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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
53% (02:22) correct
47%
(02:26)
wrong
based on 840
sessions
History
Date
Time
Result
Not Attempted Yet
64 candidates are competing for 5 positions at a consulting firm. The hiring process consists of 3 interviews. After each interview, n% of the remaining candidates will be dismissed. The candidates will be selected from among those complete all three rounds. Each candidate is equally qualified and has an equal probability of getting hired at every point in the process. What is the probability that a candidate will complete all three interviews but fail to get the job?
(1) n = 25
(2) 12 candidates completed the first interview but were dismissed after the second interview.
(1) n = 25
(2) 12 candidates completed the first interview but were dismissed after the second interview.
23 May 2013, 09:12
Kudos
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64 candidates are competing for 5 positions at a consulting firm. The hiring process consists of 3 interviews. After each interview, n% of the remaining candidates will be dismissed. The candidates will be selected from among those complete all three rounds. Each candidate is equally qualified and has an equal probability of getting hired at every point in the process. What is the probability that a candidate will complete all three interviews but fail to get the job?
(1) n = 25
So \(75%\) remains after each interview
\(64=>48=>36=>27\), \(27\) will arrive at the last step. So the probability that a candidate will complete all three interviews but fail to get the job is \(\frac{22}{64}\).
Sufficient
(2) 12 candidates completed the first interview but were dismissed after the second interview.
So there is a difference between the first and second interview of 12. People who completed the first interview = \(64(\frac{100-n}{100})\); people who completed the second interview = \(64(\frac{100-n}{100})^2\).
Call \(x=\frac{100-n}{100}\) and solve the equation \(64x=64x^2+12\) \(x=0.75\) => \(n=25%\) or \(x=0.25\) => \(n=75%\).
If \(n=75%\) this means that they keep 25% each time, so the sequence would be \(64=>16=>4=>1\); in this scenario there are no 5 people to be chosen for the final 5 spots, so \(n=75%\) is not a realistic rate (given the conditions above).
If \(n=25%\) the sequence is the same as A. So IMO sufficient
IMO D
(1) n = 25
So \(75%\) remains after each interview
\(64=>48=>36=>27\), \(27\) will arrive at the last step. So the probability that a candidate will complete all three interviews but fail to get the job is \(\frac{22}{64}\).
Sufficient
(2) 12 candidates completed the first interview but were dismissed after the second interview.
So there is a difference between the first and second interview of 12. People who completed the first interview = \(64(\frac{100-n}{100})\); people who completed the second interview = \(64(\frac{100-n}{100})^2\).
Call \(x=\frac{100-n}{100}\) and solve the equation \(64x=64x^2+12\) \(x=0.75\) => \(n=25%\) or \(x=0.25\) => \(n=75%\).
If \(n=75%\) this means that they keep 25% each time, so the sequence would be \(64=>16=>4=>1\); in this scenario there are no 5 people to be chosen for the final 5 spots, so \(n=75%\) is not a realistic rate (given the conditions above).
If \(n=25%\) the sequence is the same as A. So IMO sufficient
IMO D
General Discussion
23 May 2013, 09:16
Kudos
Bookmarks
Start - 64
1st Interview : 64x (where x= 1-n/100)
2nd Interview: 64x²
3rd Interview: 64x³
Getting a job: 5 (No relation to above.
What is asked?
(65x³-5)/64
Statement 1:
n=25
So, x=0.75
So, probability = 64*3/4*3/4*3/4 or (27-5)/64 = 22/64
SUFFICIENT
Statement 2:
Given: 64x-64x² = 12
Solve this quadratic equation: 16x²-16x+3=0
You get x=1/4 or x=3/4
BUT
If x=1/4, 64x² becomes 4. As no. of students who got the job is 5, so no. of students left after 2nd interview can't be less than this number.
Check 3/4, you get the case as in statement 1., so same answer.
SUFFICIENT
EITHER SUFFICIENT
1st Interview : 64x (where x= 1-n/100)
2nd Interview: 64x²
3rd Interview: 64x³
Getting a job: 5 (No relation to above.
What is asked?
(65x³-5)/64
Statement 1:
n=25
So, x=0.75
So, probability = 64*3/4*3/4*3/4 or (27-5)/64 = 22/64
SUFFICIENT
Statement 2:
Given: 64x-64x² = 12
Solve this quadratic equation: 16x²-16x+3=0
You get x=1/4 or x=3/4
BUT
If x=1/4, 64x² becomes 4. As no. of students who got the job is 5, so no. of students left after 2nd interview can't be less than this number.
Check 3/4, you get the case as in statement 1., so same answer.
SUFFICIENT
EITHER SUFFICIENT
thx 
