Difference between revisions of "1986 AJHSME Problems/Problem 14"

Revision as of 18:33, 24 January 2009

If $200\leq a \leq 400$ and $600\leq b\leq 1200$ , then the largest value of the quotient $\frac{b}{a}$ is

$\text{(A)}\ \frac{3}{2} \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 300 \qquad \text{(E)}\ 600$

Obviously, $\frac{b}{a}$ will be largest if $b$ is the largest it can be, and $a$ is the smallest it can be.

Since $b$ can be no larger than $1200$ , $b = 1200$ . Since $a$ can be no less than $200$ , $a = 200$ . $\frac{1200}{200} = 6$

6 is C.

@@ Line 7: / Line 7: @@
 ==Solution==
-{{Solution}}
+Obviously, <math>\frac{b}{a}</math> will be largest if <math>b</math> is the largest it can be, and <math>a</math> is the smallest it can be.
+Since <math>b</math> can be no larger than <math>1200</math>, <math>b = 1200</math>. Since <math>a</math> can be no less than <math>200</math>, <math>a = 200</math>. <math>\frac{1200}{200} = 6</math>
+is C.
 ==See Also==
 [[1986 AJHSME Problems]]