Question

Answer question given below by reading the following information:
Elle is three times older than Yogesh; Zaheer is half the age of Wahida. Yogesh is older than Zaheer.
Which of the following information will be sufficient to estimate Elle's age?

• A. Zaheer is 10 years old.
• B. Both Yogesh and Wahida are older than Zaheer by the same number of years.
• C. Wahida is 20 years old.
• D. Zaheer is 12 years old and yogesh has the same age as wahida.

Hint:

In data sufficiency questions, count the number of variables and the number of independent equations. Here, we have 4 variables ($E, Y, Z, W$) and 2 initial equations. We need 2 more independent equations to solve completely, which is provided only by Option (D).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
To estimate a specific value (Elle's age, $E$) uniquely, we must have enough independent equations to solve for all the variables involved ($E$, $Y$, $Z$, and $W$).
Detailed Explanation:
Let us evaluate each option to see if it allows us to compute $E$ uniquely, using the base relations:
- $E = 3Y$
- $W = 2Z$
- $Y > Z$
- Option (A) analysis: "Zaheer is 10 years old" $\implies Z = 10 \implies W = 20$. Since we only know $Y > 10$, $Y$ can be any value, meaning $E$ cannot be determined uniquely. Insufficient.
- Option (B) analysis: "Yogesh and Wahida are older than Zaheer by the same number of years" $\implies Y - Z = W - Z \implies Y = W = 2Z$. This gives $E = 3(2Z) = 6Z$. Since we do not know $Z$, $E$ cannot be determined. Insufficient.
- Option (C) analysis: "Wahida is 20 years old" $\implies W = 20 \implies Z = 10$. This is identical to Option (A). Insufficient.
- Option (D) analysis: "Zaheer is 12 years old and yogesh has the same age as wahida":
- $Z = 12$
- $W = 2Z = 2 \times 12 = 24$ years old.
- $Y = W \implies Y = 24$ years old.
- Now, we can uniquely calculate $E$: \[ E = 3Y = 3 \times 24 = 72 \text{ years old} \] This information is completely sufficient.

Step 2: Final Answer:
The sufficient information is given by Option (D).