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A die with x sides has consecutive integers on its sides. If

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A die with x sides has consecutive integers on its sides. If [#permalink] New post 06 Sep 2004, 18:06
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A die with x sides has consecutive integers on its sides. If the probability of NOT getting a 4 on either of two tosses is 36/49, how many sides does the die have?

(A) 4
(B) 5
(C) 7
(D) 8
(E) 13
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 [#permalink] New post 06 Sep 2004, 19:05
Hi,

could you explain the logic behind this working:


(x-1)/x = sqrt 36/49
or x = 7
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 [#permalink] New post 06 Sep 2004, 20:29
ywilfred wrote:
Hi,

could you explain the logic behind this working:


(x-1)/x = sqrt 36/49
or x = 7


for a die with x sides, to not get a particular number (say 4)
= 1 - [1(x-1) + (x-1)1 + 1)] / x^2
= (x-1)^2/x^2

=> (x-1)^2/x^2 = 36/49
and n = 7

But, a very quicker way, I saw "49" in the denominator and "two rolls" (which requires x^2 in denominator), so decided it should be 7.
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 [#permalink] New post 06 Sep 2004, 22:26
7

let x=no of sides
P(no 4 on either toss) = P(no 4 on 1st toss) * P(no 4 on 2nd toss)
=[1-P(4 on 1st toss)] * [1-P(4 on 2nd toss)]
= [1- 1/x] * [1-1/x]

36/49 = [1-1/x]^2
=> x=7
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 [#permalink] New post 06 Sep 2004, 22:53
yep, no need for me to repeat what you've all said very well on previous posts...but on this one plug in the answers seems to be the fastest way.

I confirm OA is C
  [#permalink] 06 Sep 2004, 22:53
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