Study the following coding system and find the appropriate code for the number group given at the end.
Excluding the exceptions mentioned below, the digit are to be transformed into letter codes as follows:
Digit |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
Letter Code |
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
Exeptions:
i. If a number begins with a nonzero even prime digit, that digit should be coded as E.
ii. If a number begins with a nonzero odd digit, that digit should be coded as S.
iii. If a number begins and also ends with nonzero even digits, those two digits at the extreme ends should be coded as K.
iv. If a number begins and also ends with nonzero odd digits, those two digits at the extreme ends should be coded as J.
v. If the middle digit of a number is in multiples of 2, that digit should be coded as N.
vi. if the sum of the digits of a number is divisible by 6, then the second and eighth digits should be coded as Q.
Number to be coded: 531784062
Excluding the exceptions mentioned below, the digit are to be transformed into letter codes as follows:
Digit |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
Letter Code |
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
Number Given: 531784062
i. If a number begins with a nonzero even prime digit, that digit should be coded as E.
The number begins with 5 and 5 is not the nonzero even prime number.
So, the word does not start with E.
ii. If a number begins with a nonzero odd digit, that digit should be coded as S.
The number begins with 5 and 5 is an odd nonzero number.
So, the word is starting from S.
iii. If a number begins and also ends with nonzero even digits, those two digits at the extreme ends should be coded as K.
The number begins with 5 and 5 is not the nonzero even prime number.
The number begins with 2 and 2 is the nonzero even prime number.
But one is true and one is false.
So, the word does not have K at extreme ends.
iv. If a number begins and also ends with nonzero odd digits, those two digits at the extreme ends should be coded as J.
The number begins with 5 and 5 is an odd nonzero number.
The number ends with 2 and 2 is not an odd nonzero number.
But one is true and one is false.
So, the word does not have J at extreme ends.
v. If the middle digit of a number is in multiples of 2, that digit should be coded as N.
The middle digit of the number is 8 which is a multiple of 2.
So, the middle digit is coded as N.
vi. if the sum of the digits of a number is divisible by 6, then the second and eighth digits should be coded as Q.
The sum of digits of number = (5 + 3 + 1 + 7 + 8 + 4 + 0 + 6 + 2) = 36
36 is the completely divisible by 6.
So, the Second and Eighth digits are coded as Q.
According to all the conditions the number may be coded as:
Number | 5 | 3 | 1 | 7 | 8 | 4 | 0 | 6 | 2 |
Code | S | Q | N | Q |
Rest numbers will be coded according to the table given:
Number | 5 | 3 | 1 | 7 | 8 | 4 | 0 | 6 | 2 |
Code | S | Q | B | H | N | E | A | Q | C |
So, the given number is coded as:
531784062: SQBHNEAQC
Hence, "SQBHNEAQC" is the correct answer.