2010 AMC 12B Problems/Problem 5

Problem 5

Lucky Larry's teacher asked him to substitute numbers for $a$ , $b$ , $c$ , $d$ , and $e$ in the expression $a-(b-(c-(d+e)))$ and evaluate the result. Larry ignored the parenthese but added and subtracted correctly and obtained the correct result by coincidence. The number Larry sustitued for $a$ , $b$ , $c$ , and $d$ were $1$ , $2$ , $3$ , and $4$ , respectively. What number did Larry substitude for $e$ ?

$\textbf{(A)}\ -5 \qquad \textbf{(B)}\ -3 \qquad \textbf{(C)}\ 0 \qquad \textbf{(D)}\ 3 \qquad \textbf{(E)}\ 5$

Solution

We simply plug in the numbers $1 - 2 - 3 - 4 + e = 1 - (2 - (3 - (4 + e)))$ $-8 + e = -2 - e$ $2e = 6$ $e = 3 \;\;(D)$

2010 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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2010 AMC 12B Problems/Problem 5

Problem 5

Solution

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