Study the following details carefully and answer the questions that follow:
Seven individuals, S, T, U, V, W, X, and Y, are sitting in a single linear row facing the north direction. Each of them uses a different laptop brand among HP, MSI, Dell, Apple, Lenovo, Asus, and Acer, though not necessarily in the same order.
S sits at the extreme left end of the row and uses an HP laptop. X is seated second from the right end of the row. Y sits to the immediate right of the individual who uses an Asus laptop, while the person using Acer sits at the extreme right end. There are two people sitting between U and the person who uses an Asus laptop. U is positioned somewhere to the left of V. The individual who uses a Dell laptop sits to the immediate left of V. T sits adjacent to the person using the Dell laptop. W sits adjacent to V. The person using an MSI laptop sits three places to the left of the Lenovo user.
Which of the following statements is/are true?
Correct Answer :
All of the statements are true
Solution :
Correct Answer: All of the statements are true
Let us analyze the given information step-by-step to determine the seating arrangement and the laptop brand used by each individual from left to right (Positions 1 to 7).
Step 1: Determine positions of individuals and laptop brands at the extreme ends.
1. Seven individuals sit in a single row facing North (Positions 1 to 7 from left to right).
2. "S sits at the extreme left end of the row and uses an HP laptop."
So, Position 1 = S (HP).
3. "X is seated second from the right end of the row."
So, Position 6 = X.
4. "the person using Acer sits at the extreme right end."
So, Position 7 uses Acer.
Current arrangement framework:
Position 1: S (HP)
Position 2: [ ]
Position 3: [ ]
Position 4: [ ]
Position 5: [ ]
Position 6: X
Position 7: [ ] (Acer)
Step 2: Place MSI and Lenovo laptop users.
1. "The person using an MSI laptop sits three places to the left of the Lenovo user."
This means there are two people between the MSI user and the Lenovo user (MSI, _, _, Lenovo).
2. S at Position 1 uses HP, so MSI user can be at Position 2, 3, or 4.
- If MSI is at Position 2, Lenovo user is at Position 5.
- If MSI is at Position 3, Lenovo user is at Position 6 (X).
- If MSI is at Position 4, Lenovo user is at Position 7 (Acer - invalid, as 7 is Acer).
Step 3: Analyze the positions of Dell, V, T, W, and Asus.
1. "The individual who uses a Dell laptop sits to the immediate left of V." → (Dell, V)
2. "T sits adjacent to the person using the Dell laptop."
3. "W sits adjacent to V."
4. "U is positioned somewhere to the left of V."
5. "Y sits to the immediate right of the individual who uses an Asus laptop." → (Asus, Y)
6. "There are two people sitting between U and the person who uses an Asus laptop."
Let us test the arrangement:
If T uses an MSI laptop at Position 2:
- Position 1: S (HP)
- Position 2: T (MSI)
- Position 3: U (Dell)
- Position 4: V (Asus)
- Position 5: Y (Lenovo)
- Position 6: X (W's neighbor/Dell neighbor check)
Wait, let's verify: W sits adjacent to V. If V is at Position 4, W can be at Position 5. Then Lenovo is at Position 5 or 6.
Let's place carefully:
Positions 1 to 7:
Position 1: S (HP)
Position 2: U (MSI)
Position 3: T (Asus)
Position 4: Y (Dell)
Position 5: V (Lenovo)
Position 6: X (W)
Wait, if Position 4 is Dell, then V is at Position 5. T is at Position 3 (adjacent to Dell). W is adjacent to V (at Position 6, so X = W is not possible unless X is at 6). But X is at Position 6, so W can be at Position 6? No, X is at Position 6, so W must be at Position 4 or 6. But Y is at 4 or 7.
Let's refine:
People: S, T, U, V, W, X, Y
Positions: 1, 2, 3, 4, 5, 6, 7
- Position 1 = S (HP)
- Position 6 = X
- Position 7 = Acer
Dell is immediate left of V. T is adjacent to Dell. W is adjacent to V.
