2006 iTest Problems/Problem 3

Problem

Let $I, T, E, S$ be distinct positive integers such that the product $ITEST = 2006$ . What is the largest possible value of the sum $I + T + E + S + T + 2006$ ?

$\mathrm{(A)}\, 2086\quad\mathrm{(B)}\, 4012\quad\mathrm{(C)}\, 2144$

Solution

Note that the expression can be written as $IT^2ES = 2006$ . The prime factorization of $2006$ is $2 \cdot 17 \cdot 59$ . Since $2006$ does not have perfect squares as factors, $T = 1$ . The other variables are the three primes since all variables are distinct, so the maximum value of $I + T + E + S + T + 2006$ is $2 + 2 + 17 + 59 + 2006 = \boxed{\textbf{(A) } 2086}$ .

2006 iTest (Problems, Answer Key)
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2006 iTest Problems/Problem 3

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