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Each question is followed by two statements, I and II. Mark the answer:
1. If the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
2. If the question can be answered by using either statement alone.
3. If the question can be answered by using both statements together, but cannot be answered using either statement alone.
4. If the question cannot be answered even by using both statements together.
Three professors A, B and C are separately given three sets of numbers to add. They were expected to find the answers to 1 + 1, 1 + 1 + 2 and 1 + 1 respectively. Their respective answers were 3, 3 and 2. How many of the professors are mathematicians?
I. A Mathematician can never add two numbers correctly, but can always add three numbers correctly.
II.When a mathematician makes a mistake in a sum, the error is + 1 and – 1.
1
2
3
4
Alright, let’s break it down:
Given:
- Three professors: A, B, and C.
- Sums and their answers:
- A got 1+1 ? 3
- B got 1+1+2 ? 3
- C got 1+1 ? 2
What you need to find:
How many are mathematicians, given two clues.
Statement I Explained:
- Mathematician always gets 3-number sums right.
- Mathematician *never* gets 2-number sums right.
Statement II Explained:
- If a mathematician makes a mistake, it’s only by +1 or –1.
Let’s see what we can infer with each statement:
---
- Using Statement I alone:
- Only B had a 3-number sum (1+1+2). Got it right (3). So B could be a mathematician.
- Both A and C had 2-number sums. A’s answer was 3 (should be 2—so wrong), C’s answer was 2 (should be 2—so right).
- Mathematicians never get 2-term sums right, so:
- A could be a mathematician (got 2-number sum wrong).
- C cannot be mathematician (got 2-number sum right!).
- So maybe A and B are mathematicians.
- Using Statement II alone:
- If someone’s wrong, error is always +1 or –1.
- A: 1+1=2 but answered 3 (+1 error) ? could be mathematician.
- B: 1+1+2=4 but answered 3 (–1 error) ? could be mathematician.
- C: 1+1=2, answered 2 (no error) ? not conclusive.
- So A and B again could be mathematicians.
- Using BOTH Statements Together:
- From I: B *could* be mathematician, so could A. C *cannot*.
- From II: The error patterns fit for A and B as mathematicians.
- So, both together only confirm that A and B are mathematicians, not C.
Options Recap:
1. Can answer with one statement, not the other.
2. Can answer with either statement alone.
3. Need both together, can’t answer with either alone.
4. Can’t answer even with both statements.
Correct answer:
We CAN determine the answer (A and B are mathematicians) with either statement alone.
Option 2 is correct.
.
By: Sandeep Dubey ProfileResourcesReport error
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