Anita, Biplove, Cheryl, Danish, Emily and Feroze compared their marks among themselves. Anita scored the highest marks, Biplove scored more than Danish, Cheryl scored more than at least two others and Emily had not scored the lowest.
Statement I: Exactly two members scored less than Cheryl.
Statement II: Emily and Feroze scored the same marks.
Which of the following statements would be sufficient to identify the one with the lowest marks?
Statement I: Exactly two members scored less than Cheryl.
Statement II: Emily and Feroze scored the same marks.
Which of the following statements would be sufficient to identify the one with the lowest marks?
Show Hint
- Statement I only.
- Statement II only.
- Both Statement I and Statement II are required together.
- Neither Statement I nor Statement II is sufficient.
- Either Statement I or Statement II is sufficient.
The Correct Option is B
Solution and Explanation
Given base facts:
- There are six people.
- Anita is the highest.
- \( \text{Biplove} > \text{Danish} \).
- Cheryl is above at least two people (so the bottom two are not Cheryl).
- Emily is not the lowest.
Check Statement I alone:
“Exactly two scored less than Cheryl.”
Then precisely two people are below Cheryl. - Possible bottom two: \(\{ \text{Danish}, \text{Feroze} \}\) or \(\{ \text{Danish}, \text{Biplove} \}\). - Order between them is not uniquely determined. - Emily is not lowest, and Biplove \(>\) Danish can still hold (e.g., Biplove second-lowest, Danish lowest).
\(\Rightarrow\) The lowest is **not uniquely determined** by Statement I. (Insufficient.)
Check Statement II alone:
“Emily and Feroze scored the same.”
- Emily is not the lowest \(\Rightarrow\) Feroze (with equal score) is also not the lowest. - Cheryl is above at least two people, and the pair below Cheryl cannot include Emily or Feroze. - With Biplove \(>\) Danish, the **only possible candidate** for the lowest is Danish.
\(\Rightarrow\) Statement II alone is sufficient.
Final Answer: \[ \boxed{\text{B (Statement II only is sufficient).}} \]
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