1985 AJHSME Problems/Problem 18

From AoPSWiki

Problem

Nine copies of a certain pamphlet cost less than $ $10.00$ while ten copies of the same pamphlet (at the same price) cost more than $ $11.00$ . How much does one copy of this pamphlet cost?

$\text{(A)}$ $ $1.07$

$\text{(B)}$ $ $1.08$

$\text{(C)}$ $ $1.09$

$\text{(D)}$ $ $1.10$

$\text{(E)}$ $ $1.11$

Solution

Let $p$ be the cost of the first pamphlet, in dollars. The first part tells us $9p<10 \Rightarrow p<1.\overline{1}$

The second part tells us that $10p>11\Rightarrow p>1.1$

Combining these two parts, the only possible value for $p$ is $1.11$ , since $p$ represents a monetary value.

$\boxed{\text{E}}$

1985 AJHSME (Problems • Resources)
Preceded by Problem 17	Followed by Problem 19
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

Personal tools

Navigation

Search

Toolbox

1985 AJHSME Problems/Problem 18

From AoPSWiki

Problem

Solution

See Also