Track / Stage 5 / 89 of 400 #689 of 1964

Problem 689

AIME late

Algebra Difficulty 5.2 Find the answer

Suppose that

$\begin{aligned} M & =1^{5}+2^{4} \times 3^{3}-4^{2} \div 5^{1} \\ N & =1^{5}-2^{4} \times 3^{3}+4^{2} \div 5^{1} \end{aligned}$

What is the value of $M+N$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Since $M=1^{5}+\left(2^{4} \times 3^{3}\right)-\left(4^{2} \div 5^{1}\right)$ and $N=1^{5}-\left(2^{4} \times 3^{3}\right)+\left(4^{2} \div 5^{1}\right)$ , then when $M$ and $N$ are added the terms $\left(2^{4} \times 3^{3}\right)$ and $\left(4^{2} \div 5^{1}\right)$ "cancel" out.

Thus, $M+N=1^{5}+1^{5}=2$ .

ANSWER: 2

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.