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A secret society gives each its members a five-digit code,

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kevincan
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A secret society gives each its members a five-digit code, [#permalink] New post   07 Jul 2006, 23:49
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A secret society gives each its members a five-digit code, each letter of which must be one of { 1,2,3,5,6,7 }. When a new member joins, he is issued a code that is greater that those of all existing members. A certain member has just been issued the code 37676. He knows that no members have joined after him and that everyone who has joined the society is still a member. How many elements of { 3251, 3449, 3852, 3955 } COULD be the number of members in the club?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4



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Re: A secret society gives each its members a five-digit code, [#permalink] New post   08 Jul 2006, 00:09
A

To simplify,

how many 5 digits numbers can be made using 1,2,3,5,6,7 that are less than or equal to 37676.

My answer is 3 * 6 * 5 * 6 * 5 = 2700

So the maximum members could be 2700. None of the values in the set is less than equal to 2700. So answer should be A.
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Re: A secret society gives each its members a five-digit code, [#permalink] New post   08 Jul 2006, 09:43
kevincan wrote:
A secret society gives each its members a five-digit code, each letter of which must be one of { 1,2,3,5,6,7 }. When a new member joins, he is issued a code that is greater that those of all existing members. A certain member has just been issued the code 37676. He knows that no members have joined after him and that everyone who has joined the society is still a member. How many elements of { 3251, 3449, 3852, 3955 } COULD be the number of members in the club?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4


I got the answer as 4......(E)...
its tough to explain.,.....but I will give a shot.....

I went through the same approach that we need to find total 5 number combinations that can be formed from the given set & that are smaller than 37675....
I solved this by finding the possibility of changing each individual digit

1) Just chaning units digit: 37675
Total combinatioins possible that are smaller than 37675 are 4 (37671--37674)...............(1)

2) Changing Tens digit: 37675
First 3 digits are fixed.....thus total combinations would be
1*1*1*6*7 = 42........(2)

3) Changing Hundereds digit: 37675
First 2 digits are fixed....total combinations
1*1*5*7*7 = 245.............(3)

4) Changing Thousands digit: 37675
Combinatiions: 1*6*7*7*7 = 1758............(4)

5) Changing ten thousands digit: 37675
Combinations: 2*7*7*7*7 = 4802......(5)

Thus total members = Add (1) thru (5) = 6851
Thus all 4 numbers can be a set of the members.....hence.....answer is (E)....
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Re: A secret society gives each its members a five-digit code, [#permalink] New post   08 Jul 2006, 12:24
You're counting many possibilities several times!
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Re: A secret society gives each its members a five-digit code, [#permalink] New post   08 Jul 2006, 20:48
kevincan wrote:
ps_dahiya wrote:
A

To simplify,

how many 5 digits numbers can be made using 1,2,3,5,6,7 that are less than or equal to 37676. (Good approach)

My answer is 3 * 6 * 5 * 6 * 5 = 2700 ( This needs rethinking!)

So the maximum members could be 2700. None of the values in the set is less than equal to 2700. So answer should be A.


What am I doing wrong?
First digit can have 1,2,3
Second digit can have 1,2,3,5,6,7
Third digit can have 1,2,3,5,6
Fourth digit can have 1,2,3,5,6,7
Fifth digit can have 1,2,3,5,6

So I got 3*6*5*6*5 = 2700 :roll: :roll: :roll: :roll:
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Re: A secret society gives each its members a five-digit code, [#permalink] New post   09 Jul 2006, 02:05
If the first digit is 1, why can't the third digit be 7?
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Re: A secret society gives each its members a five-digit code, [#permalink] New post   09 Jul 2006, 15:15
kevincan wrote:
A secret society gives each its members a five-digit code, each letter of which must be one of { 1,2,3,5,6,7 }. When a new member joins, he is issued a code that is greater that those of all existing members. A certain member has just been issued the code 37676. He knows that no members have joined after him and that everyone who has joined the society is still a member. How many elements of { 3251, 3449, 3852, 3955 } COULD be the number of members in the club?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4


B.

think of any possibility first digit will have 2 or 3 options

for those that have 3 as the option there will be atleast 1 position with even options

hence i picked the only even number.

