Basic combinatorics

[razorback]

Book 4 from MGMAT...

A British spy is trying to escape from his prison cell. The lock requires him to enter one number, from 1-9, and then push a pair of colored buttons simultaneously. He can make one attempt every 3 seconds. If there are 6 colored buttons, what is the longest possible time it could take the spy to escape from the prison cell?

OA: 6m 45 seconds

side note: I was posting this b/c I thought MGMAT had it wrong, that the answer was 6m 42s since I thought the 1st attempt was instantaneous, but upon a second look, it turns out, per usual, that I was mistaken! So here is the Q anyway.

[shankar.ashwin]

9 * 6C2 * 3 = 9 * 15 * 3 = 405 [spoiler](6m 45s)[/spoiler]

I think you do need to assume, that the 1st attempt takes 3 sec too, you cannot consider the 1st attempt at 0 sec.

[smackmartine]

Ashwin, Your calculation is absolutely correct , however assuming that 1st attempt 3 sec doesn't sound convincing.

The question is actually asking for maximum time the spy can delay before he escapes. So total delay means TOTAL of every 3 sec he has to wait till he takes next attempt. As per your calculation the spy wasted 405 sec just waiting. Question doesn't mentions that how many seconds each attempt took, so we cannot assume each attempt took exactly 3 sec.

I hope the reasoning is clear,but if you have some counter reasoning/ideas, do share.

[shankar.ashwin]

No, I didn't mean to say each attempt took 3 seconds. We know the maximum possible attempts were 135.
Assuming the first attempt was instantaneous, then we have 134 attempts with a delay of 3 sec in between each of the attempts. Then it would be only (135-1)*3 = 402 seconds instead of 405.

P.S The MGMAT book although explains this problem saying, each attempt took 3 seconds and hence 135 attempts would take 405 seconds. I think the explanation is ambiguous. As per the question I would go for 402 Sec instead of 405, just that the book says the OA is 405.

I believe GMAT would never ask such ambiguous problems.

[razorback]

Or if it did, I would hope two answer choices would not be 402s and 405s.

That would just be dirrrrty.