Question

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?

• A. Each canoe has both males and females in it
• B. One of the canoes has only females in it
• C. One of the canoes has only males in it
• D. The sisters ride in the same canoe
• A. Dan, Jerome, Kate
• B. Dan, Jerome, William
• C. Dan, Kate, Tommy
• D. Jerome, Kate, Mary
• A. Dan, Ellen, Susan
• B. Ellen, Robert, Tommy
• C. Ellen, Susan, William
• D. Ellen, Tommy, William
• A. Only I
• B. Only II
• C. I and II
• D.

Answer 1

The Correct Option is B

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: \[ \boxed{\text{(B) One of the canoes has only females in it}} \]

Answer 2

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).
\[ \boxed{\text{(C)}} \]

Answer 3

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. \[ \boxed{\text{(D)}} \]

Answer 4

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. \[ \boxed{\text{(A)}} \]