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4th Std Scholarship · Intelligence Test

Ranking and order

5 concepts · 40 practice questions with answers · Free to read

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Place in a row : from the left and from the right

From daily life

People stand in a queue at a bus stop. If 4 people are ahead of you, you are 5th in the queue. Looking the other way, your number from the back depends on how many stand behind you. You are counted in both counts, so when finding the total we must subtract one.

Simple definition

In a row there are two numbers : the number from the left (L) and the number from the right (R). Total people = L + R − 1, because the same person is counted in both.

Live figure

Place in a row : from the left and from the right

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Example of a row of 10 people

PlaceFrom leftFrom rightSum
First person11011
Fourth person4711
Sixth person6511
1
Rule 1

Total = number from left + number from right − 1.

  • E.g. 6th from the left and 9th from the right. Total 6 + 9 − 1 = 14.
2
Rule 2

Number from the other side = total + 1 − number from this side.

  • E.g. Total 20, 8th from the left. From the right 20 + 1 − 8 = 13.
3
Rule 3

If two numbers are from the same side, the people between them = bigger number − smaller number − 1.

  • E.g. 5th and 12th from the left. Between them 12 − 5 − 1 = 6 people.
4
Rule 4

There is a middle person only if the total is odd. Their number = (total + 1) ÷ 2.

  • E.g. Total 21 people. Middle number (21 + 1) ÷ 2 = 11.
Example 1 · easy

In a row of 15, Rohan is 7th from the left. What is his number from the right?

  1. Total + 1 − 7 = 15 + 1 − 7.
  2. Answer : 9th from the right.
Example 2 · medium

In a row of 20, Anu is 8th from the left and Bina is 6th from the right. How many people are between them?

  1. Bina is 20 + 1 − 6 = 15th from the left.
  2. Between them 15 − 8 − 1 = 6 people.
Example 3 · exam type

In a row Ravi is 5th from the left and Meena is 7th from the right. There are 4 people between them. How many people are in the row?

  1. Ravi's place is 5. With 4 people between, Meena is 5 + 4 + 1 = 10th from the left.
  2. Total 10 + 7 − 1 = 16.
Remember

The same person is in both counts "from the left" and "from the right", so subtract one.

Common mistake

Taking total = L + R. This is wrong. The right answer is L + R − 1.

Shortcut

Memory clue : "Left + right − 1 = total."

Shortcut

To find how many people are between, do "difference − 1". E.g. 5 and 12 : difference 7, between 6.

Spot the difference

What is askedHow to find itExample
Total numberL + R − 16 and 9 : 14
Number from the other sideTotal + 1 − numberTotal 20, 8 : 13
People between twoDifference − 15 and 12 : 6

Practice questions

Easy
  1. 1In a row a boy is 5th from the left and 8th from the right. How many boys are in the row?
  2. 2In a row of 25, Seema is 10th from the left. What is her number from the right?
  3. 3How many people are there between the 4th and the 9th from the left?
Medium
  1. 4In a row of 30, Gauri is 12th from the left and Hari is 11th from the right. How many people are between them?
  2. 5In a row of 23 children, what is the number of the middle child?
  3. 6In a row Ajay is 7th from the left and Balu is 5th from the right. When they exchange places, Ajay becomes 12th from the left. How many people are in the row?
Challenging
  1. 7In a row of 40 children, how many children are to the left of the 18th child from the right?
  2. 8In a row Amit is 12th from the left and Kavita is 15th from the right. There are 8 people between them (Amit is on the left). How many people are in the row?
Show answers (try them yourself first)
  1. 15 + 8 − 1 = 12.
  2. 225 + 1 − 10 = 16th.
  3. 39 − 4 − 1 = 4 people.
  4. 4Hari is 30 + 1 − 11 = 20th from the left. Between them 20 − 12 − 1 = 7 people.
  5. 5(23 + 1) ÷ 2 = 12th.
  6. 6Ajay took Balu's place. Balu was earlier 12th from the left and 5th from the right. Total 12 + 5 − 1 = 16.
  7. 7This child is 40 + 1 − 18 = 23rd from the left. There are 22 children to the left.
  8. 8Kavita is 12 + 8 + 1 = 21st from the left. Total 21 + 15 − 1 = 35.

Rank : from the top and from the bottom

From daily life

In exam results the class gets numbers by marks : first, second and so on. The highest marks get number 1. If a boy is "7th from the top", there are 6 people above him.

Simple definition

Rank means the number by marks. Rank from the top (T) is counted from the highest marks, rank from the bottom (B) from the lowest. As in a row, total students = T + B − 1.

Ranks in a class

Rank from topStudents aboveStudents below (total 30)
1029
7623
30290
1
Rule 1

Total students = rank from top + rank from bottom − 1.

  • E.g. 10th from the top and 15th from the bottom. Total 10 + 15 − 1 = 24.
2
Rule 2

Rank from bottom = total + 1 − rank from top. The reverse works too.

