Comprehension
A volunteer who sends packages to hospital patients is preparing three packages containing exactly five items each from a supply of eighteen available items-four games, six jigsaw puzzles, and eight novels. The packages must conform to the following.
conditions:
The three packages together contain all of the novels. Each package contains at least one jigsaw puzzle. No package contains more games than novels.
Question: 1
Which of the following can be a complete and accurate list of the contents of one of the packages?
Which of the following can be a complete and accurate list of the contents of one of the packages?
Updated On: Oct 1, 2025
- Five jigsaw puzzles
- One game. four novels
- One jigsaw puzzle, four novels
- Two games, two jigsaw puzzles, two novels
- Three games, one jigsaw puzzle, one novel
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The Correct Option is C
Solution and Explanation
Step 1: Each package must have 5 items. Options (A) and (D) have the wrong total (A = 5 but only puzzles, which violates ""at least one novel""; D = 6 items).
Step 2: Check condition “No package contains more games than novels.”
- (B) 1G, 4N → Games (1) ≤ Novels (4) ✅, and contains ≥1 puzzle? ❌ (fails, no puzzle).
- (C) 1P, 4N → Games = 0, Novels = 4 ✅, contains ≥1 puzzle ✅. This works.
- (E) 3G, 1P, 1N → Games (3)>Novels (1) ❌.
Answer: The only valid package is (C).
\[ \boxed{\text{One jigsaw puzzle, four novels}} \]
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Question: 2
If the first two packages contain exactly two games each, then the third package must contain exactly
If the first two packages contain exactly two games each, then the third package must contain exactly
Updated On: Oct 1, 2025
- one jigsaw puzzle and four novels
- two jigsaw puzzles and three novels
- four jigsaw puzzles and one novel
- one game, one jigsaw puzzle, and three novels
- two games, one jigsaw puzzle and two novels
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The Correct Option is B
Solution and Explanation
Step 1: Total games available = 4. If first two packages use 2 games each, all 4 games are used. So third package cannot have any games.
Step 2: Third package must have 5 items (no games). So only puzzles and novels. It must have ≥1 puzzle.
Step 3: Options check:
- (A) 1P + 4N = 5 ✅ possible.
- (B) 2P + 3N = 5 ✅ possible.
- (C) 4P + 1N = 5 ✅ possible.
- (D) includes 1G ❌ impossible (all games already used).
- (E) includes 2G ❌ impossible.
Step 4: Must ensure all novels = 8 across 3 packages. If first two had 4 games already, they each also must have puzzles and novels. The only consistent third package is (B) 2P, 3N.
\[ \boxed{\text{Two jigsaw puzzles and three novels}}
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Question: 3
If one of the packages contains exactly three jigsaw puzzles and none of the packages contains more than three novels, which of the following must be true?
If one of the packages contains exactly three jigsaw puzzles and none of the packages contains more than three novels, which of the following must be true?
Updated On: Oct 1, 2025
- The package that contains three jigsaw puzzles also contains exactly one game.
- One of the two packages that do not contain three jigsaw puzzles contains exactly two games.
- One of the two packages that do not contain three jigsaw puzzles contains exactly two jigsaw puzzles.
- Each of the two packages that do not contain three jigsaw puzzles contains exactly one game.
- Each of the two packages that do not contain three jigsaw puzzles contains exactly three novels.
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The Correct Option is C
Solution and Explanation
Step 1: Package with 3P must also have 2 other items. Since max novels per package = 3, this package cannot hold 4N. Likely composition = 3P + 2 others.
Step 2: Total novels = 8. If no package >3N, distribution must be 3+3+2 across 3 packages. So each non-3P package must hold either 2 or 3 novels.
Step 3: To satisfy counts, one of the other packages must contain exactly 2 puzzles (balancing the 6 puzzles total).
Answer: The must-be-true statement is (C).
\[ \boxed{\text{One of the other two packages contains exactly two jigsaw puzzles.}} \]
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Question: 4
If the first two packages contain exactly two jigsaw puzzles each, which of the following can be a complete and accurate list of the contents of the third package?
If the first two packages contain exactly two jigsaw puzzles each, which of the following can be a complete and accurate list of the contents of the third package?
Updated On: Oct 1, 2025
- One game, four novels
- Two games, three novels
- Two jigsaw puzzles, three novels
- One game, three jigsaw puzzles, one novel
- Two games, two jigsaw puzzles, one novel
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The Correct Option is C
Solution and Explanation
Step 1: Total puzzles = 6. If first two packages contain 2P each = 4 total, then third must contain exactly 2 puzzles.
Step 2: Among options, only (E) has exactly 2 puzzles.
Step 3: (E) = 2G + 2P + 1N, check rules: Games (2) vs Novels (1) ❌ violates rule (games cannot exceed novels). So impossible.
Step 4: (C) also shows 2P, 3N = 5 items, 0 games. This is valid!
Answer: (C).
\[ \boxed{\text{Two jigsaw puzzles, three novels}} \]
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Question: 5
If each of the packages contains at least one game, then it must be true that one of the package contains exactly
If each of the packages contains at least one game, then it must be true that one of the package contains exactly
Updated On: Oct 1, 2025
- two games
- two jigsaw puzzles
- one novel
- two novels
- four novels
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The Correct Option is A
Solution and Explanation
Step 1: Total games = 4, distributed across 3 packages with ≥1 each.
Distribution must be 2+1+1.
Step 2: So at least one package has 2 games.
Answer: (A).\[ \boxed{\text{Two games}} \]
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Question: 6
If each of the packages contains a different number of novels from the others, which of the following can be true?
If each of the packages contains a different number of novels from the others, which of the following can be true?
Updated On: Oct 1, 2025
- There are exactly three games among the items in one of the packages.
- There are exactly two jigsaw puzzles among the items in one of the packages.
- There are exactly four games among the items in the three packages together.
- There are exactly four jigsaw puzzles among the items in the three packages together.
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The Correct Option is B
Solution and Explanation
Step 1: Novels = 8 must be split into 3 distinct numbers. Possible splits: (1,2,5), (1,3,4), (2,3,3) invalid since not distinct. So one package can have as few as 1 novel.
Step 2: If a package has 1N, it can have max 1G (cannot exceed novels). Remaining items are puzzles. So one package must contain exactly 2 puzzles (because 1N + 1G + 3 left = 2P +1 item).
Answer: (B).\[ \boxed{\text{One package has exactly two jigsaw puzzles.}} \]
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