1986 AMC 8 Problem 8

Attempt Problem 8 of the 1986 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1986 AMC 8 solutions, or check the answer key.

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In the multiplication shown, $B$ represents a digit. What is the value of $B?$

$\begin{array}{r} B2 \\ \times\, 7B \\ \hline 6396 \end{array}$

$3$

$5$

$6$

$7$

$8$

Answer: E

Concepts:cryptarithm units digit

Difficulty rating: 930

Solution:

The units digit of the product comes from $B \times 2,$ which ends in $6$ only when $B = 3$ or $B = 8.$ Since the product $6396$ exceeds $6000,$ $B$ must be $8:$ indeed $82 \times 78 = 6396.$

Thus, the correct answer is E .

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Problem 8 in Other Years

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