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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

8.

In the multiplication shown, BB represents a digit. What is the value of B?B?
B2× 7B6396\begin{array}{r} B2 \\ \times\, 7B \\ \hline 6396 \end{array}
33
55
66
77
88
Answer: E
Concepts:cryptarithmunits digit
Small hint:
The units digit of the product is 6,6, and it comes from B×2B \times 2
Big hint:
B×2B \times 2 ends in 66 when B=3B = 3 or B=8;B = 8; the product is large, so test which value works
Solution:
The units digit of the product comes from B×2,B \times 2, which ends in 66 only when B=3B = 3 or B=8.B = 8. Since the product 63966396 exceeds 6000,6000, BB must be 8:8: indeed 82×78=6396.82 \times 78 = 6396.
Thus, the correct answer is E .
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