Directions: Read the following information carefully and answer the questions that follow:
14 individuals are seated in two parallel rows containing seven people each. H, I, J, K, L, M, and N sit in Row 1 facing north, while T, U, V, W, X, Y, and Z sit in Row 2 facing south, but not necessarily in the same order. Each person in Row 1 directly faces a person in Row 2.
I sits at one of the extreme ends of Row 1. Three persons sit between I and J. The person facing J sits second to the right of V, who does not sit at any extreme end. Two persons sit between V and W, who faces H. Two persons sit between H and M. K sits to the immediate left of M. L sits to the left of N, and N does not sit adjacent to H. T sits at one of the extreme ends of Row 2. X sits third to the left of T. Y sits to the left of Z, and Y does not face N.
How many persons sit between U and Z?
Correct Answer :
Two
Solution :
The correct answer is Two.
Step-by-Step Explanation:
Let us arrange the 14 individuals in two parallel rows of 7 people each, numbered from Position 1 to Position 7 from left to right on paper.
• Row 1 (Facing North): Left is towards Position 1, and Right is towards Position 7.
• Row 2 (Facing South): Right is towards Position 1, and Left is towards Position 7.
Step 1: Determine the positions of I, J, and V
• I sits at an extreme end of Row 1 (Position 1 or Position 7).
• Three persons sit between I and J.
- Case A: If I is at Position 1, then J is at Position 5.
- Case B: If I is at Position 7, then J is at Position 3.
• The person facing J sits second to the right of V (which corresponds to two positions to the left on paper, or lower position number), and V does not sit at any extreme end.
- In Case A (J at Position 5), the person facing J is at Position 5, which means V must be at Position 7. However, V cannot be at an extreme end, so Case A is invalid.
- In Case B (J at Position 3), the person facing J is at Position 3, which means V must be at Position 5 of Row 2. This is valid.
Thus, I is at Position 7 of Row 1, J is at Position 3 of Row 1, and V is at Position 5 of Row 2.
Step 2: Determine the positions of W, H, M, and K
• Two persons sit between V (Position 5) and W in Row 2, so W must be at Position 2 of Row 2.
• W faces H, so H is at Position 2 of Row 1.
• Two persons sit between H (Position 2) and M in Row 1, placing M at Position 5 of Row 1.
• K sits to the immediate left of M (facing North), so K is at Position 4 of Row 1.
Step 3: Determine the positions of L and N
• The remaining open positions in Row 1 are Position 1 and Position 6.
• N does not sit adjacent to H (Position 2), so N cannot be at Position 1. Therefore, N is at Position 6, and L is at Position 1 of Row 1.
Complete Row 1 Arrangement (Facing North):
Position 1: L | Position 2: H | Position 3: J | Position 4: K | Position 5: M | Position 6: N | Position 7: I
Step 4: Determine the positions of T, X, Y, Z, and U in Row 2
• T sits at an extreme end of Row 2 (Position 1 or 7), and X sits third to the left of T (facing South, moving towards higher position numbers).
- If T were at Position 7, third to its left would be out of bounds. Thus, T must be at Position 1, placing X at Position 4 of Row 2.
• The remaining empty positions in Row 2 are Positions 3, 6, and 7.
• Y does not face N (Position 6), so Y cannot be at Position 6. Since Y sits to the left of Z (higher position number), Y must be at Position 7.
• The remaining positions 3 and 6 are occupied by U and Z.
Complete Row 2 Arrangement (Facing South):
Position 1: T | Position 2: W | Position 3: Z/U | Position 4: X | Position 5: V | Position 6: U/Z | Position 7: Y
Conclusion:
Regardless of whether U is at Position 3 and Z is at Position 6 (or vice versa), the two positions lying between them are Position 4 (occupied by X) and Position 5 (occupied by V).
Therefore, exactly Two persons sit between U and Z.
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