probability

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mitaliisrani: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Sun Mar 21, 2010 11:06 am

by mitaliisrani » Tue Aug 31, 2010 12:07 pm

A speaks truth in 60% of the cases while B speaks truth in 70% of the cases. When they lie they say the same lie. In what percent cases are they likely to contradict each other?
A) 30%
B) 40%
C)46%
D) 54%
E) 80%

ANs: OA is C

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Source: Beat The GMAT — Problem Solving | Tue Aug 31, 2010 12:07 pm

Arcane66: Senior | Next Rank: 100 Posts; Posts: 81; Joined: Sat Aug 08, 2009 1:16 pm; Thanked: 2 times

by Arcane66 » Tue Aug 31, 2010 12:17 pm

Here is how I did it:
First, I figured that since A speaks truth 60% of the time and B speaks truth 70% of the time and from the fact that they both tell the same lie...I figured that there are only two possible ways for a contridiction to occur.

First way: A tells truth and B lies
Second way: B tells truth and A lies

First way solve: (6/10)*(3/10)..this gives you 9/50 and the 6/10 came from A telling the truth and the 3/10 came from probability that B will lie. You multiply these together because it's a proability question.

Second way solve: (7/10)*(4/10).. this gives you 14/50 and the 7/10 came from B telling the truth and 4/10 came from probability that A will lie.

Third step is to combine 9/50 with 14/50. this gives you 23/50 or 46/100 = 46%

Answer is C

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Wed Sep 01, 2010 3:21 pm

mitaliisrani wrote:A speaks truth in 60% of the cases while B speaks truth in 70% of the cases. When they lie they say the same lie. In what percent cases are they likely to contradict each other?
A) 30%
B) 40%
C)46%
D) 54%
E) 80%

ANs: OA is C

or A speaks the truth and B speaks lies or A speaks lies and B speaks the truth
1. A speaks the truth and B speaks lies = 60%*30%=18%
2. A speaks lies and B speaks the truth = 40*70/10000=28%
total= 18+28=46
C is the answer

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brijesh: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Mon Apr 26, 2010 2:51 amFollowed by: 1 member; Thanked: 6 times

by brijesh » Wed Sep 01, 2010 8:03 pm

mitaliisrani wrote:A speaks truth in 60% of the cases while B speaks truth in 70% of the cases. When they lie they say the same lie. In what percent cases are they likely to contradict each other?
A) 30%
B) 40%
C)46%
D) 54%
E) 80%

ANs: OA is C

Hi fieinds! what may be the answer when the Q is as follows:

A speaks truth in 60% of the cases while B speaks truth in 70% of the cases. When they lie they say the same lie. In what percent cases are they likely to contradict each other?

thanks

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