Comprehension
Two families are planning to go on a canoe trip together. The families consist of the following people: Robert and Mary Henderson and their three sons Tommy, Don and William; Jerome and Ellen Penick and their two daughters Kate and Susan.
There will be three canoes with three people in each canoe. At least one of the four parents must be in each canoe. At least one person from each family must be in each canoe.
Question: 1
If the two mothers ride together in the same canoe and the three brothers each ride in a different canoe, which of the following must be true?
If the two mothers ride together in the same canoe and the three brothers each ride in a different canoe, which of the following must be true?
Show Hint
Use constraints like "each in a separate canoe" and parent-child balance to infer gender composition of each group.
Updated On: Mar 23, 2026
- Each canoe has both males and females in it
- One of the canoes has only females in it
- One of the canoes has only males in it
- The sisters ride in the same canoe
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The Correct Option is B
Solution and Explanation
The two families are:
Hendersons: Robert, Mary, Tommy, Don, William
Penicks: Jerome, Ellen, Kate, Susan
There are 3 canoes, 3 people in each, total 9 people.
Given: - The two mothers (Mary and Ellen) ride in the same canoe.
- The three brothers (Tommy, Don, William) each ride in separate canoes.
Let’s analyze: Canoe 1: Mary, Ellen, X → This canoe already has 2 females. To satisfy the "at least one person from each family" rule, X must be someone from Hendersons (if Ellen is Penick), so perhaps Kate or Susan.
That makes Canoe 1: Mary, Ellen, Kate/Susan (All females) ✓
Canoe 2: Tommy, ?, ?
Canoe 3: Don, ?, ?
Canoe 4: William, ?, ?
Each brother must ride separately. That leaves only 4 more people to fill the other two canoes: Robert, Jerome, Kate, Susan.
So: - One canoe will be Tommy + Robert + Susan
- Another will be Don + Jerome + Kate
- Third will be Mary + Ellen + the remaining girl
But crucially, the canoe with Mary and Ellen must be all female (Mary, Ellen, one of the daughters). So: \[ \boxed{\text{(B) One of the canoes has only females in it}} \]
Given: - The two mothers (Mary and Ellen) ride in the same canoe.
- The three brothers (Tommy, Don, William) each ride in separate canoes.
Let’s analyze: Canoe 1: Mary, Ellen, X → This canoe already has 2 females. To satisfy the "at least one person from each family" rule, X must be someone from Hendersons (if Ellen is Penick), so perhaps Kate or Susan.
That makes Canoe 1: Mary, Ellen, Kate/Susan (All females) ✓
Canoe 2: Tommy, ?, ?
Canoe 3: Don, ?, ?
Canoe 4: William, ?, ?
Each brother must ride separately. That leaves only 4 more people to fill the other two canoes: Robert, Jerome, Kate, Susan.
So: - One canoe will be Tommy + Robert + Susan
- Another will be Don + Jerome + Kate
- Third will be Mary + Ellen + the remaining girl
But crucially, the canoe with Mary and Ellen must be all female (Mary, Ellen, one of the daughters). So: \[ \boxed{\text{(B) One of the canoes has only females in it}} \]
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Question: 2
If Ellen and Susan are together in one of the canoes, which of the following could be a list of the people together in another canoe?
If Ellen and Susan are together in one of the canoes, which of the following could be a list of the people together in another canoe?
Show Hint
Always ensure the canoe satisfies: one parent + members from both families.
Updated On: Jul 28, 2025
- Dan, Jerome, Kate
- Dan, Jerome, William
- Dan, Kate, Tommy
- Jerome, Kate, Mary
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Given:
- Ellen and Susan are in one canoe (Penick mother and daughter)
- Total 3 canoes, 3 people each
- Each canoe must have at least one parent and one person from each family
If Ellen and Susan are together, then their canoe must include one more person — likely from Henderson family to satisfy the constraint. Now analyze the options: Option (A) – Dan, Jerome, Kate: No parent in this group.
Option (B) – Dan, Jerome, William: No female. Also questionable parent mix.
Option (C) – Dan, Kate, Tommy: Dan (Henderson child), Kate (Penick daughter), Tommy (Henderson child). Two families . Could work if parent is in third canoe.
Option (D) – Jerome, Kate, Mary: Two parents (Jerome and Mary) in one canoe? Possibly, but makes satisfying other canoes harder.
Best working configuration is in Option (C).
\[ \boxed{\text{(C)}} \]
- Total 3 canoes, 3 people each
- Each canoe must have at least one parent and one person from each family
If Ellen and Susan are together, then their canoe must include one more person — likely from Henderson family to satisfy the constraint. Now analyze the options: Option (A) – Dan, Jerome, Kate: No parent in this group.
