Question

How much money does Alice have?
I) Alice has Rs.50 more than Bob.
II) Alice and Bob together have Rs.200.

• A. Statement I alone is sufficient to answer the question
• B. Statement II alone is sufficient to answer the question.
• C. Statement I and II together are sufficient to answer the question but neither statement alone is sufficient.
• D. Statement I and II together are not sufficient to answer the question and additional data is required.

Hint:

When two variables are involved, look for two independent equations to get a unique solution.

Answer 1

The Correct Option is C

Concept: To determine individual values, we need sufficient independent equations involving all variables.
Step 1: Analyze Statement I alone.
Let Bob = \(x\), then Alice = \(x + 50\).
Infinite values possible.
Statement I alone is NOT sufficient.
Step 2: Analyze Statement II alone.
\[ {Alice} + {Bob} = 200 \] Two variables, one equation → infinite solutions.
Statement II alone is NOT sufficient.
Step 3: Combine both statements.
Let Bob = \(x\), then Alice = \(x + 50\).
\[ x + (x + 50) = 200 \Rightarrow 2x + 50 = 200 \Rightarrow 2x = 150 \Rightarrow x = 75 \] So, \[ {Alice} = 75 + 50 = 125 \] A unique value is obtained.
Hence, both statements together are sufficient, but neither alone is sufficient.