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

(New page: ==Problem== If <math>200\leq a \leq 400</math> and <math>600\leq b\leq 1200</math>, then the largest value of the quotient <math>\frac{b}{a}</math> is <math>\text{(A)}\ \frac{3}{2} \qqua...)
 
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==Solution==
 
==Solution==
  
{{Solution}}
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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.
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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>
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6 is C.
  
 
==See Also==
 
==See Also==
  
 
[[1986 AJHSME Problems]]
 
[[1986 AJHSME Problems]]

Revision as of 18:33, 24 January 2009

Problem

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

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

Solution

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.

See Also

1986 AJHSME Problems

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