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All of the citizens of a certain country have a five-charact
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24 Jul 2020, 11:01
24 Jul 2020, 11:01
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Question Stats:
62% (01:26) correct
37% (01:48) wrong based on 16 sessions
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All of the citizens of a certain country have a five-character or six-character national identification code that is created using the 26 letters of the alphabet and the 10 digits from 0 to 9. Which of the following gives the maximum number of citizens who can be designated with these codes?
A. \(2(36^6)\)
B. \(36(36^5)\)
C. \(37(36^5)\)
D. \(36(36^6)\)
E. \(37(36^6)\)
Kudos for the right solution and explanation
A. \(2(36^6)\)
B. \(36(36^5)\)
C. \(37(36^5)\)
D. \(36(36^6)\)
E. \(37(36^6)\)
Kudos for the right solution and explanation
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GMAT 1: 700 Q51 V31
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Re: All of the citizens of a certain country have a five-charact
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24 Jul 2020, 22:40
24 Jul 2020, 22:40
2
Refer attached image
There are be two type of locks 5 digit and 6 digit
5-Digit Locks
Each of the places can be filled using any of the 26 alphabets or the 10 digits so 36 possibilities for 1st place
Similarly, we have 36 possibilities for remaining 4 places
So, total number of 5 digit locks = 36*36*36*36*36 = \(36^5\)
6-Digit Locks
Each of the places can be filled using any of the 26 alphabets or the 10 digits so 36 possibilities for 1st place
Similarly, we have 36 possibilities for remaining 5 places
So, total number of 5 digit locks = 36*36*36*36*36*36 = \(36^6\)
Total possibilities = \(36^5\) + \(36^6\) = \(36^5\) + 36*\(36^5\) = \(36^5\)(1+36) = 37*\(36^5\)
So, answer will be C
Hope it helps!
There are be two type of locks 5 digit and 6 digit
5-Digit Locks
Each of the places can be filled using any of the 26 alphabets or the 10 digits so 36 possibilities for 1st place
Similarly, we have 36 possibilities for remaining 4 places
So, total number of 5 digit locks = 36*36*36*36*36 = \(36^5\)
6-Digit Locks
Each of the places can be filled using any of the 26 alphabets or the 10 digits so 36 possibilities for 1st place
Similarly, we have 36 possibilities for remaining 5 places
So, total number of 5 digit locks = 36*36*36*36*36*36 = \(36^6\)
Total possibilities = \(36^5\) + \(36^6\) = \(36^5\) + 36*\(36^5\) = \(36^5\)(1+36) = 37*\(36^5\)
So, answer will be C
Hope it helps!
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gmatclubot
Re: All of the citizens of a certain country have a five-charact [#permalink]
24 Jul 2020, 22:40
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