Comprehension

The following charts depict details of research papers written by four authors, Arman, Brajen, Chintan, and Devon. The papers were of four types, single-author, two-author, three-author, and four-author, that is, written by one, two, three, or all four of these authors, respectively. No other authors were involved in writing these papers.

The following additional facts are known.
1. Each of the authors wrote at least one of each of the four types of papers.
2. The four authors wrote different numbers of single-author papers.
3. Both Chintan and Devon wrote more three-author papers than Brajen.
4. The number of single-author and two-author papers written by Brajen were the same.

Question: 1

What was the total number of two-author and three-author papers written by Brajen?

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When faced with inconsistent data in a DILR set, first check for simple misinterpretations. If the data is truly contradictory, look for the most minimal change that resolves the inconsistency (like changing one bar value). Then, use the answers to other questions in the set as "checkpoints" to confirm you are on the right track to the intended (though flawed) solution.
Updated On: Jul 4, 2026
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Correct Answer: 4

Solution and Explanation

Step 1: Brajen's total papers = 8, and every author (including Brajen) has exactly 2 four-author papers, leaving 6 papers split between single, two- and three-author types.
Step 2: Brajen's single-author count equals his two-author count (given); the only value consistent with his total and with the "Chintan, Devon > Brajen" three-author rule is 2 each, leaving \(6-2-2=2\) three-author papers for him.
Step 3: Add his two-author and three-author counts.
\[ \boxed{2+2=4} \]
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Question: 2

Which of the following statements is/are NECESSARILY true?
i. Chintan wrote exactly three two-author papers.
ii. Chintan wrote more single-author papers than Devon.

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For "Necessarily True" questions, you must be a skeptic. Your goal is to try and break the statement. If you can construct a single valid counterexample, the statement is not necessarily true. If all your attempts to break it fail and logic confirms it must always hold, then it is necessarily true.
Updated On: Jul 2, 2026
  • Neither i nor ii
  • Both i and ii
  • Only i
  • Only ii
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The Correct Option is A

Solution and Explanation

Approach: Disprove each “necessarily true” claim with a single counterexample grid — the fastest way to kill a must-be-true statement.

Step 1 — Two legal grids exist: All facts are satisfied by both (Chintan two-author $=4$, single $=3$; Devon single $=4$, two-author $=1$) and (Chintan two-author $=3$, single $=4$; Devon single $=3$, two-author $=2$). Both keep three-author at 3 each and four-author at 2 each.

Step 2 — Kill statement i: The first grid has Chintan with 4 two-author papers, not 3. One counterexample is enough — i is not necessarily true.

Step 3 — Kill statement ii: In the first grid Chintan’s singles $(3) <$ Devon’s singles $(4)$, so “Chintan more than Devon” is false there. Not necessarily true.

Step 4 — Verdict: Each statement has a valid grid where it fails, so neither is forced.

Answer: Neither i nor ii.
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Question: 3

Which of the following statements is/are NECESSARILY true?
i. Arman wrote three-author papers only with Chintan and Devon.
ii. Brajen wrote three-author papers only with Chintan and Devon.

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In sets involving author contributions, remember that the sum of individual counts is equal to the number of papers multiplied by the number of authors per paper. For instance, `sum($s3_counts$) = 3 * ($total_s3_papers$)`. This relationship is often the key to unlocking the distribution.
Updated On: Jul 2, 2026
  • Only ii
  • Neither i nor ii
  • Both i and ii
  • Only i
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The Correct Option is C

Solution and Explanation

Approach: Reconstruct the three three-author papers explicitly as “everyone except one” teams, then just read membership.

Step 1 — Each three-author paper $=$ all four minus one: A three-author paper has exactly 3 of the 4 writers, so name it by the one missing person. The count of papers missing $X$ equals $3 - th_X$ (total threes minus how many $X$ is in). With $th_A=1,\ th_B=2,\ th_C=3,\ th_D=3$: missing-Arman $=2$, missing-Brajen $=1$, missing-Chintan $=0$, missing-Devon $=0$.

Step 2 — The explicit three papers: Two are {Brajen, Chintan, Devon} (Arman missing) and one is {Arman, Chintan, Devon} (Brajen missing). Chintan and Devon appear in all three — matching $th_C=th_D=3$.

Step 3 — Statement i: Arman appears only in {Arman, Chintan, Devon}, so his three-author co-authors are exactly Chintan and Devon. True.

Step 4 — Statement ii: Brajen appears only in the two {Brajen, Chintan, Devon} papers, so his three-author co-authors are exactly Chintan and Devon. True.

Step 5 — Both forced: This team structure is the only one consistent with the counts, so both statements are necessarily true.

Answer: Both i and ii.
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Question: 4

If Devon wrote more than one two-author papers, then how many two-author papers did Chintan write?

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For conditional questions in a DILR set ("If X is true, then what is Y?"), first solve the set as much as possible without the new condition. Then, apply the condition. It may either confirm your existing unique solution or force you to choose one specific path in a scenario that had multiple possibilities.
Updated On: Jul 4, 2026
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Correct Answer: 3

Solution and Explanation

Step 1: Brajen always contributes 2 two-author papers (fixed). The other 2 two-author slots are shared among Arman, Chintan and Devon.
Step 2: Given Devon wrote more than one (so exactly 2) two-author papers, and Arman only ever contributes 1, the four two-author papers work out as: Chintan-Arman, Chintan-Brajen, Chintan-Devon, and Brajen-Devon.
Step 3: Count Chintan's appearances among these four papers.
\[ \boxed{3} \]
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