Ranking & Order Test
Ranking and Order Test is a practical topic of the verbal reasoning paper of ADRE Grade IV. In these questions a group of people or things is arranged in a row or a line and the candidate has to find the position of one of them from the left or right end, or from the top or bottom. The topic needs simple counting and careful reading rather than heavy calculation. The questions are short and appear frequently, so they are a good source of marks for a well-practised candidate.
Meaning of Ranking
Ranking means arranging persons or objects in a definite order on the basis of a quality such as height, age, marks or position. The order may be a queue from left to right, a stack from top to bottom, or a list from first to last. The position may be counted from either end, and the two counts are related. If a person is twelfth from the left in a row of thirty, that person is the nineteenth from the right because the total minus the left position plus one gives the right position.
Basic Formulas
- Total = (position from left) + (position from right) − 1.
- Position from right = Total − position from left + 1.
- Position from left = Total − position from right + 1.
- If A is nth from the left and mth from the right, then total = n + m − 1.
- Number of persons between two persons = (sum of their positions) difference minus one.
Types of Ranking Questions
The most common type gives the total number of persons and the position of one person from one end and asks the position from the other end. Another type gives the positions of two persons from opposite ends and asks the total number. A third type asks how many persons are between two persons whose positions from the same end are given. Sometimes the order is given in words such as "taller than" or "older than", and the candidate has to arrange the whole group before answering.
Worked Examples
If Rina is eighth from the left in a row of twenty students, her position from the right is 20 − 8 + 1 = 13, so she is thirteenth from the right. If A is fifth from the left and B is ninth from the right in a row of fifteen, the number of persons between them is 15 − (5 + 9) = 1, so one person stands between A and B. In an order question, if Ram is taller than Shyam but shorter than Hari, the order from tallest to shortest is Hari, Ram, Shyam.
How This Topic Appears in the Examination
Ranking and order questions usually appear as two to four objective questions of one mark each. They are short and can be solved in less than a minute with a small diagram or a rough number line. The most common questions are the position from one end given the other end, and the total strength given both positions. Because a single wrong count changes the answer, the candidate must write the numbers clearly instead of calculating in the head.
Memory Tips
Always write a rough line and mark the positions instead of trying to hold the whole row in your head. Remember that when both positions are counted from opposite ends, the total is the sum of the two positions minus one, because the person himself is counted twice. In order questions, draw a small vertical ladder from tallest to shortest or oldest to youngest. Read the question twice to see clearly from which end the position is being asked.
Common Mistakes to Avoid
- Forgetting to subtract one when adding the two positions.
- Mixing up the left end and the right end.
- Counting the given person again while finding the persons between two.
- Assuming an order in words without drawing it.
- Rushing and making a small counting error.
How to Prepare This Topic
- Memorise the three basic formulas of ranking.
- Practise with a rough number line for every question.
- Solve both position-based and order-based questions.
- Check your answer by working backwards from the other end.
- Practise ten questions daily until the formulas become automatic.
More Solved Examples
If A is tenth from the left and fifteenth from the right in a row, the total number of persons is 10 + 15 − 1 = 24. If in a class of forty students Sita is twelfth from the top, she is 40 − 12 + 1 = 29th from the bottom. If Ram is seventh from the left and Shyam is ninth from the right in a row of twenty-five, the number of persons between them is 25 − (7 + 9) = 9. In an order question, if A is taller than B, B is taller than C and C is taller than D, the order from tallest to shortest is A, B, C, D.
Advanced Tips for the Exam
Draw a rough line for every question and mark both ends clearly, because the most common mistake is mixing the left and the right. When a person is counted from both ends, remember that the total is the sum of the two positions minus one. In order questions, draw a ladder and place each person according to every statement. Read the words "above", "below", "left", "right", "elder" and "younger" very carefully. Check the answer by working back from the other end.
Quick Revision Checklist
- Total = left position + right position − 1.
- Position from the other end = total − given position + 1.
- Persons between two = larger position − smaller position − 1.
- Left-to-right order in age, height or marks.
- A clear rough line for every question.
- Answer checked from the other end.
Frequently Asked Questions
What is the formula for ranking?
Total = position from left + position from right − 1. From this, the position from either end can be found when the total and the other position are known.
Why do we subtract one in the ranking formula?
Because when the position from the left and the position from the right are added, the same person is counted twice, so one is subtracted to correct the double count.
How do I find how many persons are between two persons?
Subtract the sum of the two positions from the total, or subtract the smaller position and one from the larger position, to get the number of persons standing between them.
How should I handle order questions in words?
Draw a small ladder and place each person above or below the other according to the statements, then read the final order from the diagram.
How much time should each question take?
A ranking question should take less than a minute. Writing a rough line makes the counting quick and free from mistakes.