Professor wrote:

Praetorian wrote:

Please explain your answers

If 40% of unsuccessful suicide attempts are repeated within 6 months and 25% of suicides are successful, what percentage of suicides in any 6 months period is the first attempt?

(A) 30

(B) 40

(C) 50

(D) 60

(E) 70

suppose total sucide attempts = 100%

sucessful = 25%

unsuccessful = 75%

repeate = 40% of unsuccessful=40% of 75% = 30%

so every month 30% sucide attempts are repeate. therefore, first attemp = 100%-30%=70%

Well, I have a little different thought process here and wanted to put it out there. Any takers /thoughts ?

The solution might be clearer once we divide the explanation into two parts -

Part I - First Attempts:

For any month, 100% of original attempts are first attempts.

Part II - Second Attempts:

40% of failed attempts (= 75 % of original attempts) are attempted again => (40/100) * (75/100) = 3/10 = 30%

This 30% is the percentage which denotes "The percentage of the UNSUCCESSFUL attempts which are tried again". And NOT, "the percentage of ALL attempts".

So, from part 1, we get 25% or 1/4

and from part 2, we get 30% or 3/10.

Now, the question is "What percentage of ALL the attempts are first attempts" ?

ALL attempts = Original attempts (all these are first attempts) + Retry attempts

= 100 + 30 = 130%.

Percentage of First attempts from ALL attempts = 100/130 = 77% (which is not in the answer choice listed).

Did I over analyze too much, but logically, sounds right.

For example, if 40 attempts were made. 10 were good and 30 were bad. Out of these bad attempts, 40% were tried again = 0.4 * 30 = 12 attempts were retried. So, total attempts = 40 + 12.

Percentage of First attempts from ALL attempts = 40/52 = 77 %.

(Using the example above)Obviously, the question didn't say/mean that the 40 attempts included the retry attempts as well. If it did, then it would be like asking the same question again and again.