Question

Set $P$ consists of all the single digit prime numbers. Set $Q$ contains all of the elements of Set $P$, as well as an additional positive integer $x$. If the sum of all of the elements of Set $Q$ is $30$, calculate the value of the expression $x^2-11x-25$.

• A. 1
• B. 7
• C. -11
• D. -3

Answer 1

The correct option is A 1

First, you need to determine the content of Set $R$.

If Set $R$ consists of all the one-digit prime numbers, then $R=2,3,5,7$.

The sum of the elements of Set $S$ would therefore be $2+3+5+7+x=30$.

Combine like terms: $17+x=30$.

Subtract $17$ from both sides and you find $x=13$.

Plug $x=13$ into the equation and solve: $(13{)}^2-11(13)-25=169-143-25=169-168=1$

Then, $1$ is the answer.