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Power of 2

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by Anurag@Gurome » Fri Jan 28, 2011 1:05 am
diehard_gmat wrote:What is the highest power of 2 in (1! + 2! + 3! + 4!.....100!)?

A. 0
B. 2
C. 10
D. 50
E. 100
Note that factorial of any integer greater than 1 is even.
Hence, the sum (2! + 3! + 4! + ... + 100!) is even too.

Now when we add 1! = 1 to this sum, we will have an odd number. Hence, the given expression is odd, i.e. not divisible by 2.

Therefore, highest power of 2 in the expression is zero.

The correct answer is A.
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by prachich1987 » Fri Jan 28, 2011 2:05 am
nice question and a very nice explanation !!!
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by arora007 » Fri Jan 28, 2011 6:44 am
A. good prb.
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