For all nonnegative integers a, b, and c, the… | GMAT Sprint

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PS · Problem Solving

705-805

Functions

For all nonnegative integers a, b, and c, the function G is defined by G(a,b,c)= $7^2a+7^1b+7^0*c$ . Which of the following is equal to G(5,4,1)–G(3,6,4)?

Correct answer marked below

G(0, 8, 1)

G(1, 4, 4)

Correct

G(1, 7, 7)

G(2, 2, 3)

G(3, 4, 2)

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Explanation

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Official Explanation

Official

G(5,4,1)–G(3,6,4) =

[49 \cdot 5 + 7 \cdot 4 + 1] - [49 \cdot 3 + 7 \cdot 6 + 4]

[245 + 28 + 1] - [147 + 42 + 4]

274 - 193 = 81

Now evaluate each option:

A. G(0, 8, 1) =

49 \cdot 0 + 7 \cdot 8 + 1 = 0 + 56 + 1 = 57

(not 81)

B. G(1, 4, 4) =

49 \cdot 1 + 7 \cdot 4 + 4 = 49 + 28 + 4 = 81

(matches)…

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What this question tests

Your ability to evaluate and compose functions, including unusual defined operations.

Applying function operations in the wrong order or ignoring domain restrictions.