Question

Six friends — Alice, Bob, Carol, David, Eve, and Frank — are sitting in a row facing south. Each has a different favorite subject: History, Math, English, Science, Geography, and Art. They also have different pets: Dog, Cat, Rabbit, Parrot, Turtle, and Goldfish. The information:
1) Alice, who likes Science, is at one of the ends.
2) Frank sits third to the left of Alice.
3) Bob, who likes History, is not at any end.
4) The Geography-lover sits second to the right of Carol.
5) Eve, who has a Rabbit, is at one of the ends.
6) David is sitting between Eve and Alice.
7) The Math-lover is sitting next to the person with a Goldfish.
8) Carol, who likes English, is not sitting next to Bob.
9) The person with a Cat sits immediately right of the Math-lover. \ (Remember: facing south, “right” is our left.)
. Based on the given information, answer the following:
Who likes Math, and what is their pet?

• A. Carol, Rabbit
• B. Eve, Goldfish
• C. Frank, Turtle
• D. David, Parrot

Hint:

For south-facing rows, reverse “left/right” relative to your diagram. First lock ends/middle} and fixed offsets (“third to the left”, “second to the right”), then propagate subject/pet constraints. If multiple items remain free, the MCQ often hinges on the person}, not the leftover label.

Answer 1

The Correct Option is C

Step 1 (Fix the ends and use “third to the left”).
Let positions be \(1\) to \(6\) from left to right as we look. Facing south means a person’s left} is our right}.
If Alice is at an end and Frank is third to her left, the only workable placement is: Alice at \(1\) \(\) Frank at \(4\). (If Alice were at \(6\), Frank would need to be at \(9\), impossible.)
Step 2 (Place Eve and use “between Eve and Alice”).
Eve is at an end (clause 5), so Eve must be at \(6\) (since \(1\) has Alice). “David is between Eve and Alice” \(\) David must be somewhere from \(2\)–\(5\) and lie between them. (We’ll pin this down soon.)
Step 3 (Use Carol–Geography relation).
“The Geography-lover sits second to the right of Carol.” Facing south, “right of Carol” is \(our left\). So \(\text{Geo position} = \text{Carol position} - 2\). Carol cannot be at \(3\) because that would force Geo at \(1\) (already Alice = Science). Trying Carol at \(5\) gives Geo at \(3\), which is valid. (Carol at \(4\) is Frank; \(6\) is Eve; \(2\) would place Geo at \(0\), impossible.) \(\) \({\text{Carol at }5\ \text{(English)}}\) and \({\text{Geography at }3}\).
Step 4 (Place Bob and Davi(d).
Bob (History) is not at an end (clause 3) and not next to Carol (clause 8), hence Bob cannot be \(4\) or \(6\) (ends are \(1,6\), but \(4\) is adjacent to \(5\)). Available non-end seats are \(2,3,4\). Seat \(3\) is Geo (not History), seat \(4\) is Frank, so \({\text{Bob at }2\ \text{(History)}}\). Since Geo is at \(3\), \({\text{David at }3\ \text{(Geography)}}\). This also satisfies “David is between Eve (6) and Alice (1)”.
Step 5 (Pin down Math and the pets via (7) and (9)).
Open subjects left: \(\{\text{Math, Art}\}\) for \(\{\text{Frank (4), Eve (6)}\}\).
Assume \(Frank = Math\):
- By (9), the Cat sits immediately right} of Math \(\) the neighbor at our left} of seat \(4\), i.e., seat \(3\), has the Cat \(\) \({\text{David has Cat}}\).
- By (7), Math (seat \(4\)) sits next to Goldfish \(\) the other neighbor (seat \(5\), Carol) must have \({\text{Goldfish}}\).
This is perfectly consistent with all constraints and with Eve already having \({\text{Rabbit}}\).
Check the alternative \(Eve = Math\): then seat \(5\) (only neighbor of seat \(6\)) would need to have both} Goldfish (by (7)) and Cat (by (9), immediate right of Math), which is impossible. \(\) \({\text{Frank is the Math-lover}}\).
Step 6 (About Frank’s pet).
Assigned pets so far: Eve = Rabbit, Carol = Goldfish, David = Cat. Remaining pets \(\{\text{Dog, Parrot, Turtle}\}\) are to be distributed among \(\{\text{Alice, Bob, Frank}\}\). The clues give no further restriction, so Frank’s specific pet is not uniquely determined}. However, among the options, only (c) names Frank as the Math-lover; hence (c) is the only viable choice.
\[ {\text{Frank is the Math-lover. Among the given options, (c) Frank, Turtle is the only correct pairing.}} \]