Option (B) – Dan, Jerome, William: No female. Also questionable parent mix.
Option (C) – Dan, Kate, Tommy: Dan (Henderson child), Kate (Penick daughter), Tommy (Henderson child). Two families . Could work if parent is in third canoe.
Option (D) – Jerome, Kate, Mary: Two parents (Jerome and Mary) in one canoe? Possibly, but makes satisfying other canoes harder.
Best working configuration is in Option (C).
\[ \boxed{\text{(C)}} \]
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Question: 3
If Jerome and Mary are together in one of the canoes, each of the following could be a list of the people together in another canoe \textbf{except:}
If Jerome and Mary are together in one of the canoes, each of the following could be a list of the people together in another canoe \textbf{except:}
Show Hint
Watch out for canoe combinations missing a parent or failing to represent both families.
Updated On: Mar 23, 2026
- Dan, Ellen, Susan
- Ellen, Robert, Tommy
- Ellen, Susan, William
- Ellen, Tommy, William
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Jerome (Penick father) and Mary (Henderson mother) are in one canoe. That canoe already has a parent from each family.
So, remaining 6 people must be split into 2 canoes satisfying:
- Each must still have a parent and both families represented.
Check: Option (A) – Dan, Ellen, Susan: Dan (Henderson child), Ellen (Penick mother), Susan (Penick daughter). Both families , 1 parent .
Option (B) – Ellen, Robert, Tommy: Ellen (Penick), Robert (Henderson parent), Tommy (Henderson child). 2 parents .
Option (C) – Ellen, Susan, William: Ellen and Susan (Penick), William (Henderson). .
Option (D) – Ellen, Tommy, William: Ellen (Penick), Tommy + William (Henderson children). No Penick child other than Ellen, no Penick child parent to balance.
So (D) violates the parent-from-each-family rule. \[ \boxed{\text{(D)}} \]
Check: Option (A) – Dan, Ellen, Susan: Dan (Henderson child), Ellen (Penick mother), Susan (Penick daughter). Both families , 1 parent .
Option (B) – Ellen, Robert, Tommy: Ellen (Penick), Robert (Henderson parent), Tommy (Henderson child). 2 parents .
Option (C) – Ellen, Susan, William: Ellen and Susan (Penick), William (Henderson). .
Option (D) – Ellen, Tommy, William: Ellen (Penick), Tommy + William (Henderson children). No Penick child other than Ellen, no Penick child parent to balance.
So (D) violates the parent-from-each-family rule. \[ \boxed{\text{(D)}} \]
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Question: 4
If each of the Henderson children rides in a different canoe, which of the following must be true?
I. The Penick children do not ride together.
II. The Penick parents do not ride together.
III. The Henderson parents do not ride together.
If each of the Henderson children rides in a different canoe, which of the following must be true?
I. The Penick children do not ride together.
II. The Penick parents do not ride together.
III. The Henderson parents do not ride together.
II. The Penick parents do not ride together.
III. The Henderson parents do not ride together.
Show Hint
Use seating constraints and total canoe count to force distribution logic.
Updated On: Jul 28, 2025
- Only I
- Only II
- I and II
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Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The Henderson children are Tommy, Don, and William. If they are all riding in different canoes, it takes up 3 canoes (one each).
Only 3 canoes exist. Therefore: - No two of them can be together.
Now, since each canoe must have a member from each family, and there are only 3 Penick children (Kate, Susan) and parents (Jerome, Ellen), they have to be distributed carefully. Let’s test the statements: I. The Penick children do not ride together. Correct: if they did, they'd take 2 seats in one canoe, violating the one-from-each-family rule somewhere.
II. The Penick parents do not ride together. Not necessarily true. If Ellen and Jerome are in same canoe, other 2 canoes can have one Penick daughter each. So not a must.
III. The Henderson parents do not ride together. Also not a necessity. One of them could be with one child, another with different child.
Only Statement I must be true. \[ \boxed{\text{(A)}} \]
Only 3 canoes exist. Therefore: - No two of them can be together.
Now, since each canoe must have a member from each family, and there are only 3 Penick children (Kate, Susan) and parents (Jerome, Ellen), they have to be distributed carefully. Let’s test the statements: I. The Penick children do not ride together. Correct: if they did, they'd take 2 seats in one canoe, violating the one-from-each-family rule somewhere.
II. The Penick parents do not ride together. Not necessarily true. If Ellen and Jerome are in same canoe, other 2 canoes can have one Penick daughter each. So not a must.
III. The Henderson parents do not ride together. Also not a necessity. One of them could be with one child, another with different child.
Only Statement I must be true. \[ \boxed{\text{(A)}} \]
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