Sample Question 4:

The sum of two positive numbers is 5 times their difference. What is the ratio of the larger number to the smaller?

$\textbf{(A)}\ \frac54 \qquad\textbf{(B)}\ \frac32 \qquad\textbf{(C)}\ \frac95 \qquad\textbf{(D)}\ 2 \qquad\textbf{(E)}\ \frac52$

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Answer Keys

Question 4: B

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Solutions

Question 4
Step 1: Let's denote the larger number as $a$ and the smaller number as $b$.

Step 2: According to the problem, the sum of these two numbers is 5 times their difference. Mathematically, this can be represented as $a + b = 5(a - b)$.

Step 3: Expanding the right side of the equation gives $a + b = 5a - 5b$.

Step 4: By rearranging the terms, we obtain $4a = 6b$.

Step 5: Factoring the equation results in $2a = 3b$.

Step 6: Solving for the ratio of $a$ to $b$ gives $\frac{a}{b} = \frac{3}{2}$.

So, the ratio of the larger number to the smaller number is $\frac{3}{2}$, which corresponds to answer choice $\textbf{(B)}\ \frac{3}{2}$.