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

Question

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

ps_dahiya · Answer

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.

shahsac · Answer

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: 3767 5 
Total combinatioins possible that are smaller than 37675 are 4 (37671--37674)...............(1)

2) Changing Tens digit: 376 75 
First 3 digits are fixed.....thus total combinations would be
1*1*1*6*7 = 42........(2)

3) Changing Hundereds digit: 37 675 
First 2 digits are fixed....total combinations
1*1*5*7*7 = 245.............(3)

4) Changing Thousands digit: 3 7675 
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)....

kevincan · Answer

You're counting many possibilities several times!

ps_dahiya · Answer

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:

kevincan · Answer

If the first digit is 1, why can't the third digit be 7?

old_dream_1976 · Answer

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 ?

kevincan · Answer

Hint: (number of codes possible) - (numbers above 37676)

jeunesis · Answer

tough one...too tough..

anyhow my answer is B because the anwer must be multiple of 5. 
if it is right, i will explain....

Yurik79 · Answer

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

jaynayak · Answer

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

Yurik79 · Answer

I knew that I am missing something.I think your approach is correct

game over · Answer

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.

kevincan · Answer

Great work, game over! You are on the ball today. Yours is OA and OE!

jaynayak · Answer

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.

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

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