U, V, W, X, Y, and Z live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2, and so on, till the topmost floor is numbered 6. Only two people live between W and Z. Only X lives above V. Y lives on an even-numbered floor. W lives on the lowermost floor.
How many people live between U and X?
Correct Answer :
Two
Solution :
The correct option is Two.
Let us solve this step-by-step to find the floor arrangement of the six people: U, V, W, X, Y, and Z on six floors (numbered 1 to 6 from bottom to top).
1. Determine W's floor:
We are given that W lives on the lowermost floor. Therefore, W lives on Floor 1.
2. Determine Z's floor:
Only two people live between W and Z. Since W is on Floor 1, the floors between W and Z must be Floor 2 and Floor 3. This places Z on Floor 4.
3. Determine X and V's floors:
We are told that "Only X lives above V". This implies that V is on Floor 5 and X is on the topmost floor, Floor 6. No one else can live above V except X.
4. Determine Y's floor:
Y lives on an even-numbered floor. The even floors are 2, 4, and 6. Floors 4 and 6 are already occupied by Z and X, respectively. Therefore, Y must live on Floor 2.
5. Determine U's floor:
The remaining unoccupied floor is Floor 3, which must be occupied by U.
Let us write down the complete arrangement from Floor 6 to Floor 1:
Floor 6: X
Floor 5: V
Floor 4: Z
Floor 3: U
Floor 2: Y
Floor 1: W
6. Find the number of people between U and X:
U lives on Floor 3 and X lives on Floor 6. The floors between them are Floor 4 and Floor 5, occupied by Z and V. Thus, there are exactly two people (Z and V) living between U and X.
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