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ruplun: Master | Next Rank: 500 Posts; Posts: 232; Joined: Fri Jun 18, 2010 7:09 amFollowed by: 2 members; Thanked: 1 times

by ruplun » Fri Jul 29, 2011 5:18 am

A die with x sides has consecutive integers on its sides.If the probability of not getting a 4 on either of the 2 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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Source: Beat The GMAT — Problem Solving | Fri Jul 29, 2011 5:18 am

naveen451: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Sat Jul 16, 2011 11:56 pmFollowed by: 1 member; Location: hyderabad; Thanked: 2 times

by naveen451 » Fri Jul 29, 2011 9:02 am

ruplun wrote:A die with x sides has consecutive integers on its sides.If the probability of not getting a 4 on either of the 2 tosses is 36/49, how many sides does the die have?

a. 4
b. 5
c. 7
d. 8
e. 13

IMO C

I AM NOT SURE BUT
explanation

if suppose there are 7 sides
then probability of getting 4 =1/7

probability of not getting 4=1-1/7 =6/7

probability pf not getting 4 for two times =6/7*6/7=36/49

thus die has 7 sides.

if i am wrong plz correct me

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tauseef10jan2004: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Fri Jul 29, 2011 3:03 am

by tauseef10jan2004 » Wed Aug 03, 2011 2:24 am

let the die has n sides

then probability of getting 4 = 1/n
probability of not getting 4 = 1-(1/n) = (n-1)/n

probability of not getting 4 twice = ((n-1)/n)*((n-1)/n) = sqr((n-1)/n) = 36/49

i.e. (n-1)/n = 6/7
on solving this n = 7

answer is c. 7

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edge: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Sun Jun 26, 2011 5:45 pm; Thanked: 2 times

by edge » Wed Aug 03, 2011 3:58 am

I just saw 7^2 in the denominator and chose C, knowing that in most of the probability-of-die-rolls questions I have faced, the solution often had 6^n in the denominator (n = the number of rolls of a standard dice).

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Wed Aug 03, 2011 4:33 am

Its quite simple. Let there be n sides of die.
so probability of getting 4 in one throw = 1/n
and probability of not getting 4 in one throw = (n-1)/n
so probability of not getting a 4 i n both the 2 throw = {(n-1)/n}^2
--> {(n-1)/n}^2 = 36/49
--> {(n-1)/n} = 6/7
--> n = 7.
Hence Ans C

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