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Combinations

by Deepthi Subbu » Sat Nov 27, 2010 1:00 am
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?

1. 5 min
2. 8 min
3. 8.75 min
4. 6 min
5.6.75 min
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by beat_gmat_09 » Sat Nov 27, 2010 4:26 am
Deepthi Subbu wrote: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?

1. 5 min
2. 8 min
3. 8.75 min
4. 6 min
5.6.75 min
[9*C(6,2)*3]/60 = 6.75
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by rishab1988 » Sat Nov 27, 2010 8:23 am
Same logic as my previous post

The dashes _ _ _

First dash for the no.
The two other dashes for the color code.

Possible choices for no ->9 [1 to 9,inclusive]

9 _ _

Possible choices for first color

9 6 _

Possible choices for second color =5 [ 1 has been chosen]

9 6 5.

Divide by 2! for the 2 color codes have been pressed simultaneously,so order does not matter.

Reasoning: The security system will taken in only 2 color codes and that too as a single entity.This is a MGMAT quant Q.Sometimes they tend to phrase their questions not so clearly.There is an another question on credit card balance that is unclear.(Platinum and Gold credit card).Rest assured,GMAT will be crystal clear about what it is asking.

9 3 5.

Multiply by 3 for each attempt is allowed only after 3 seconds have passed.

9* 3 * 5 * 3= 405

Divide by 60 to convert into minutes -> 6.75 minutes or E.

I hope the explanation was helpful
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by sandeepraghuvanshi » Thu Dec 01, 2016 12:10 pm
Lets go with the basics:

1st Lock-He is standing in front of the lock and can select any of the 9 numbers in 9c1 ways.Therefore 9 ways.

Now he is standing in front of alarm and has to choose 2 out of 6 buttons that he will press.He can choose any 2 out of those 6.There will be 6C2 such options in his hand.

So,ANS 9*6c2*3 sec


had there be an option that he presses one after another.Then there would be question of what is pressed first.Then after selection,we would again arrange the combination in 2! ways.


Remember.Permuation is the arrangement of combinations.

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by regor60 » Fri Dec 02, 2016 11:00 am
It's unclear if he has to wait 3 seconds for his initial attempt, yet that is what the 6.75 assumes.

If he can make his first attempt immediately, there are 134 intervals, not 135
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by Jay@ManhattanReview » Tue Dec 06, 2016 1:31 am
Hi ragor60,

While there is a little ambiguity in the James Bond question, it is relatively a simple one. The spy completes two things or an attempt in 3 seconds: key-in a numeral (1-9) and press a pair of two differently colored buttons.

Since there is an AND in the events, we would multiply the number of ways:

1. Total possible number of ways to key-in a number = 9;

2. Total number of ways to press a pair of two differently colored buttons = 6C2 = (6*5)/(1*2) = 15. Note that we need not apply permutation here (6P2) as the order of the colors of two buttons is not important (Not stated). Since he is James Bond, it smacks of order too! Anyways, had this been the case, the answer would have been more than the last option E (6.75 min.), which is not possible.

Total longest possible time means that the spy is able to unlock at the very last attempt. Thus the longest possible time = (9*15*3)/60 = 6.75''.

It takes 3 seconds to execute every successful and unsuccessful attempt.


-Jay

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