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A British spy is trying to escapre from the prison cell. [#permalink]

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24 Oct 2009, 21:54

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A British spy is trying to escapre from the prison cell. The lock code requires him to enter one number, from 1 to 9, and then push a pair of colored buttons simultaneously. Threre are a total of 6 colored buttons. He can make 1 attempt every 3 seconds. What is the longest possible time it may take him to escape from the cell.
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A British spy is trying to escapre from the prison cell. The lock code requires him to enter one number, from 1 to 9, and then push a pair of colored buttons simultaneously. Threre are a total of 6 colored buttons. He can make 1 attempt every 3 seconds. What is the longest possible time it may take him to escape from the cell.

A British spy is trying to escapre from the prison cell. The lock code requires him to enter one number, from 1 to 9, and then push a pair of colored buttons simultaneously. Threre are a total of 6 colored buttons. He can make 1 attempt every 3 seconds. What is the longest possible time it may take him to escape from the cell.

= 9c1 x 2 (6c2) x 3 sec, or, = 9c1 x (6x5) x 3 sec ..... order matters. = 9 x 2 (15) x 3 sec = 810 second
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GMAT TIGER do you mean the order he pushes the two buttons matter?

Maybe I didn't understand the stem correctly but ".. push a pair of colored buttons simultaneously". Doesn't that mean that the order doesn't matter? He pushes two at a time, simultaneously. I got it like there are no button 1 and 2.
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GMAT TIGER do you mean the order he pushes the two buttons matter?

Maybe I didn't understand the stem correctly but ".. push a pair of colored buttons simultaneously". Doesn't that mean that the order doesn't matter? He pushes two at a time, simultaneously. I got it like there are no button 1 and 2.

Probably I did not understand the question on the pair of colored buttons.

I assumed that if it is a code, then probably how you press the colored buttons "red and black" matters. If these colored buttons are seperately placed, then still it matters. If the two buttons are placed simulteneously and can be pressed at a time, then the order doesnot matter.

However it seems the order doesnot mattter per the originator's post.
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Second thought- Should we start counting the time from t+3 instead of t. you need to count the time between the attempts and not the attempts itself - i.e 1 st attempt 0 secs 2 nd attempt 3 secs 9C1*6C2 attempt (9C1*6C2 -1)*3 = 402 seconds.

The question says "He can make 1 attempt every 3 seconds" which could mean he needs to wait 3 seconds before making the first attempt (Kinda dumb IMO).

Anyhow I won't be surprised if the answer is 405 but for similar questions I would watch what is asked for very closely to rule out the possibility of a 402.
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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?

9 x 15 (there are 135 combinations) x 3 (one attempt per 3 seconds) = 405 seconds

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?

9 x 15 (there are 135 combinations) x 3 (one attempt per 3 seconds) = 405 seconds

I guess you arrived at 15 by doing 6C2. So if there are 6 different colors then: is 4, greeen, red combination same as 4, red, green???

Since he pushes the buttons SIMULTANEOUSLY #4 green, red combination is exactly the same as #4 red green

Yes, it shud be the same.. when I solved the problem I too picked 6C2 subconsciously and came up with 405 .. but yes, to your point.. when you use a combination the order doesnt matter..

Once you find 405 seconds, shouldn't you subtract 3 seconds from that answer because the 1st try doesn't require a three second wait while the other ones do. Essentially, only 134 tries require a 3 second wait, and thus shouldn't the answer be 402 seconds (134x3)?

Please let me know where I may be understanding the question differently.

Once you find 405 seconds, shouldn't you subtract 3 seconds from that answer because the 1st try doesn't require a three second wait while the other ones do. Essentially, only 134 tries require a 3 second wait, and thus shouldn't the answer be 402 seconds (134x3)?

Please let me know where I may be understanding the question differently.

I don't know where the question is from, and I wouldn't be at all surprised if 405 was the answer the question designer considers to be correct, but I agree with you. 405 is the number of possible codes, but 402 seconds is, by my interpretation of the question, the length of time required to test them, which is what the question asks for. That said, the wording isn't all that clear - can the spy test the first code immediately, or does it take 3 seconds to try the first code? Hard to say, and not really worth worrying about anyway since any real GMAT question will be precise about these types of points.
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Re: Permutation and Combination
[#permalink]
19 Jan 2012, 00:05

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