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)
Read the directions carefully and give the answer from the given options.
P, Q, R, S, T, K, L, M and N are sitting around a circle facing the centre.
K is $4^{th}$ to the right of P and P is $3^{rd}$ to the right of Q.
N is $4^{th}$ to the left of Q and $3^{rd}$ to the right of S.
R is $2^{nd}$ to the right of M and M is the immediate neighbour of P.
T is $2^{nd}$ to the left of L.
Who is to the immediate left of K?
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Six people, B, C, D, I, J and K, are sitting around a circular table facing the centre. Only two people sit between B and I when counted from the right of I. K sits to the immediate left of J. I sits to the immediate right of C. Who among the following are the immediate neighbours of D?
Each of P, Q, R, S, T, U and V has an exam on a different day of the week starting on Monday and ending on Sunday of the same week. V has an exam on Friday. Only two people have an exam between Q and V. Only four people have an exam between R and Q. S has an exam immediately after T. P does not have an exam on Monday. Who has an exam on Sunday?
