candidate selection -- probability

[pappueshwar]

hi all,
can any one explain how stmnt 2 is also a good choice.

the answer is: D

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.

[WhiteWNNoise]

[sanju09]

hi all,
can any one explain how stmnt 2 is also a good choice.

the answer is: D

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.

If 12 candidates completed the first interview but were dismissed after the second interview, then 12 is equal to n percent the remaining candidates exposed to the interview number 2. It's sort of an exponential decay where the number of remaining candidates exposed to the interview number 2 can be had from the expression 64 × [1 - (n/100) ^1].

Hence, n percent of 64 × [1 - (n/100) ^1] is 12. Solve and neglect the impossible (75) possibility and believe n = 25, then call statement (2) sufficient if you understand why statement (1) is sufficient.

[tpr-becky]

The trick of this problem is recognizing that you need to do two things - percent and then probability. The probability part will be easy if you know the percent because you can figure out how many candidates are left and the probability of not being the one picked.

Statement 1 tells you the percent - in theory you could subract 25% of 64, then 25% of the result then 25% of that result and then you would how many total people are left and can calculate the possibility of one of them not being picked. So it is sufficient (you would never want to do all that work on the actual GMAT).

Statement 2 says that 12 candidates = n% of the number of candidates after the first cut. since the percentage remains stable you could find out what percent that is - [(65(1-n/100))1-n/100] = 12 This is ultimately solveable so it is sufficient - therefore the Answer s D.

[[email protected]]

In statemen 2: All I am getting is n = 75 or n = 25.

As per normal DS rules, the statement 2 is insufficient.

But in this question, go back and solve the entire process as mentioned in the stimulus.

With n = 75%, in the end there is only one candidate left after the clearing of all the 3 interviews. There are 5 positions and only one candidate selected from a lot of 64 candidates.

The stimulus very clearly states that 'The candidates will be selected from among those complete all three rounds'.

So n = 75 becomes wrong...

Now put in 25 and you will see that it satisfies the conditions...

A bit tricky in the end, but got to find a solution for that as well...


Hope this helped...