Difference between revisions of "1986 AJHSME Problems/Problem 8"
5849206328x (talk | contribs) (New page: ==Problem== In the product shown, <math>\text{B}</math> is a digit. The value of <math>\text{B}</math> is <cmath>\begin{tabular}[t]{r} \text{B}2 \\ \times 7\text{B} \\ \hline 6396 \\ \e...) |
Mathgeek2006 (talk | contribs) m (→Problem) |
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In the product shown, <math>\text{B}</math> is a digit. The value of <math>\text{B}</math> is | In the product shown, <math>\text{B}</math> is a digit. The value of <math>\text{B}</math> is | ||
− | <cmath>\begin{ | + | <cmath>\begin{array}{rr} |
− | \text{B}2 \\ | + | &\text{B}2 \\ |
− | \times 7\text{B} \\ \hline | + | \times& 7\text{B} \\ \hline |
− | 6396 \\ | + | &6396 \\ |
− | \end{ | + | \end{array}</cmath> |
<math>\text{(A)}\ 3 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 8</math> | <math>\text{(A)}\ 3 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 8</math> | ||
Line 13: | Line 13: | ||
==Solution== | ==Solution== | ||
− | {{ | + | Note that in any multiplication problem, the only 2 digits that will influence the last digit of the number will be the last digits of each number being multiplied. |
+ | |||
+ | So, <math>2 \times \text{B}</math> has a units digit of <math>6</math>, so <math>\text{B}</math> is either <math>3</math> or <math>8</math>. If <math>\text{B}=3</math>, then the product is <math>32\times 73</math>, which is clearly too small, so <math>\text{B}=8</math> | ||
+ | |||
+ | <math>\boxed{\text{E}}</math> | ||
==See Also== | ==See Also== | ||
− | [[ | + | {{AJHSME box|year=1986|num-b=7|num-a=9}} |
+ | [[Category:Introductory Number Theory Problems]] | ||
+ | [[Category:Introductory Algebra Problems]] | ||
+ | {{MAA Notice}} |
Latest revision as of 19:35, 10 March 2015
Problem
In the product shown, is a digit. The value of
is
Solution
Note that in any multiplication problem, the only 2 digits that will influence the last digit of the number will be the last digits of each number being multiplied.
So, has a units digit of
, so
is either
or
. If
, then the product is
, which is clearly too small, so
See Also
1986 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.