Latest CTS Aptitude Question SOLUTION: A credit card number has 5 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, and the fourth digit is 3 times the 5th digit. How

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A credit card number has 5 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, and the fourth digit is 3 times the 5th digit. How many different credit card combinations are possible?

Asked In CTS chaitanya (10 years ago)

Unsolved Read Solution (14)

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Read Solution (14) :

swarnava roy  (10 years ago)

9
third digit can be-> 7,8,9
4th & 5th digit-> (3,1),(6,2),(9,3)
total no of combination-> 3*3=9

Is this solution Helpfull? Yes (76) | No   

snehik podder  (10 years ago)

there will be 9 different combinations
no's are
12731
12762
12793
12831
12862
12893
12931
12962
12993

Is this solution Helpfull? Yes (41) | No   

PARAG KAMRA  (10 years ago)

This problem actually makes sense. We have 5 slots which we need to fill with different numbers. And we are given that the first and the second are 1 & 2 respectively.
_1_ _2_ __ __ __

The third digit is bigger than 6, therefore it could be either 7 or 8 or 9, since the range is [1.....9].
the fourth digit is 3 times the 5th digit,so
The fourth digit is divisible by 3, therefore it could be either 3 or 6 or 9.
The fifth digit is 3 times the sixth, therefore it's multiple of 3, so in a given range it could be either 3 or 6 or 9. By the way, the sixth digit could be either 1 or 2 or 3, since the product of 5th and 6th can't be more than 9. So the reference to the 6th digit in the question is absolutely sensible.
From this point, it looks like a simple combinatorics problem. We have 3 options in each of three decisions. So to calculate possible numbers we need to multiply 3 by 3 by 3. So the answer is 27

Is this solution Helpfull? Yes (10) | No (28)  

shanu  (10 years ago)

9
12731 12831 12931
12762 12862 12962
12793 12893 12993

Is this solution Helpfull? Yes (4) | No (1)  

yojana  (10 years ago)

9
Given that first two digits are 12 which are fixed
3rd digit is greater than 6 so no. of possibilities are 7,8,9 i.e., 3
4th digit = 3 * 5th digit
=> (9,3),(3,1),(6,2) i.e., 3
=> 3*3 = 9

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manoher gupta  (10 years ago)

manohar gupta
first two digit is fixed 12 then no of combination 1
and third digid may be 7or8or9 then no of combination 3
and 4th and 5th digid may be 31,62,93 because of fourth digid is 3 times of 5th digid so no of combination 3
then total combination 1*3*1*3=9ans

Is this solution Helpfull? Yes (4) | No   

Sivakumar  (10 years ago)

@parag : the credit card has only 5 digit.. but are using sixth digit ??

Is this solution Helpfull? Yes (3) | No (4)  

ARIJIT KOLEY  (10 years ago)

9 possible ways.

Is this solution Helpfull? Yes (2) | No (3)  

neha jaiswal  (10 years ago)

1st digit given=1
2nd digit given=2
3rd digit can be 7 or 8
as 1 and 2 is already used so only 3*3

Is this solution Helpfull? Yes (1) | No (7)  

abhishek singh  (10 years ago)

repeation of digits is not allowed... how can u make a combination starting from 12 and ending with, a/c to me, 4th amd 5th digits are 9,3 only.... which results in only 2 possible combinations

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Smruti Ranjan Pardhi  (10 years ago)

Answer is 3*3*3 = 27

Is this solution Helpfull? Yes | No (21)  

Arijit Roy  (10 years ago)

ANS: 72
1 2 7 3 1 1 2 7 6 2 1 2 7 9 3
1 2 8 6 2 1 2 8 3 1 1 2 8 9 3
1 2 9 9 3 1 2 9 6 2 1 2 9 3 1

now the above 9 patterns will be for 2,3; 3,4; 4,5; 5,6; 6,7; 7,8; 8,9 for 1st nd 2nd positions...
so 9*8=72

Is this solution Helpfull? Yes | No (20)  

HAREESH POTHUGUNTLA  (10 years ago)

12711,12,13,21,22,23,31,32,33
12811,12,13,21,22,23,31,32,33
12911,12,13,21,22,23,31,32,33
== 27 combinations !!

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rinki kirar  (9 years ago)

correct ans is 9

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