what is the OA ?
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Re: A secret society gives each its members a five-digit code, [#permalink] New post   Updated on: 12 Jul 2006, 13:01
Hint: (number of codes possible) - (numbers above 37676)

Originally posted by kevincan on 09 Jul 2006, 15:32.
Last edited by kevincan on 12 Jul 2006, 13:01, edited 1 time in total.
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Re: A secret society gives each its members a five-digit code, [#permalink] New post   12 Jul 2006, 06:38
tough one...too tough..

anyhow my answer is B because the anwer must be multiple of 5.
if it is right, i will explain....
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Re: A secret society gives each its members a five-digit code, [#permalink] New post   12 Jul 2006, 09:52
ps_dahiya wrote:
A

To simplify,

how many 5 digits numbers can be made using 1,2,3,5,6,7 that are less than or equal to 37676.

My answer is 3 * 6 * 5 * 6 * 5 = 2700

So the maximum members could be 2700. None of the values in the set is less than equal to 2700. So answer should be A.

Used same approach but got a different answer
3*6*5*6*4=2240
ps_dahiya last digit can't be 6 or 7
because no members have joined after him :wink:
But the answer is still A
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Re: A secret society gives each its members a five-digit code, [#permalink] New post   13 Jul 2006, 03:48
Getting A but using a different approach

When first digit is 1
Number of ways the second digit can be chosen = 6
Number of ways the third digit can be chosen = 6
Number of ways the fourth digit can be chosen = 6
Number of ways the fifth digit can be chosen = 6
Hence 6^4

When the first digit is 2
Number of ways the second digit can be chosen = 6
Number of ways the third digit can be chosen = 6
Number of ways the fourth digit can be chosen = 6
Number of ways the fifth digit can be chosen = 6
Hence 6^4

When the first digit is 3
Number of ways the second digit can be chosen = 6
Number of ways the third digit can be chosen = 5
Number of ways the fourth digit can be chosen = 6
Number of ways the fifth digit can be chosen = 5
Hence 25.6^2

Total = 2.6^4 + 25.6^2
=36( 72+25) = 36*97 = 3492
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Re: A secret society gives each its members a five-digit code, [#permalink] New post   13 Jul 2006, 07:08
jaynayak wrote:
Getting A but using a different approach

When first digit is 1
Number of ways the second digit can be chosen = 6
Number of ways the third digit can be chosen = 6
Number of ways the fourth digit can be chosen = 6
Number of ways the fifth digit can be chosen = 6
Hence 6^4

When the first digit is 2
Number of ways the second digit can be chosen = 6
Number of ways the third digit can be chosen = 6
Number of ways the fourth digit can be chosen = 6
Number of ways the fifth digit can be chosen = 6
Hence 6^4

When the first digit is 3
Number of ways the second digit can be chosen = 6
Number of ways the third digit can be chosen = 5
Number of ways the fourth digit can be chosen = 6
Number of ways the fifth digit can be chosen = 5
Hence 25.6^2

Total = 2.6^4 + 25.6^2
=36( 72+25) = 36*97 = 3492

:oops: I knew that I am missing something.I think your approach is correct
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Re: A secret society gives each its members a five-digit code, [#permalink] New post   13 Jul 2006, 08:13
37676 is equal to 3852 in our decimal system:
2*6^4+5*6^3+4*6^2+5*6^1+6*6^0=1296*2+216*5+36*4+30+6=2592+1080+144+30+6=3852

Therefore 3852-1=3851 numbers can be smaller than 37676.

Hence C.
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Re: A secret society gives each its members a five-digit code, [#permalink] New post   13 Jul 2006, 08:39
Great work, game over! You are on the ball today. Yours is OA and OE!
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Re: A secret society gives each its members a five-digit code, [#permalink] New post   13 Jul 2006, 21:52
game over wrote:
37676 is equal to 3852 in our decimal system:
2*6^4+5*6^3+4*6^2+5*6^1+6*6^0=1296*2+216*5+36*4+30+6=2592+1080+144+30+6=3852

Therefore 3852-1=3851 numbers can be smaller than 37676.

Hence C.


Great answer.... got it right till 2 but forgot the fact that when the first digit is 3 and the second digit is 1....... the rest of the digits can take any of the six values....... similarily for all the places.



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Re: A secret society gives each its members a five-digit code, [#permalink]
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