Since Dell is immediately left of V, the block is (Dell, V).
T is adjacent to Dell, and W is adjacent to V. Since X is at 6, the block containing T, Dell, V, W can be:
T at 2, Dell at 3, V at 4, W at 5.
Let's check this block (T, Dell, V, W) at Positions 2, 3, 4, 5:
- Pos 2: T
- Pos 3: Dell
- Pos 4: V
- Pos 5: W
Then where is U? U must be to the left of V.
Wait! If T, Dell, V, W are at 2, 3, 4, 5, then U can be at Position 2? But T is at 2.
What if U is at 2, T is at 2? Not possible.
What if U is at 2, T is at 3 (MSI), Dell is at 4, V is at 5, W is at 4? Wait, Dell is immediate left of V.
Let's set:
- Pos 1: S (HP)
- Pos 2: U (MSI)
- Pos 3: T (Asus)
- Pos 4: Y (Dell)
- Pos 5: V (Lenovo)
- Pos 6: X (W? No, X is X)
Wait, W sits adjacent to V. V is at 5, so W must be at 4 or 6. But Pos 4 is Y, Pos 6 is X. So V cannot be at 5.
Let's check V at 4:
- Pos 3: Dell
- Pos 4: V
- Pos 5: W (Lenovo)
- Pos 2: T (MSI)
- Pos 1: S (HP)
Now check MSI and Lenovo:
MSI is at Pos 2 (T). Lenovo is 3 places to the right, which is Pos 5 (W). This fits!
Now check Asus and Y:
Y sits to the immediate right of Asus.
Remaining laptop positions to assign: Pos 3 (Dell), Pos 4 (V), Pos 6 (X), Pos 7 (Acer).
Wait, which position uses Asus?
If Pos 6 (X) uses Asus, then Pos 7 (Y) is to immediate right of Asus! So Y is at Pos 7 (Acer).
Let's check U and Asus:
"There are two people sitting between U and the person who uses an Asus laptop."
Asus is at Pos 6 (X). Two people between Pos 6 and U means U is at Pos 3!
Let's check U's position: Pos 3 = U.
Then T is at Pos 2 (MSI).
Is T adjacent to Dell (Pos 3)? Yes, Pos 2 (T) is adjacent to Pos 3 (Dell)!
Is U to the left of V (Pos 4)? Yes, Pos 3 is to the left of Pos 4!
Is Dell immediate left of V? Yes, Pos 3 (Dell) is immediate left of Pos 4 (V).
Let's review the complete arrangement:
Positions & Individuals:
1: S
2: T
3: U
4: V
5: W
6: X
7: Y
Laptops:
1: S - HP
2: T - MSI
3: U - Dell
4: V - Apple (remaining brand)
5: W - Lenovo
6: X - Asus
7: Y - Acer
Verification of all conditions:
1. S at extreme left (Pos 1) using HP: True.
2. X seated second from right (Pos 6): True.
3. Acer at extreme right (Pos 7, Y): True.
4. Y immediately right of Asus (Pos 6, X): True.
5. Two people between U (Pos 3) and Asus (Pos 6): True (V and W sit between them).
6. U (Pos 3) is to the left of V (Pos 4): True.
7. Dell (Pos 3) immediate left of V (Pos 4): True.
8. T (Pos 2) adjacent to Dell (Pos 3): True.
9. W (Pos 5) adjacent to V (Pos 4): True.
10. MSI (Pos 2) three places to the left of Lenovo (Pos 5): True (2 + 3 = 5).
Evaluating the given statements:
1. "U sits adjacent to T": U (Pos 3) and T (Pos 2) are adjacent. (True)
2. "S sits at one of the extreme ends of the row": S sits at Pos 1 (extreme left). (True)
3. "T uses an MSI laptop": T uses MSI. (True)
4. "More than two individuals sit to the right of V": V is at Pos 4, so 3 individuals (W, X, Y) sit to his right, which is more than two. (True)
Since all individual statements are true, the correct option is All of the statements are true.
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