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A+B+C+D=D+E+F+G=G+H+I=17 where each letter represent a number from 1 to 9. Find out what does letter D and G represent if letter A=4.
- a)D=5 G=1
- b)D=7 G=1
- c)D=2 G=1
- d)D=3 G=1
Correct answer is option 'A'. Can you explain this answer?
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A+B+C+D=D+E+F+G=G+H+I=17 where each letter represent a number from 1 t...
Answer:
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- a)D=5 G=1
a + b + c + d = d + e + f + g = g + h + i = 17
Means, ( a + b + c + d )+ (d +e + f + g )+ (g +h + i ) = 17 +17+17 = 17 x 3 = 51
a + b + c + d + e + f + g + h + i +( d + g ) = 51
Step 2.
But 'a' to ' i ' takes values only from 1 to 9
So a + b + c + d + e + f + g + h + i = sum of the numbers from 1 to 9 = 45
Step 3.
From step 1 and step 2
d + g = 51 - 45 = 6
possible values of d & g are (1, 5), ( 5,1 ), (2,4) & (4, 2 )
( 2, 4 ) & ( 4 , 2 ) are not possible as "a = 4 "
We have to try with other values (1, 5 ) & ( 5 , 1 )
Step 4.
When d = 1 and g = 5
1. a + b + c + d = 4 + b +c + 1 = 17
b + c = 12 ; only possible values of b & c are ( 9, 3 ) or ( 3, 9 )
2. d + e + f + g = 1 + e + f + 5 = 17
e + f = 17 - 6 = 11
possible combinations for 11 are ( 2,9 ) ; ( 3,8 ) ; (4,7 ) & ( 5,6 )
b & c takes values 3 & 9 g = 5 (assumed) and a = 4 (given).
So, d = 1 & g = 5 is not the solution.
Case 2.
When d = 5 and g = 1
1. a + b + c + d = 4 + b + c + 5 = 17
b + c = 17 - 9 = 8
only possible combination is 2 & 6
a + b + c + d = 4 + ( 2 + 6 ) + 5 = 17
2. d + e + f + g = 5 + e + f + 1 = 17
e + f = 17 - 6 = 11
The only possible value is 3 & 8
d + e + f + g = 5 + ( 3 + 8 ) + 1 = 17
g + h + i = 1 + h + i = 17
h + i = 17 - 1 = 16
The only possible value for h & i are 7 & 9
g + ( h+ i ) = 1 + ( 7 + 9 ) + 17
So the values of d = 5 & g = 1
Most Upvoted Answer
A+B+C+D=D+E+F+G=G+H+I=17 where each letter represent a number from 1 t...
Solution:
Given, A=4 and B, C, E, F, H, I are unknown.
Also, D = 2 * G
Hence, we need to find out the value of D and G.
Let's analyze the given conditions and solve the problem step by step.
1. A B C D = D E F G = H I = 17
As per the given condition, the sum of A, B, C, D is equal to the sum of D, E, F, G, which is equal to 17. Hence, we can write:
A + B + C + D = D + E + F + G = 17
Substituting the value of A as 4, we get:
4 + B + C + D = D + E + F + G = 17
Simplifying the expression, we get:
B + C + D = E + F + G = 13
2. D = 2 * G
As per the given condition, D is twice the value of G. Hence, we can write:
D = 2G
Substituting this value of D in the first equation, we get:
B + C + 3G = E + F + G = 13
Simplifying the expression, we get:
B + C + 2G = E + F = 13 - G
3. Finding the possible values of G
Since G should be a single digit integer, we can try different values of G from 1 to 9 and see which value satisfies the above equation.
Let's start with G = 1:
B + C + 2 = E + F = 12
The only possible values of B and C that satisfy this equation are 4 and 6 (since they should be distinct and their sum should be 6). Hence, we get:
B = 4, C = 2, E = 6, F = 6
Substituting these values in the equation, we get:
4 + 2 + 2 = 6 + 6 + 1 = 13
Hence, the possible values of D and G are:
D = 2G = 2 * 1 = 2
G = 1
Therefore, option 'A' is the correct answer.
Given, A=4 and B, C, E, F, H, I are unknown.
Also, D = 2 * G
Hence, we need to find out the value of D and G.
Let's analyze the given conditions and solve the problem step by step.
1. A B C D = D E F G = H I = 17
As per the given condition, the sum of A, B, C, D is equal to the sum of D, E, F, G, which is equal to 17. Hence, we can write:
A + B + C + D = D + E + F + G = 17
Substituting the value of A as 4, we get:
4 + B + C + D = D + E + F + G = 17
Simplifying the expression, we get:
B + C + D = E + F + G = 13
2. D = 2 * G
As per the given condition, D is twice the value of G. Hence, we can write:
D = 2G
Substituting this value of D in the first equation, we get:
B + C + 3G = E + F + G = 13
Simplifying the expression, we get:
B + C + 2G = E + F = 13 - G
3. Finding the possible values of G
Since G should be a single digit integer, we can try different values of G from 1 to 9 and see which value satisfies the above equation.
Let's start with G = 1:
B + C + 2 = E + F = 12
The only possible values of B and C that satisfy this equation are 4 and 6 (since they should be distinct and their sum should be 6). Hence, we get:
B = 4, C = 2, E = 6, F = 6
Substituting these values in the equation, we get:
4 + 2 + 2 = 6 + 6 + 1 = 13
Hence, the possible values of D and G are:
D = 2G = 2 * 1 = 2
G = 1
Therefore, option 'A' is the correct answer.
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A+B+C+D=D+E+F+G=G+H+I=17 where each letter represent a number from 1 to 9. Find out what does letter D and G represent if letter A=4.a)D=5 G=1b)D=7G=1c)D=2G=1d)D=3G=1Correct answer is option 'A'. Can you explain this answer?
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