(8)(7)(6)(5)(4)(3)(2)(1)
10 = 5x2 --> one 2
8 = 2x2x2 --> three 2s
6 = 3x2 --> one 2
4 = 2x2 --> two 2s
2 = 1x2 --> one 2
1+3+1+2+1 = eight 2s
Final Answer:
GMAT assassins aren't born, they're made,
Rich
Many Test Takers get these types of questions wrong because they move too quickly through the work and don't do enough work on their pads. It's a relatively straight-forward prompt though...
We're essentially asked to find all the "2"s inside 10!
The 'key' to this question is to realize that some values have MORE THAN ONE 2 in them....
10! = (10)(9)(8)(7)(6)(5)(4)(3)(2)(1)
10 = 5x2 --> one 2
8 = 2x2x2 --> three 2s
6 = 3x2 --> one 2
4 = 2x2 --> two 2s
2 = 1x2 --> one 2
1+3+1+2+1 = eight 2s
Final Answer:
GMAT assassins aren't born, they're made,
Rich
25 Dec 2012, 10:18
Kudos
Bookmarks
In the questions where you are supposed to find out the maximum power of a prime factor which is a factor of n!, keep one only on thing in mind:
Let the prime number you are looking for be x, then:
\(n/x + n/x^2 + n/x^3.........n/x^k\) where \(x^k\) <=n.
If you apply this rule here,
\(10/2 +10/2^2 +10/2^3\) or 5+2+1=8.
Hence maximum power of 2 in \(10!\) will be 8.
Let the prime number you are looking for be x, then:
\(n/x + n/x^2 + n/x^3.........n/x^k\) where \(x^k\) <=n.
If you apply this rule here,
\(10/2 +10/2^2 +10/2^3\) or 5+2+1=8.
Hence maximum power of 2 in \(10!\) will be 8.
