There are eight different two-digit numbers: AD, BA, BG, CE, DB, DH, EF and
FC. Each is less than 70 and divisible by 7. Each of the distinct letters
represents a different digit. The same letter represents the same digit. Given E
= 5, what is G?
G=8
To determine the value of G, we need to find the number represented by the letter G and check if that number is divisible by 7.
From the given information, we know that each of the letters represents a different digit, so we need to find the number represented by the letter G.
Let's examine the given two-digit numbers:
AD < 70 and divisible by 7
BA < 70 and divisible by 7
BG < 70 and divisible by 7
CE < 70 and divisible by 7
DB < 70 and divisible by 7
DH < 70 and divisible by 7
EF < 70 and divisible by 7
FC < 70 and divisible by 7
We are given that E = 5. Looking at the given numbers, the only number containing E (5) is EF. So, E = 5 implies that F = 5.
Now, let's find G. We need to check if the number represented by G is divisible by 7. We have the following possibilities for G:
AD, BA, BG, CE, DB, DH, FC
From these options, we see that only BG satisfies the condition. So G = 7.
Therefore, G = 7.