| B | H | A | A | G | F | ||
| + | A | H | J | F | K | F | |
| A | A | F | G | C | A | F |
Which digit does the letter A represent?
Correct Answer: 1
Solution and Explanation
Let's summarize the key findings:
Identification of H: The units digit of 2H must be 0, leading to the conclusion that H = 5.
Determination of A and B: Since the sum of both 6-digit numbers is a 7-digit number, the leftmost digit in the 7-digit number has to be 1. Therefore, A = 1. With H = 5, B can be calculated as 9.
Calculation of C: C is determined as A + 1, which is 2.
Possible values for G and K: The units digit of the sum of G + K is 1, leading to two possible pairs (3 and 8 or 4 and 7).
Exploration of possible values for J: Analyzing the possibilities for J based on the pairs for G and K.
- If J = 3, G = 4, K = 7, and D and E are 6 and 8.
- If J = 6, G = 7, K = 4, and D and E are 3 and 8.
- If J = 7, G = 8, K = 3, and D and E are 4 and 6.
The analysis efficiently eliminates some possibilities based on distinct digits for each letter and leads to potential solutions for the values of G, K, J, D, and E.
A represents 1.
Which digit does the letter B represent?
Correct Answer: 9
Solution and Explanation
Let's summarize the key findings:
Identification of H: The units digit of 2H must be 0, leading to the conclusion that H = 5.
Determination of A and B: Since the sum of both 6-digit numbers is a 7-digit number, the leftmost digit in the 7-digit number has to be 1. Therefore, A = 1. With H = 5, B can be calculated as 9.
Calculation of C: C is determined as A + 1, which is 2.
Possible values for G and K: The units digit of the sum of G + K is 1, leading to two possible pairs (3 and 8 or 4 and 7).
Exploration of possible values for J: Analyzing the possibilities for J based on the pairs for G and K.
- If J = 3, G = 4, K = 7, and D and E are 6 and 8.
- If J = 6, G = 7, K = 4, and D and E are 3 and 8.
- If J = 7, G = 8, K = 3, and D and E are 4 and 6.
The analysis efficiently eliminates some possibilities based on distinct digits for each letter and leads to potential solutions for the values of G, K, J, D, and E.
B represents 9.
Which among the digits 3, 4, 6 and 7 cannot be represented by the letter D?
Correct Answer: 7
Solution and Explanation
Let's summarize the key findings:
Identification of H: The units digit of 2H must be 0, leading to the conclusion that H = 5.
Determination of A and B: Since the sum of both 6-digit numbers is a 7-digit number, the leftmost digit in the 7-digit number has to be 1. Therefore, A = 1. With H = 5, B can be calculated as 9.
Calculation of C: C is determined as A + 1, which is 2.
Possible values for G and K: The units digit of the sum of G + K is 1, leading to two possible pairs (3 and 8 or 4 and 7).
Exploration of possible values for J: Analyzing the possibilities for J based on the pairs for G and K.
- If J = 3, G = 4, K = 7, and D and E are 6 and 8.
- If J = 6, G = 7, K = 4, and D and E are 3 and 8.
- If J = 7, G = 8, K = 3, and D and E are 4 and 6.
The analysis efficiently eliminates some possibilities based on distinct digits for each letter and leads to potential solutions for the values of G, K, J, D, and E.
D cannot be 7.
Which among the digits 4, 6, 7 and 8 cannot be represented by the letter G?
Which among the digits 4, 6, 7 and 8 cannot be represented by the letter G?
Correct Answer: 6
Solution and Explanation
Let's summarize the key findings:
Identification of H: The units digit of 2H must be 0, leading to the conclusion that H = 5.
Determination of A and B: Since the sum of both 6-digit numbers is a 7-digit number, the leftmost digit in the 7-digit number has to be 1. Therefore, A = 1. With H = 5, B can be calculated as 9.
Calculation of C: C is determined as A + 1, which is 2.
Possible values for G and K: The units digit of the sum of G + K is 1, leading to two possible pairs (3 and 8 or 4 and 7).
Exploration of possible values for J: Analyzing the possibilities for J based on the pairs for G and K.
- If J = 3, G = 4, K = 7, and D and E are 6 and 8.
- If J = 6, G = 7, K = 4, and D and E are 3 and 8.
- If J = 7, G = 8, K = 3, and D and E are 4 and 6.
The analysis efficiently eliminates some possibilities based on distinct digits for each letter and leads to potential solutions for the values of G, K, J, D, and E.
G cannot be 6.
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