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 = 25So \(75%\) 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
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My QuantRules for Posting in the Verbal Forum -

Rules for Posting in the Quant Forum[/size][/color][/b]