Question 10: A Parking Lot A parking lot has several vehicles facing North.
Texas Instruments technical mcq question, verified with a worked answer. Free to practise - no sign-up.
A Parking Lot**
A parking lot has several vehicles facing North. In a particular row, V1 is 20th from the left of V2, who is 27th from the right end. Another vehicle V3 is 19th from the left end and 11th from the right of V1.
How many vehicles are there in this row?
Show answer & explanation
The total number of vehicles is determined by finding the absolute position of a single vehicle from both ends. By calculating V1's position from the left using V3's position and then using V1's relative position to V2, we can find V2's position from the left and combine it with its position from the right.
Step-by-step Derivation:
Step 1: Identify the position of V3. V3 is 19th from the left end. Position(V3) = 19.
Step 2: Identify the position of V1 relative to V3. V3 is 11th from the right of V1. This means V1 is to the left of V3. Specifically, if V3 is 11th from the right of V1, there are 10 vehicles between them, and V1 is (11 - 1) = 10 positions to the left of V3.
Position(V1) = Position(V3) - 10 = 19 - 10 = 9th from the left.
Step 3: Identify the position of V2 relative to V1. V1 is 20th from the left of V2. This means V2 is to the right of V1. Specifically, there are 19 vehicles between them, and V2 is 20 positions to the right of V1.
Position(V2) = Position(V1) + 20 = 9 + 20 = 29th from the left.
Step 4: Use V2's position from the right to find the total. V2 is 27th from the right end.
Total = (Position from left) + (Position from right) - 1
Total = 29 + 27 - 1 = 56 - 1 = 55.
Wait, let me re-evaluate the phrasing 'V1 is 20th from the left of V2'. In standard ranking puzzles, 'X is nth from the left of Y' usually means X is the nth person when counting from the left starting at Y's position (inclusive) or simply that the distance is n. If V1 is 20th from the left of V2, then V2 is the 20th person to the right of V1.
Let's re-calculate:
Position(V1) = 9.
If V2 is the 20th person to the right of V1: Position(V2) = 9 + 20 = 29.
Total = 29 + 27 - 1 = 55. (Not in options).
Let's re-read: 'V3 is 11th from the right of V1'. This means V1 is the reference. Counting to the right from V1, V3 is the 11th.
Position(V3) = Position(V1) + 11 - 1 = Position(V1) + 10.
19 = Position(V1) + 10 => Position(V1) = 9.
'V1 is 20th from the left of V2'. This means counting to the left from V2, V1 is the 20th.
Position(V1) = Position(V2) - 20 + 1 => 9 = Position(V2) - 19 => Position(V2) = 28.
Total = Position(V2) + RightPosition(V2) - 1 = 28 + 27 - 1 = 54.