Bunuel wrote:
For all nonnegative integers a, b, and c, the function G is defined by G(a,b,c)=7^2*a+7^1*b+7^0*c. Which of the following is equal to G(5,4,1)–G(3,6,4)?
A. G(0, 8, 1)
B. G(1, 4, 4)
C. G(1, 7, 7)
D. G(2, 2, 3)
E. G(3, 4, 2)
We are given that the function G is defined by G(a,b,c) = 7^2*a + 7^1*b + 7^0*c = 49a + 7b + c and need to determine which answer choice is equal to G(5,4,1) – G(3,6,4).
G(5,4,1) = 49(5) + 7(4) + 1 = 274
G(3,6,4) = 49(3) + 7(6) + 4 = 193
G(5,4,1) – G(3,6,4) = 274 – 193 = 81
Although we could go through each answer choice and see which one will yield the result of 81, an easier approach is to express 81 in the form of 49a + 7b + c. That is, if 81 = 49a + 7b + c, what are the values of a, b, and c? Keep in mind that a, b, and c are nonnegative integers.
81 = 49a + 7b + c
Since 81 is more than 49 but less than 2 times 49, a must be 1. In that case, we have:
81 = 49(1) + 7b + c
81 = 49 + 7b + c
32 = 7b + c
Since 32 is more than 4 times 7 but less than 5 times 7, b must be 4. In that case, we have:
32 = 7(4) + c
32 = 28 + c
4 = c
Therefore, a = 1, b = 4, and c = 4. In other words, 81 = 49(1) + 7(4) + 4.
However, 49(1) + 7(4) + 4 = G(1, 4, 4), so 81 = G(1, 4, 4).
Answer: B
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