A British spy is trying to escapre from the prison cell.

Question

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.

Bunuel · Answer

9C1(numbers)*6C2(buttons)*3sec(time)=9*15*3=405sec

GMAT TIGER · Answer

= 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

rlevochkin · Answer

The order does not matter because the buttons are pressed simultaneously vs. one at a time

Bunuel · Answer

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.

GMAT TIGER · Answer

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.

abhi758 · Answer

I get 405sec going by bunnel's method..

GTChE · Answer

I got 405s, but I'm pretty certain that the spy is boned.

atish · Answer

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.

katealpha · Answer

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

Sudhanshuacharya · Answer

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???

gladvijay · Answer

Could you pls explain this, sounds interesting..

katealpha · Answer

So if there are 6 different colors then: is 4, greeen, red combination same as 4, red, green???

Could you pls explain this, sounds interesting..

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

gladvijay · Answer

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..

Anonymous · Answer

6C2 * 9 * 3 = 15 * 9 * 3 = 405 seconds

Spidy001 · Answer

6 colors - total possible pairs = 6c2 = 15

1-9 - total possible options = 9

every attempt takes 3 seconds.

Total possible combinations = 15*9*3 = 405 seconds.

workingonit121 · Answer

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.

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

IanStewart · Answer

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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A British spy is trying to escapre from the prison cell.

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