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permutation/combination

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by shashank.ism » Sat Feb 06, 2010 4:25 am
An 'n' digit number is formed using the digits 3, 4, 5 and 6 where repetition of the digits is allowed. If the number of all such possible 'n' digits numbers exceeds 10000, then what is the minimum value of n?

a.) 5
b.) 6
c.) 7
d.) 8
e.) 9
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by harsh.champ » Sat Feb 06, 2010 4:26 am
shashank.ism wrote:An 'n' digit number is formed using the digits 3, 4, 5 and 6 where repetition of the digits is allowed. If the number of all such possible 'n' digits numbers exceeds 10000, then what is the minimum value of n?

a.) 5
b.) 6
c.) 7
d.) 8
e.) 9
_______________

IMO ,the answer is C.

Over here,we have to plug-in values and check by using hit-and-trial method.
Since,repetition of digits is allowed,
units place can be filled in 4 ways(3,4,5,6).
Corresponding to it,tens place can be filled in 4 ways (3,4,5,6).
And so and so forth.

So in case of a n digit no:-the answer will be 4^n.

Now,checking when 4^n crosses 10,000 we get 4^6 = 4096 and 4^7 = 16384.
Hence,minimum value of n is 7.
Last edited by harsh.champ on Sat Feb 06, 2010 4:33 am, edited 1 time in total.
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by shashank.ism » Sat Feb 06, 2010 4:33 am
IMO ,the answer is C.
Harsh will you please post the detailed solution of the question.
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by ajith » Sat Feb 06, 2010 4:33 am
shashank.ism wrote:An 'n' digit number is formed using the digits 3, 4, 5 and 6 where repetition of the digits is allowed. If the number of all such possible 'n' digits numbers exceeds 10000, then what is the minimum value of n?

a.) 5
b.) 6
c.) 7
d.) 8
e.) 9
No of 4 digit numbers = 4*4*4*4 = 4^4
no of n digit numbers = 4*4*...*4 (n times) =4^n

no of words possible with 6 digits =4^6 =4096

no of words possible with 7 digits =4^7 = 16384

7 is the minimum value of n if the possible numbers exceed 10000
C
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by harsh.champ » Sat Feb 06, 2010 5:00 am
shashank.ism wrote:
IMO ,the answer is C.
Harsh will you please post the detailed solution of the question.
Actually,I didn't post the soln. before as I wanted to check the answer.
Also,I try to solve the ques. in 2 min,and hence only type the answer.I post the detailed soln. afterwards as when I actually solve the question,my notepad looks something like:-
4 ways (3,4,5,6 ) ok


4^6= 4096 4^7=16384

SO,C.
Now,I can't post this solution as it will be very vague for rest of the members,though completely understood by me.
Hence,then aftertwards do I post the detailed solution in the same post.


I learned this strategy through komal.
It is very beneficial as it keeps you in sync with the test-taking mentality. :)
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by vscid » Sat Feb 06, 2010 1:01 pm
harsh.champ wrote:
shashank.ism wrote:An 'n' digit number is formed using the digits 3, 4, 5 and 6 where repetition of the digits is allowed. If the number of all such possible 'n' digits numbers exceeds 10000, then what is the minimum value of n?

a.) 5
b.) 6
c.) 7
d.) 8
e.) 9
_______________

IMO ,the answer is C.

Over here,we have to plug-in values and check by using hit-and-trial method.
Since,repetition of digits is allowed,
units place can be filled in 4 ways(3,4,5,6).
Corresponding to it,tens place can be filled in 4 ways (3,4,5,6).
And so and so forth.

So in case of a n digit no:-the answer will be 4^n.

Now,checking when 4^n crosses 10,000 we get 4^6 = 4096 and 4^7 = 16384.
Hence,minimum value of n is 7.
C with the same reasoning.
The GMAT is indeed adaptable. Whenever I answer RC, it proficiently 'adapts' itself to mark my 'right' answer 'wrong'.
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