Question

Which of the following is an acceptable seating arrangement, with the driver listed first under "Front Seat" and the passengers in the back seat listed from one side to the other side?

• A. \(\underline{Front\ Seat}\): Mohsen, Ursula
  \(\underline{Back\ Seat}\): Theo, Orlando, Shelly
• B. \(\underline{Front\ Seat}\): Orlando, Mohsen
  \(\underline{Back\ Seat}\): Shelly, Theo, Ursula
• C. \(\underline{Front\ Seat}\): Orlando, Shelly
  \(\underline{Back\ Seat}\): Mohsen, Ursula, Theo
• D. \(\underline{Front\ Seat}\): Shelly, Mohsen
  \(\underline{Back\ Seat}\): Ursula, Orlando, Theo
• E. \(\underline{Front\ Seat}\): Shelly, Orlando
  \(\underline{Back\ Seat}\): Theo, Mohsen, Ursula
• A. Orlando will be the driver.
• B. Orlando will sit next to Ursula.
• C. Shelly will sit in the middle position in the back.
• D. Shelly will be the driver.
• J. Ursula will sit in the middle position in the back seat.
• A. Mohsen and Shelly will sit side by side.
• B. Mohsen and Ursula will sit side by side.
• C. Orlando and Theo will sit side by side.
• D. Orlando and Ursula will sit side by side.
• O. Shelly and Ursula will sit side by side.
• A. exactly one person sitting in the back seat speaks Russian
• B. neither speaker of Farsi is sitting in the front seat
• C. no one sitting in the front seat speaks Russian
• D. no one sitting in the back seat speaks Hebrew
• T. a speaker of Russian is sitting in the middle position in the back seat
• A. If Shelly sits in the front seat, Ursula will sit in the middle position in the back seat.
• B. If Shelly sits in the back seat, she will sit next to Ursula.
• C. If Theo sits in the front seat, Ursula will sit in the middle position in the back seat.
• D. If Theo sits in the back seat, he will sit between Mohsen and Ursula.
• Y. If Ursula sits in the back seat, she will sit in the middle position in the back seat.seat.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
We need to evaluate each option against the given rules: 1. The driver must be Orlando or Shelly.
2. Any two people sitting side-by-side must share a common language. This applies to the two people in the front, the left and middle person in the back, and the middle and right person in the back.
Step 2: Detailed Explanation:
Let's analyze each option based on the rules.
(A) Front: Mohsen, Ursula. Back: Theo, Orlando, Shelly


Driver Rule: The driver is Mohsen. This violates the rule that the driver must be Orlando or Shelly. So, (A) is incorrect.

(B) Front: Orlando, Mohsen. Back: Shelly, Theo, Ursula


Driver Rule: The driver is Orlando. This is acceptable.

Language Rule (Front): Orlando (Italian, Russian) and Mohsen (Farsi, Hebrew) do not share any language. This violates the side-by-side rule. So, (B) is incorrect.

(C) Front: Orlando, Shelly. Back: Mohsen, Ursula, Theo


Driver Rule: The driver is Orlando. This is acceptable.

Language Rule (Front): Orlando (Italian, Russian) and Shelly (Hebrew, Russian) share the language Russian. This is acceptable.

Language Rule (Back):

Mohsen (Farsi, Hebrew) and Ursula (Farsi, German, Hebrew) share Farsi and Hebrew. This is acceptable.

Ursula (Farsi, German, Hebrew) and Theo (German, Italian) share German. This is acceptable.


All conditions are met. So, (C) is a valid arrangement.

(D) Front: Shelly, Mohsen. Back: Ursula, Orlando, Theo


Driver Rule: The driver is Shelly. This is acceptable.

Language Rule (Front): Shelly (Hebrew, Russian) and Mohsen (Farsi, Hebrew) share Hebrew. This is acceptable.

Language Rule (Back): Ursula (Farsi, German, Hebrew) and Orlando (Italian, Russian) do not share any language. This violates the side-by-side rule. So, (D) is incorrect.

(E) Front: Shelly, Orlando. Back: Theo, Mohsen, Ursula


Driver Rule: The driver is Shelly. This is acceptable.

Language Rule (Front): Shelly (Hebrew, Russian) and Orlando (Italian, Russian) share Russian. This is acceptable.

Language Rule (Back): Theo (German, Italian) and Mohsen (Farsi, Hebrew) do not share any language. This violates the side-by-side rule. So, (E) is incorrect.

Step 3: Final Answer:
Option (C) is the only arrangement that satisfies all the given restrictions.

Answer 2

Step 1: Understanding the Concept:
We are given a condition (Mohsen sits in the front seat) and must determine which of the given statements can be true based on this condition and the initial rules.
Step 2: Detailed Explanation:
1. Analyze the initial condition: Mohsen sits in the front seat. Since he cannot be the driver (only Orlando or Shelly can), he must be the passenger.
2. Determine the driver: The driver sits next to Mohsen in the front seat and must share a language with him. Mohsen speaks Farsi and Hebrew.

