Question

Which one of the following must have two sources?

• A. : A
• B. : B
• C. : C
• D. : D
• A. : 2
• B. : 3
• C. : 4
• D. : 5
• A. : F
• B. : E
• C. : A
• D. : None of the above
• A. : A introduced the wrong answer to question 27
• B. : E introduced the wrong answer to question 46
• C. : F introduced the wrong answer to question 14
• D. : H introduced the wrong answer to question 46
• A. Only (I)
• B. Only (II)
• C. Neither (I) nor (II)
• D. Both (I) and (II)

Answer 1

The Correct Option is B

B has 1 wrong answer and 3 blank answers (46, 90, 25). According to the rules: - A person with 1 source will only have 1 blank (when the source had no answer), and 1 wrong answer (which is compulsory).
- A person with 2 sources will have blanks where the sources disagreed (i.e., answer keys didn't match).
Since B has 3 blanks, it's impossible for a person with only one source to have so many blanks.
Therefore, B must have compared answer keys from two sources, found mismatches for Q46, Q90, and Q25, and left them blank. \[ \Rightarrow \text{B must have two sources.} \]

Answer 2

Let’s trace how C could have created their answer key: - C has blank answers: 17, 46, 90 ⇒ implying two sources.
- That means C must have had access to answer keys of two others, who already had their keys ready.
- Each of these two sources must have created their own keys from others or directly from the mastermind. - For example:
G and A could be the sources.
→ A copied from mastermind (no blanks, just 1 wrong).
→ G copied from A.
→ F copied from A and G (has blanks).
→ Then C uses F and G (or F and A) and then introduces its own wrong answer.
So, C’s formation required:
- A (1),
- G (2),
- F (3),
- Then C itself (4th in line). Thus, 4 people needed to make keys before C could make theirs. \[ \Rightarrow \boxed{4} \]

Answer 3

To identify the correct person who had both G and H as sources, we must look for someone:
- With multiple blanks (indicating 2 sources), - Whose blanks overlap with G and H.
From the table:
- G has wrong 25; - H has wrong 46, 92. Now check if anyone else has blanks at these positions (25, 46, 92):
- F has blanks: 92, 90 ⇒ Possibly H but not G.
- C has blanks: 17, 46, 90 ⇒ 46 overlaps with H.
- But no one shares blanks with both G and H.
Hence, no person has both G and H as sources. \[ \Rightarrow \boxed{\text{None of the above}} \]

Answer 4

To find the person who introduced a wrong answer (not copied), we must remember: Each person compulsorily introduces one wrong answer that is not a blank and is not from sources.
- F has wrong: 14, 46 and blank: 92.
- Source mismatch can explain 92 (blank), 46 may be from source.
- But 14 is not listed in any other person’s wrongs/blanks, and hence uniquely belongs to F.
So F must have introduced wrong answer to 14. \[ \Rightarrow \boxed{\text{F introduced wrong answer to 14}} \]

Answer 5

Identical sources will produce: - Identical wrong answers - Identical blanks Let’s analyze: (I) A, D, G - A: wrong 46 - D: wrong 17 - G: wrong 25 All have 1 wrong, no blanks, and all unique ⇒ likely copied from same person (mastermind). (II) E and H - Both have wrongs: 46, 92 → Perfect match of wrongs ⇒ likely they copied from same source and introduced same errors. Thus, both groups have identical sources. \[ \Rightarrow \boxed{\text{Both (I) and (II)}} \]