This one is a tough one. Good luck If 2^n = : PS Archive
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# This one is a tough one. Good luck If 2^n =

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This one is a tough one. Good luck If 2^n = [#permalink]

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06 Nov 2004, 13:53
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This one is a tough one. Good luck

If 2^n = 29*30*31*...100, then n = ?

a) 90
b) 97
c) 79
d) 70
e) None of the above
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Paul

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06 Nov 2004, 14:54
I think E. There will be a '0' in the unit digit of the big number (in 100!/28!. Note: 29*30*31...*100 = 100!/28!)and anything to the power of 2 will have a unit digit other than 0.

So, E.
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06 Nov 2004, 20:08
I thought of the same.....

do you guyz have good practice material to improve on numbers and factors on DS?? Plus....rate and time and distance.....this is what iam really bad at and this is what pulls down my score!
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07 Nov 2004, 10:33
I also think it's E.

This number will have some other prime factors except 2...
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07 Nov 2004, 14:40
OA is E or exact answer should be 72
I used "possessed"'s method.
100/2 = 50
50/2 = 25
25/2 = 12
12/2 = 6
6/2 = 3
3/2 = 1
Sum is 97
But the series start at 29 so you have to remove all factors of 2 included in first 29 integers.
29/2 = 14
14/2 = 7
7/2 = 3
3/2 = 1
Sum is 25
Answer should be 97-25 = 72
The reason why we are succinctly dividing by 2 is because we are trying to find the succinct exponents of 2. The first time we are dividing by 2, we are finding all numbers divisible by 2. The second time we are dividing by 2, we are finding all numbers divisible by 4 which contain 2^2 and so on so forth.
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Best Regards,

Paul

07 Nov 2004, 14:40
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