1985 AJHSME Problems/Problem 18

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.

$\boxed{\text{E}}$

Also, just by quickly going over the answers, it is seen that all of the answers satisfy the first statement: The cost of 9 pamphlet is less that 10 dollars.

The second statement states that 10 pamphlets cost more than 11 dollars. Therefore, since there are only two statements and the first one can be satisfied with all of the answer choices, the answer choice that is the most expensive of them all will be the right answer choice, thus the answer is $\boxed{\text{E}}$

See Also

1985 AJHSME (ProblemsAnswer KeyResources)
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
All AJHSME/AMC 8 Problems and Solutions


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