Question

Given the following information:
Sally is 2 years younger than Abby.
Daisy is 5 years older than Tracy.
Abby is 6 years older than Tracy.

Quantity A: Sally's age
Quantity B: Daisy's age

• A. Quantity A is greater.
• B. Quantity B is greater.
• C. The relationship cannot be determined.
• D. The two quantities are equal.
• E.

Hint:

In problems with multiple relative relationships (ages, heights, etc.), the key is to find a "bridge" variable that connects the different pieces of information. Here, Tracy's age was the bridge that allowed us to compare Sally and Daisy directly.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a logic problem involving relative ages. To compare Sally's age and Daisy's age, we need to express both of their ages in terms of a common reference person.
Step 2: Key Formula or Approach:
Let S, A, D, and T be the ages of Sally, Abby, Daisy, and Tracy, respectively. Translate the sentences into equations: \begin{itemize} \item \(S = A - 2\) \item \(D = T + 5\) \item \(A = T + 6\) \end{itemize} Tracy's age (T) is a common link between the relationships. We will express both S and D in terms of T.
Step 3: Detailed Explanation:
Expressing Daisy's age in terms of T:
We are directly given this relationship: \[ D = T + 5 \] Expressing Sally's age in terms of T:
We know that \(S = A - 2\). We also know that \(A = T + 6\). We can substitute the expression for A into the equation for S: \[ S = (T + 6) - 2 \] \[ S = T + 4 \] Comparing the quantities:
Quantity A: Sally's age = \(T + 4\)
Quantity B: Daisy's age = \(T + 5\)
Since T represents a person's age, it must be a positive number. For any value of T, \(T + 5\) will always be 1 greater than \(T + 4\).
Therefore, Daisy's age is always greater than Sally's age.
Step 4: Final Answer:
Quantity B is greater than Quantity A.