  • E.g. Total 40, 8th from the top. From the bottom 40 + 1 − 8 = 33.
3
Rule 3

Students above = rank from top − 1. Students below = rank from bottom − 1.

  • E.g. Rank 9 from the top. There are 8 students above.
4
Rule 4

If the rank improves, subtract the number of students overtaken from the rank from the top.

  • E.g. Last year 12th from the top. This year 5 students were left behind. New rank 12 − 5 = 7.
Example 1 · easy

In a class of 40, Neha is 8th from the top. What is her rank from the bottom?

  1. 40 + 1 − 8.
  2. Answer : 33rd from the bottom.
Example 2 · medium

Tanvi is 14th from the top and 19th from the bottom. How many students are in the class? How many are below her?

  1. Total 14 + 19 − 1 = 32.
  2. Below her 19 − 1 = 18 students.
Example 3 · exam type

In a class of 35, Omkar was 12th from the bottom. In the half-yearly exam he left 5 students behind. What is his rank from the top now?

  1. Earlier from the top 35 + 1 − 12 = 24.
  2. Now 24 − 5 = 19. Now from the bottom 12 + 5 = 17. Check : 35 + 1 − 17 = 19.
Remember

When the rank improves, the number of the rank from the top goes down and the number of the rank from the bottom goes up.

Common mistake

Taking "students above = rank from top". Students above = rank − 1, because you must not count the student himself.

Shortcut

Memory clue : "Top + bottom − 1 = total; and take away the student himself."

Shortcut

To check a rank answer quickly, do above + below + 1 = total.

Spot the difference

What is askedHow to find itExample
Total studentsT + B − 110 and 15 : 24
How many aboveT − 1T = 9 : 8 students
Rank improvedT − students left behind12, 5 students : 7

Practice questions

Easy
  1. 1In a class of 30, Sachin is 4th from the top. What is his rank from the bottom?
  2. 2A student is 10th from the top and 15th from the bottom. How many students are in the class?
  3. 3If the rank from the top is 9, how many students are above him?
Medium
  1. 4In a class of 45, Sai is 18th from the bottom. What is his rank from the top?
  2. 5A girl's rank from the top changed from 15 to 9. How many students did she leave behind?
  3. 6In a class of 30, Mira is 7th from the top and Nita is 9th from the bottom. How many students are between them?
Challenging
  1. 7In a class of 30, Aryan is 5 ranks ahead of B. B is 14th from the top. What is Aryan's rank from the bottom?
  2. 8In a class Sagar is 11th from the top and 22nd from the bottom. Tej is 6 ranks below Sagar. What are Tej's ranks from the top and from the bottom?
Show answers (try them yourself first)
  1. 130 + 1 − 4 = 27.
  2. 210 + 15 − 1 = 24.
  3. 39 − 1 = 8 students.
  4. 445 + 1 − 18 = 28.
  5. 515 − 9 = 6 students.
  6. 6Nita is 30 + 1 − 9 = 22nd from the top. Between them 22 − 7 − 1 = 14 students.
  7. 7Aryan is 14 − 5 = 9th from the top. From the bottom 30 + 1 − 9 = 22nd.
  8. 8Total 11 + 22 − 1 = 32. Tej is 11 + 6 = 17th from the top. From the bottom 32 + 1 − 17 = 16th.

Gap between two people and exchanging places

From daily life

Two friends on a bench change seats. The one who sits in the other's seat gets the other's old number. All exchange questions can be solved with this one idea.

Simple definition

Exchange means two people change places. The total number in the row does not change; only the two places change. So the new number tells us the other person's old number, and from that we can find the total.

Two people in a row

PersonBefore (from left)After the exchange (from left)
A38
B83
1
Rule 1

If the numbers are from the same side, people between = difference − 1.

  • E.g. 6th and 14th from the left. Between them 14 − 6 − 1 = 7.
2
Rule 2

If one number is from the left and the other from the right, give the other person a number from the left too : total + 1 − number.

  • E.g. Total 18. Someone is 2nd from the right. He is 18 + 1 − 2 = 17th from the left.
3
Rule 3

After the exchange the first person comes to the second person's old place. That is the second person's old number.

  • E.g. A is 10th from the left. After going to B's place, A is 15th from the left. So B was 15th from the left earlier.
4
Rule 4

If someone comes and stands on your left, your number from the left goes up; if someone on your left leaves, it goes down. The number from the right does not change.

  • E.g. 8th from the left. One person on the left leaves. Now 7th from the left.
Example 1 · easy

How many people are between the 6th and the 14th from the left?

  1. 14 − 6 − 1.
  2. Answer : 7 people.
Example 2 · medium

In a row of 20 children, P is 5th from the left and Q is 4th from the right. How many children are between them?

  1. Q is 20 + 1 − 4 = 17th from the left.
  2. Between them 17 − 5 − 1 = 11 children.
Example 3 · exam type

In a row X is 10th from the left and Y is 12th from the right. After they exchange places, X is 15th from the left. How many people are in the row?

