Comprehension
Recently, the answers of a test held nationwide were leaked to a group of unscrupulous people. The investigative agency has arrested the mastermind and nine other people A, B, C, D, E, F, G, H, and I in this matter. Interrogating them, the following facts have been obtained regarding their operation. Initially, the mastermind obtains the correct answer key. All the others create their answer-key from one or two people who already possess the same. These people are called his/her “sources”. If the person has two sources, then he/she compares the answer-keys obtained for both sources. If the key to a question from both sources is identical, it is copied, otherwise it is left blank. If the person has only one source, he/she copies the source’s answer into his/her copy. Finally, each person compulsorily replaces one of the answers (not a blank one) with a wrong answer in his/her answer key.
The paper contained 200 questions; so the investigative agency has ruled out the possibility of two or more of them introducing wrong answers to the same question. The investigative agency has a copy of the correct answer key and has tabulated the following data. This data represents question numbers.
| Name | Wrong Answer(s) | Blank Answer(s) |
|---|---|---|
| A | 46 | — |
| B | 46, 90, 25 | — |
| C | 27, 56 | 17, 46, 90 |
| D | 17 | — |
| E | 46, 90 | — |
| F | 14, 46 | 92, 90 |
| G | 25 | — |
| H | 46, 92 | — |
| I | 17, 26, 90 | — |
Question: 1
Which one of the following must have two sources?
Which one of the following must have two sources?
Show Hint
More than one blank implies use of two sources—blanks occur only when source keys mismatch.
Updated On: Aug 7, 2025
- : A
- : B
- : C
- : D
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The Correct Option is B
Solution and Explanation
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. \[ \Rightarrow \text{B must have two sources.} \]
- 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. \[ \Rightarrow \text{B must have two sources.} \]
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Question: 2
How many people (excluding the mastermind) needed to make answer keys before C could make his answer key?
How many people (excluding the mastermind) needed to make answer keys before C could make his answer key?
Show Hint
Always count the full source chain when tracing dependencies in such logic puzzles.
Updated On: Aug 7, 2025
- : 2
- : 3
- : 4
- : 5
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The Correct Option is C
Solution and Explanation
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. \[ \Rightarrow \boxed{4} \]
- 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. \[ \Rightarrow \boxed{4} \]
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Question: 3
Both G and H were sources to ….
Both G and H were sources to ….
Show Hint
Matching blank positions is key to identifying common sources.
Updated On: Aug 7, 2025
- : F
- : E
- : A
- : None of the above
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The Correct Option is D
Solution and Explanation
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. \[ \Rightarrow \boxed{\text{None of the above}} \]
- 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. \[ \Rightarrow \boxed{\text{None of the above}} \]
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Question: 4
Which of the following statement is true?
Which of the following statement is true?
Show Hint
Check for uniquely wrong questions to find the one introduced by the person.
Updated On: Aug 7, 2025
- : A introduced the wrong answer to question 27
- : E introduced the wrong answer to question 46
- : F introduced the wrong answer to question 14
- : H introduced the wrong answer to question 46
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The Correct Option is C
Solution and Explanation
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. \[ \Rightarrow \boxed{\text{F introduced wrong answer to 14}} \]
- 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. \[ \Rightarrow \boxed{\text{F introduced wrong answer to 14}} \]
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Question: 5
Which of the following two groups of people has identical sources?
(I) A, D, G
(II) E and H
Which of the following two groups of people has identical sources?
(I) A, D, G
(II) E and H
Show Hint
Identical wrong answers imply identical sources if blank patterns also match.
Updated On: Aug 7, 2025
Only (I)
Only (II)
Neither (I) nor (II)
Both (I) and (II)
Show Solution
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The Correct Option is D
Solution and Explanation
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.
\[
\Rightarrow \boxed{\text{Both (I) and (II)}}
\]
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