In a certain code language, ‘PRAYER’ is coded as ‘7927109’ and ‘GLOVES’ is coded as ‘143641010’. How will ‘SOURCE’ be coded in that language?
- A10639610
- B10106369
- C10641658
- D10648615
Solution & Step-by-step Explanation
Let's investigate the relationship between letters and numbers by checking positional values and operations on vowels and consonants.
Let's write down position values for PRAYER:
P=16,R=18,A=1,Y=25,E=5,R=18
Look at the code digits: 7,9,2,7,10,9.
Let's see if adding digits of position or related logic works:
P=16→1+6=7
R=18→1+8=9
A=1→1×2=2 ? Let's check.
Y=25→2+5=7
E=5→5×2=10 ? Let's check.
R=18→1+8=9
This reveals a beautifully consistent rule:
For Consonants: Sum the individual digits of their standard numerical place value.
For Vowels: Multiply their standard numerical place value by 2.
Let's verify this theory on GLOVES (Code: 143641010):
G (Consonant) =7→7
L (Consonant) =12→1+2=3
O (Vowel) =15→15×2=30 (Wait, let's recheck the code block split: 14,3,6,4,10,10 or 7,12... let's look at the digits: 7,3,6,4,10,10 doesn't match 143641010 directly).
Let's try another variation: what if the positions are multiplied or opposite positions are taken?
Let's check opposite positions for GLOVES:
G→T(20)→2+0=2
Let's look at the values again: G=7×2=14. Ah! G is 7, 7×2=14.
L=12→12/4? No, let's look at the numbers: 14,3,6,4,10,10
14=7×2 (G)
3=12→1+2=3 (L)
6=15→1+5=6 (O)
4=22→2+2=4 (V)
10=5×2 (E)
10=19→1+9=10 (S)
Let's see if this mixed digit-sum and multiplication works:
G(7)→7×2=14 (Single digit multiplied by 2?)
L(12)→1+2=3 (Double digit sum?)
O(15)→1+5=6 (Double digit sum?)
V(22)→2+2=4 (Double digit sum?)
E(5)→5×2=10 (Single digit multiplied by 2?)
S(19)→1+9=10 (Double digit sum?)
Wow! The pattern is perfectly consistent:
If place value is a single-digit number (less than 10), multiply by 2.
If place value is a double-digit number (≥10), sum the digits.
Let's double check PRAYER with this newly discovered rule:
P=16→1+6=7
R=18→1+8=9
A=1→1×2=2
Y=25→2+5=7
E=5→5×2=10
R=18→1+8=9
Matches perfectly: 7927109.
Now, let's compute the code for SOURCE:
S=19→1+9=10
O=15→1+5=6
U=21→2+1=3
R=18→1+8=9
C=3→3×2=6
E=5→5×2=10
Concatenating these results yields: 10639610.
Let's write down position values for PRAYER:
P=16,R=18,A=1,Y=25,E=5,R=18
Look at the code digits: 7,9,2,7,10,9.
Let's see if adding digits of position or related logic works:
P=16→1+6=7
R=18→1+8=9
A=1→1×2=2 ? Let's check.
Y=25→2+5=7
E=5→5×2=10 ? Let's check.
R=18→1+8=9
This reveals a beautifully consistent rule:
For Consonants: Sum the individual digits of their standard numerical place value.
For Vowels: Multiply their standard numerical place value by 2.
Let's verify this theory on GLOVES (Code: 143641010):
G (Consonant) =7→7
L (Consonant) =12→1+2=3
O (Vowel) =15→15×2=30 (Wait, let's recheck the code block split: 14,3,6,4,10,10 or 7,12... let's look at the digits: 7,3,6,4,10,10 doesn't match 143641010 directly).
Let's try another variation: what if the positions are multiplied or opposite positions are taken?
Let's check opposite positions for GLOVES:
G→T(20)→2+0=2
Let's look at the values again: G=7×2=14. Ah! G is 7, 7×2=14.
L=12→12/4? No, let's look at the numbers: 14,3,6,4,10,10
14=7×2 (G)
3=12→1+2=3 (L)
6=15→1+5=6 (O)
4=22→2+2=4 (V)
10=5×2 (E)
10=19→1+9=10 (S)
Let's see if this mixed digit-sum and multiplication works:
G(7)→7×2=14 (Single digit multiplied by 2?)
L(12)→1+2=3 (Double digit sum?)
O(15)→1+5=6 (Double digit sum?)
V(22)→2+2=4 (Double digit sum?)
E(5)→5×2=10 (Single digit multiplied by 2?)
S(19)→1+9=10 (Double digit sum?)
Wow! The pattern is perfectly consistent:
If place value is a single-digit number (less than 10), multiply by 2.
If place value is a double-digit number (≥10), sum the digits.
Let's double check PRAYER with this newly discovered rule:
P=16→1+6=7
R=18→1+8=9
A=1→1×2=2
Y=25→2+5=7
E=5→5×2=10
R=18→1+8=9
Matches perfectly: 7927109.
Now, let's compute the code for SOURCE:
S=19→1+9=10
O=15→1+5=6
U=21→2+1=3
R=18→1+8=9
C=3→3×2=6
E=5→5×2=10
Concatenating these results yields: 10639610.