Difference between revisions of "1989 AJHSME Problems/Problem 8"
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We use the distributive property to get <cmath>3\times 4+2\times 4+2\times 3 = 26 \rightarrow \boxed{\text{E}}</cmath> | We use the distributive property to get <cmath>3\times 4+2\times 4+2\times 3 = 26 \rightarrow \boxed{\text{E}}</cmath> | ||
− | ==Solution 2 | + | ==Solution 2== |
Since <math>\frac12+\frac13+\frac14 > \frac12+\frac14+\frac14 = 1</math>, we have <cmath>(2\times 3\times 4)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\right) > 2\times 3\times 4 \times 1 = 24</cmath> The only answer choice greater than <math>24</math> is <math>\boxed{\text{E}}</math>. | Since <math>\frac12+\frac13+\frac14 > \frac12+\frac14+\frac14 = 1</math>, we have <cmath>(2\times 3\times 4)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\right) > 2\times 3\times 4 \times 1 = 24</cmath> The only answer choice greater than <math>24</math> is <math>\boxed{\text{E}}</math>. | ||
==Solution 3(Bash)== | ==Solution 3(Bash)== | ||
− | We can just bash it out, getting <math>24(\frac12+\frac13+\frac14)= 12 + 8 + 6 = 26 \ | + | We can just bash it out, getting <math>24(\frac12+\frac13+\frac14)= 12 + 8 + 6 = 26 \Longrightarrow \boxed{\text{E}}</math> |
+ | -fn106068 | ||
==See Also== | ==See Also== |
Latest revision as of 11:15, 28 August 2021
Problem
Solution 1
We use the distributive property to get
Solution 2
Since , we have
The only answer choice greater than
is
.
Solution 3(Bash)
We can just bash it out, getting
-fn106068
See Also
1989 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.