Seven people, F, J, M, L, R, V and X, are sitting in a row, facing north.
Only three people sit to the left of X. Only M sits to the right of R. Only three people sit between R and V. J sits at some place to the left of L but at some place to the right of F.
How many people sit to the left of V?
The problem requires determining the seating arrangement of seven people (F, J, M, L, R, V, X) in a row facing north, based on several constraints, and then finding the number of people to the left of V.
Applying Constraints Step-by-Step
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Initial Setup: There are 7 positions in the row. Since they face North, 'left' corresponds to the lower position numbers and 'right' to the higher numbers.
$_ _ _ _ _ _ _$
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Constraint 1: "Only three people sit to the left of X." This places X at position 4.
$_ _ _ X _ _ _$
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Constraint 2: "Only M sits to the right of R." This strongly implies that M is the sole person positioned to R's right. Thus, R must be in position 6 and M in position 7.
$_ _ _ _ _ R M$
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Combining Constraints 1 & 2: Placing X at position 4, R at position 6, and M at position 7 yields:
$_ _ _ X _ R M$
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Constraint 3: "Only three people sit between R and V." R is at position 6. If V were to the right of R, V would need to be at position 10 ($6 + 3 + 1$), which is impossible in a 7-person row. Therefore, V must be to the left of R.
Calculating V's position: $P_V = P_R - 3 - 1$. Given $P_R = 6$, $P_V = 6 - 3 - 1 = 2$.
The arrangement becomes:
$_ V _ X _ R M$
(Positions: V=2, X=4, R=6, M=7)
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Constraint 4: "J sits at some place to the left of L but at some place to the right of F." This establishes the required relative order F...J...L.
The remaining empty positions are 1, 3, and 5.
To satisfy the order F...J...L, F must be placed at position 1, J at position 3, and L at position 5.
The final seating arrangement is:
$F V J X L R M$
(Positions: F=1, V=2, J=3, X=4, L=5, R=6, M=7)
Verification: This arrangement satisfies all given constraints.
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Answering the Question: "How many people sit to the left of V?"
V is at position 2.
The person at position 1 is F.
Therefore, only 1 person sits to the left of V.
Important Questions from Seating Arrangement (Notes)
- Five friends are sitting on a bench in the following order :
(i) P is sitting next to Q and R is next to S.
(ii) S is not sitting with T; T is on the extreme left hand side of the bench and R is on second position from the right hand side.
(iii) P is on the right hand side of Q and to the right side of T. (iv) P and R sitting together
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P, Q, R, S, T, U and V are sitting in a row, facing north. No one sits to the left of U. Only four people sit between U and R. Only three people sit to the right of V. P sits to the immediate left of S. Q is not an immediate neighbour of V. How many people sit between P and T?
