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Whats the smallest number greater than 2 that gives a

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Whats the smallest number greater than 2 that gives a [#permalink] New post 02 Nov 2003, 13:18
1. Whats the smallest number greater than 2 that gives a remainder of 2 when divided by 15,21 and 37?

2. What is the greatest prime number that can divide 2^100 - 2^96?

3.There is a rectangle ABCD,such that One side BC = 8 and the other side AB=4.There is a point P on the side AD, which moves along AD.What is the probablity that the nime PB will not be greater than 5?

Since I dont have the answers,When mentioning the answer ,please try to explain.
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 [#permalink] New post 02 Nov 2003, 15:29
(1) Find the LCM of 15, 21, 37 and add 2. answer 3887

(2) Not sure... 2^100 - 2^96 = 2^96 x 15 so the answer could be 5.

(3) For PB to be <= 5, PA should not excced 3.

So the required probability = probability that PA <= 3
= favourable length of PA/ Possible length of PA
= 3/8
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 [#permalink] New post 07 Jan 2004, 19:01
Got the same as well
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Paul

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 [#permalink] New post 09 Jan 2004, 11:16
would anybody mind to explain the 2nd and third bit?
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shubhangi

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 [#permalink] New post 09 Jan 2004, 11:24
2^100 - 2^96 = 2^96*2^4 - 2^96
= 2^96 ( 2^4 - 1 )
= 2^96 ( 16 - 1 )
= 2^96 ( 15 )
Therefore, 2^96 has prime number 2 repeated 96 times. 15 has prime numbers 3 and 5. Since the question asks for the greatest prime number that divides them, 5 it is.

The other question is better explained with a diagram but as I said in a previous post, I suck at drawing those. Maybe I'll try later but that question is easier than the second one. It's about applying pythagore and knowing the hypothenuse.
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 [#permalink] New post 09 Jan 2004, 11:31
Oh..ok i got it..thanks paul
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shubhangi

  [#permalink] 09 Jan 2004, 11:31
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