Difference between revisions of "1968 AHSME Problems/Problem 4"

Revision as of 13:43, 28 July 2016

Define an operation $\star$ for positive real numbers as $a\star b=\frac{ab}{a+b}$ . Then $4 \star (4 \star 4)$ equals:

$\text{(A) } \frac{3}{4}\quad \text{(B) } 1\quad \text{(C) } \frac{4}{3}\quad \text{(D) } 2\quad \text{(E )} \frac{16}{3}$

$4 \star 4 \star 4 = 4 \star 2 = \frac{4}{3}$

Therefore, our answer is $\fbox{C}$

Solution by VivekA

1968 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

@@ Line 10: / Line 10: @@
 == Solution ==
-<math>\fbox{C}</math>
+<math>4 \star 4 \star 4 = 4 \star 2 = \frac{4}{3}</math>
+Therefore, our answer is <math>\fbox{C}</math>
+Solution by VivekA
 == See also ==