Can Orlando be the driver? Orlando speaks Italian and Russian. He shares no language with Mohsen. Therefore, Orlando cannot be the driver.

Can Shelly be the driver? Shelly speaks Hebrew and Russian. She shares Hebrew with Mohsen. Therefore, Shelly MUST be the driver.

3. Conclusion from the premise: If Mohsen is in the front seat, Shelly must be the driver. The front seat arrangement is (Shelly, Mohsen).
4. Evaluate the options based on this deduction:

(A) Orlando will be the driver. This is false. We proved Shelly must be the driver.

(B) Orlando will sit next to Ursula. The people in the back seat are Orlando, Theo, and Ursula. Orlando (Italian, Russian) and Ursula (Farsi, German, Hebrew) share no languages, so they cannot sit next to each other. This is false.

(C) Shelly will sit in the middle position in the back. This is false. Shelly is the driver in the front seat.

(D) Shelly will be the driver. This is true. As deduced above, this is a necessary consequence of Mohsen sitting in the front seat. Since it must be true, it also "can be true".

(E) Ursula will sit in the middle position in the back seat. The back seat has Orlando (I, R), Theo (G, I), and Ursula (F, G, H). The possible language links are between Orlando-Theo (Italian) and Theo-Ursula (German). To connect all three, Theo must be in the middle. A valid arrangement would be (Orlando, Theo, Ursula). Ursula cannot be in the middle. This is false.

Step 3: Final Answer:
The only statement that can be true is that Shelly will be the driver. In fact, it must be true.

Answer 3

Step 1: Understanding the Concept:
We are given a new condition (Theo sits in the front seat) and must find the statement that is a necessary consequence (i.e., it must be true).
Step 2: Detailed Explanation:
1. Analyze the initial condition: Theo sits in the front seat. Since he cannot be the driver, he is the passenger.
2. Determine the driver: The driver sits next to Theo and must share a language with him. Theo speaks German and Italian.

Can Orlando be the driver? Orlando speaks Italian and Russian. He shares Italian with Theo. This is possible.

Can Shelly be the driver? Shelly speaks Hebrew and Russian. She shares no language with Theo. This is not possible.

3. Conclusion from the premise: If Theo is in the front seat, Orlando MUST be the driver. The front seat arrangement is (Orlando, Theo).
4. Evaluate the options based on this deduction:

(A) Mohsen and Shelly will sit side by side. The people in the back seat are Mohsen, Shelly, and Ursula. All three share at least one language with each other (M-S: Hebrew, M-U: Hebrew/Farsi, S-U: Hebrew). An arrangement like (Mohsen, Ursula, Shelly) is possible, where Mohsen and Shelly are not side-by-side. Therefore, this statement is not necessarily true.

(B) Mohsen and Ursula will sit side by side. An arrangement like (Shelly, Mohsen, Ursula) is possible where they are side by side. However, an arrangement like (Mohsen, Shelly, Ursula) is also possible, where they are not. This is not necessarily true.

(C) Orlando and Theo will sit side by side. Orlando is the driver and Theo is the passenger. They are the two people in the front seat, so they must be sitting side by side. This statement must be true.

(D) Orlando and Ursula will sit side by side. This is false. Orlando is in the front seat and Ursula is in the back seat.

(E) Shelly and Ursula will sit side by side. An arrangement like (Mohsen, Shelly, Ursula) is possible where they are side by side. But an arrangement like (Shelly, Mohsen, Ursula) is also possible where they are not. This is not necessarily true.

Step 3: Final Answer:
The only statement that must be true is that Orlando and Theo will sit side by side, as they occupy the two front seats.

Answer 4

Step 1: Understanding the Concept:
We must first identify the possible arrangements given that both front seat occupants speak Hebrew, and then find a conclusion that holds true for all of those possibilities.
Step 2: Detailed Explanation:
1. Analyze the initial condition: Both people in the front seat speak Hebrew. The participants who speak Hebrew are Mohsen, Shelly, and Ursula.
2. Determine the occupants of the front seat:

The driver must be Orlando or Shelly. Since Orlando does not speak Hebrew, the driver must be Shelly.

The passenger must also speak Hebrew and share a language with Shelly (Hebrew, Russian). The other Hebrew speakers are Mohsen and Ursula.

Mohsen speaks Farsi and Hebrew. He can sit with Shelly (they share Hebrew).

Ursula speaks Farsi, German, and Hebrew. She can sit with Shelly (they share Hebrew).


3. Identify the two possible scenarios:

Scenario 1: Front seat is (Shelly, Mohsen). The back seat contains the remaining people: Orlando, Theo, and Ursula.

