A function V(a, b) is defined for positive in… | GMAT Sprint

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PS · Problem Solving

705-805

Functions

A function V(a, b) is defined for positive integers a, b and satisfies V(a, a) = a, V(a, b) = V(b, a), V(a, a+b) = (1 + a/b) V(a, b). The value represented by V(66, 14) is ?

Answer Choices

Correct answer marked below

364

231

455

472

None of the foregoing

Correct

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Explanation

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Official Explanation

Official

Given that:

V(a, a) = a

;

V(a, b) = V(b, a)

;

V(a, a+b) = (1 + \frac{a}{b}) V(a, b)

.

Question asks to find the value of

V(66, 14)

.

Notice that only the first function gives answer as a simple value rather than another function, thus we should manipulate with

V(66, 14)

so that to get

V(a, a) = a

in the end.

V(66,14) = V(14,66) = V(14, 14+52)

;

V(14, 14+52)=(1+\frac{14}{52})V(14,52)=\frac{33}{26}*V(14,14+38)

;

\frac{33}{26}*V(14,14+38)=\frac{33}{26}*(1+\frac{14}{38})V(14,38)=\frac{33}{19}*V(14, 14+24)

;

\frac{33}{19}*V(14,14+24)=\frac{33}{19}*(1+\frac{14}{24})V(14,24)=\frac{33}{12}*V(14,14+10)

;…

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What this question tests

What it tests

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

Common trap

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