For each positive integer k, f(k) is defined… | GMAT Sprint

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PS · Problem Solving

705-805

Functions

For each positive integer k, f(k) is defined to be the number created by reversing the digits of k. For instance, f(42) = 24. How many positive two-digit integers k are there where k + f(k) is the square of a positive integer?

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Explanation

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Official Explanation

Official

Let's represent a two-digit number

k

10a + b

, where

a

is the tens digit and

b

is the units digit.

Then

f(k)

becomes

10b + a

, and

k + f(k) = (10a + b) + (10b + a) = 11(a + b)

.

For

11(a + b)

to be the square of an integer,

(a + b)

must be 11, making

k + f(k)

equal to

11^2

.…

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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.