Scenario 2: Front seat is (Shelly, Ursula). The back seat contains the remaining people: Orlando, Theo, and Mohsen.

4. Evaluate the options (the statement must be true in both scenarios):

(A) exactly one person sitting in the back seat speaks Russian

Scenario 1 (Back: O, T, U): Orlando speaks Russian. Theo and Ursula do not. This is true.

Scenario 2 (Back: O, T, M): Orlando speaks Russian. Theo and Mohsen do not. This is true.

Since this holds for both scenarios, it must be true.

(B) neither speaker of Farsi is sitting in the front seat

Farsi speakers are Mohsen and Ursula. In Scenario 1, Mohsen is in the front. In Scenario 2, Ursula is in the front. This statement is false in both cases.


(C) no one sitting in the front seat speaks Russian

The driver is Shelly, who speaks Russian. This statement is false.


(D) no one sitting in the back seat speaks Hebrew

Scenario 1 (Back: O, T, U): Ursula speaks Hebrew. This statement is false.

Scenario 2 (Back: O, T, M): Mohsen speaks Hebrew. This statement is false.


(E) a speaker of Russian is sitting in the middle position in the back seat

The only Russian speaker in the back is Orlando. In Scenario 1 (Back: O, T, U), the valid arrangements are (O, T, U) and (U, T, O), because T must be in the middle to connect O (Italian) and U (German). Orlando is not in the middle. This statement is false.


Step 3: Final Answer:
The only statement that is true in all possible scenarios is (A).

Answer 5

Step 1: Understanding the Concept:
Given that Orlando is the driver, we need to determine which of the conditional statements ("If P, then Q") is a logical certainty. A conditional statement is true if the conclusion (Q) is true whenever the premise (P) is true, or if the premise (P) is false.
Step 2: Detailed Explanation:
1. Analyze the main condition: Orlando is the driver. He speaks Italian and Russian. His passenger must share a language with him.

Passenger can be Shelly (share Russian).
Passenger can be Theo (share Italian).
2. Identify the two possible scenarios:

Scenario 1: Front seat is (Orlando, Shelly). The back seat contains the remaining people: Mohsen, Theo, and Ursula.

Scenario 2: Front seat is (Orlando, Theo). The back seat contains the remaining people: Mohsen, Shelly, and Ursula.

3. Evaluate each conditional option:

(A) If Shelly sits in the front seat, Ursula will sit in the middle position in the back seat.

The "if" part corresponds to Scenario 1.

In this scenario, the back seat has Mohsen (F, H), Theo (G, I), and Ursula (F, G, H).

To arrange them side-by-side, we check shared languages: Mohsen-Ursula (Farsi/Hebrew), Theo-Ursula (German). Mohsen and Theo have no shared language.

Therefore, Ursula MUST sit in the middle to connect Mohsen and Theo. The arrangements can be (Mohsen, Ursula, Theo) or (Theo, Ursula, Mohsen).

The conclusion "Ursula will sit in the middle" is true for this scenario. So the conditional statement is true.


(B) If Shelly sits in the back seat, she will sit next to Ursula.

The "if" part corresponds to Scenario 2.

In this scenario, the back seat has Mohsen (F, H), Shelly (H, R), and Ursula (F, G, H). All three can be paired with each other (M-S: Hebrew, S-U: Hebrew, M-U: Farsi/Hebrew).

A possible arrangement is (Mohsen, Shelly, Ursula). Here Shelly is not next to Ursula.

Since the conclusion is not always true when the premise is true, the conditional statement is not a "must be true" statement.


(C) If Theo sits in the front seat, Ursula will sit in the middle position in the back seat.

The "if" part corresponds to Scenario 2.

The back seat has Mohsen, Shelly, and Ursula.

The conclusion is "Ursula will sit in the middle". However, an arrangement like (Shelly, Mohsen, Ursula) is valid, where Mohsen is in the middle.

The conclusion is not guaranteed.


(D) If Theo sits in the back seat, he will sit between Mohsen and Ursula.

The "if" part corresponds to Scenario 1.

As analyzed in (A), in this case, Ursula must be in the middle, between Mohsen and Theo. The statement says Theo is between Mohsen and Ursula, which is false.


(E) If Ursula sits in the back seat, she will sit in the middle position in the back seat.

The "if" part, "Ursula sits in the back seat", is true in both Scenario 1 and Scenario 2.

The conclusion, "she will sit in the middle", must therefore be true in both scenarios.

It is true for Scenario 1. However, as shown in (C), for Scenario 2, she does not have to be in the middle.

Since it's not true for all cases, the statement is not a "must be true" statement.


Step 3: Final Answer:
Only statement (A) holds true as a logical necessity under the condition that Orlando is the driver.