Logical Reasoning · Micro-test

Ranking and Order

Ranking questions come in two kinds: positions in a row, which run on one formula, and comparisons (taller, heavier, earlier), which run on a single line drawn from most to least.

10 questions · 5 minutes · instant scoring

What this topic actually tests

For rows, the rule is that a person counted from both ends is counted twice. So total = position from the left + position from the right − 1, and position from the other end = total − position from this end + 1. To count the people between two positions measured from the same end, subtract and take one more away: between the 20th and the 36th there are 36 − 20 − 1 = 15. When two people's positions are given from opposite ends, first convert one of them so that both are counted from the same end. If the two positions add up to more than the total, the two people have crossed over, and the conversion shows this at once. Interchange questions look harder than they are: after a swap, each person stands in the other's old place, so the person now has one known position from each end and the formula gives the total. For comparisons, draw one line and place each person on it as the clues come in, writing them as a chain (S > R > P > Q > T). Before answering, check whether the clues actually fix the position asked about. Clues often fix who is last while leaving the first two places open, and 'cannot be determined' is then a real answer for some questions and a trap for others. Worked example: Priya is 15th from the top and 22nd from the bottom, so the class has 15 + 22 − 1 = 36 students.

The common trap on this topic

The standard slip is forgetting the minus one, which gives 37 where the answer is 36; question setters put that number among the options. The second is in 'how many between' questions, where candidates add the two positions when they are given from opposite ends without first converting one. The third is in comparison chains: choosing 'cannot be determined' as soon as the full order is not fixed, when the particular position asked about is fixed, or the reverse, naming someone as first when two people could be.

Ranking and Order: answers and explanations

In a row of 40 students, Anil is 12th from the left end. What is his position from the right end?
Answer: B. 29th
Position from the other end = total − position + 1 = 40 − 12 + 1 = 29.
Priya ranks 15th from the top and 22nd from the bottom in her class. How many students are there in the class?
Answer: C. 36
Total = 15 + 22 − 1 = 36. Priya is counted in both rankings, so one is subtracted.
In a row of children, Asha is 10th from the left and Bhuvan is 16th from the right. When they interchange places, Asha becomes 18th from the left. How many children are in the row?
Answer: D. 33
After the swap Asha stands where Bhuvan stood, a place that is 16th from the right and, as the question says, 18th from the left. Total = 18 + 16 − 1 = 33.
Among five friends, P is taller than Q but shorter than R. S is taller than R. T is shorter than Q. Who is exactly in the middle when they stand in order of height?
Answer: A. P
The clues give S > R > P > Q > T. The third of five is P.
In a queue of 50 people, Ravi is 20th from the front and Sita is 15th from the back. How many people are standing between them?
Answer: B. 15
Sita's position from the front is 50 − 15 + 1 = 36. Between the 20th and the 36th there are 36 − 20 − 1 = 15 people.
Five parcels are compared by weight. A is heavier than B but lighter than D. C is lighter than B but heavier than E. Which parcel is the second lightest?
Answer: B. C
The clues give D > A > B > C > E. E is the lightest and C is the second lightest.
In a class of 60 students, 6 did not sit the examination and 4 failed. Rohan ranks 12th from the top among those who passed. What is his rank from the bottom among those who passed?
Answer: C. 39th
Students who passed: 60 − 6 − 4 = 50. Rank from the bottom = 50 − 12 + 1 = 39.
In a row of 25 students, Meena is 14th from the left end and Tarun is 17th from the right end. How many students are standing between them?
Answer: B. 4
Tarun's position from the left is 25 − 17 + 1 = 9. Between the 9th and the 14th there are 14 − 9 − 1 = 4 students. Here the two positions overlap, which is why they must be put on the same end first.
Four runners took part in a race. K finished before L. M finished before N. L finished before N. Who finished last?
Answer: C. N
K and L both finished before N, and so did M, so N was last. Who came first cannot be determined, since M's place among K and L is not given, but the question asks only about the last place.
In a row of girls, Rita is 8th from the left end and Mona is 12th from the right end. Rita is to the left of Mona and there are exactly 5 girls between them. How many girls are in the row?
Answer: D. 25
Counting from the left: 8 girls up to and including Rita, then 5 between, then 12 from Mona to the right end. Total = 8 + 5 + 12 = 25.

FAQ

What is the formula for the total number of people in a row?

Total = position from the left + position from the right − 1. The one is subtracted because the person has been counted from both ends.

How do I count the people between two positions?

Express both positions from the same end, subtract the smaller from the larger, and subtract one more. Between the 9th and the 14th there are 14 − 9 − 1 = 4 people.

What if the positions from the two ends add up to more than the total?

The two people overlap: each is on the far side of the other. Convert one position to the other end and count normally; the method does not change.

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