  1. X is now in Y's old place. So Y was 15th from the left earlier.
  2. Total 15 + 12 − 1 = 26. Check : X is now 26 + 1 − 15 = 12th from the right, correct.
Remember

After an exchange the total stays the same, and the other person's old number is the first person's new number.

Common mistake

Thinking the total changes after an exchange. Changing places does not add or remove people.

Shortcut

Memory clue : "New place = the other's old place."

Shortcut

If the two people are counted from different sides, first give both numbers from the same side, then do difference − 1.

Spot the difference

SituationWhat to do
Both numbers from the same sideDifference − 1
Numbers from different sidesChange one to total + 1 − number, then difference − 1
Places exchangedNew number = the other's old number

Practice questions

Easy
  1. 1How many people are between the 3rd and the 11th from the left?
  2. 2In a row of 18, one person is 5th from the left and another is 2nd from the right. How many people are between them?
  3. 3In a row of 14, how many people are to the left and how many to the right of the 8th from the left?
Medium
  1. 4In a row of 25, Ravi is 9th from the left and Shiv is 7th from the right. How many people are between them?
  2. 5Anil is 8th from the left. 3 children come and stand on his left. What is his number from the left now?
  3. 6P is 8th from the left and Q is 6th from the right. After they exchange places, P is 14th from the left. How many people are in the row?
Challenging
  1. 7In a row of 31, A is in the middle. B is 5th to his right and C is 4th to his left. How many people are between B and C?
  2. 8Dev is 7th from the left and Isha is 9th from the right. After they exchange places, Dev is 14th from the left. What is Isha's number from the right after the exchange?
Show answers (try them yourself first)
  1. 111 − 3 − 1 = 7 people.
  2. 2The other person is 18 + 1 − 2 = 17th from the left. Between them 17 − 5 − 1 = 11 people.
  3. 3To the left 8 − 1 = 7 people. To the right 14 − 8 = 6 people.
  4. 4Shiv is 25 + 1 − 7 = 19th from the left. Between them 19 − 9 − 1 = 9 people.
  5. 58 + 3 = 11th.
  6. 6Q was earlier 14th from the left. Total 14 + 6 − 1 = 19.
  7. 7Middle number (31 + 1) ÷ 2 = 16. B is 16 + 5 = 21st from the left, C is 16 − 4 = 12th. Between them 21 − 12 − 1 = 8 people.
  8. 8Isha was earlier 14th from the left. Total 14 + 9 − 1 = 22. Now Isha is 7th from the left and 22 + 1 − 7 = 16th from the right.

Arranging in order by comparing

From daily life

"Ram is taller than Shyam, and Shyam is taller than Gopal." On hearing this we say at once that Ram is the tallest. Joining the comparisons in a question one after another to get the full order is the work of this section.

Simple definition

Statements compare two people at a time, and we must find the full order. Write each statement with the sign >. A > B means A is bigger than B (taller, heavier, older or with more marks).

Live figure

Arranging in order by comparing

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Signs for comparing

SentenceSign
A is taller than BA > B
A is shorter than BB > A
C is taller than A, A is taller than BC > A > B
1
Rule 1

Write every statement in one direction (bigger > smaller). Turn "shorter", "smaller" and "lighter" statements around.

  • E.g. "P is lighter than Q" means Q > P.
2
Rule 2

Join the chain : if A > B and B > C, then A > B > C.

  • E.g. Ram > Shyam and Shyam > Gopal. So Ram > Shyam > Gopal.
3
Rule 3

The biggest is the one nobody is bigger than. The smallest is the one who is bigger than nobody.

  • E.g. In D > C > A > B, D is the biggest and B is the smallest.
4
Rule 4

If there are n people in all, below the one who is k-th from the biggest there are n − k people.

  • E.g. Among 7 people, below the 3rd from the biggest there are 7 − 3 = 4 people.
Example 1 · easy

Ram is taller than Shyam. Shyam is taller than Gopal. Who is the tallest?

  1. Ram > Shyam > Gopal.
  2. Answer : Ram.
Example 2 · medium

Four friends : A is older than B, C is younger than B, D is older than A. Who is the third oldest?

  1. D > A > B > C.
  2. The third is B.
Example 3 · exam type

Five people : P is heavier than Q but lighter than R. S is heavier than R but lighter than T. Who is the lightest and who is the third heaviest?

  1. R > P > Q and T > S > R. Join : T > S > R > P > Q.
  2. The lightest is Q. The third heaviest is R.
Remember

When all statements are written in one direction, the chain joins by itself.

Common mistake

Writing a "is shorter than" statement as it is, without turning it around. This reverses the direction and gives the order upside down.

Shortcut

Memory clue : "All arrows in one direction."

Shortcut

After finding the answer, read each statement again and check that it fits the order.

Spot the difference

StatementHow to write it
X is bigger than YX > Y
X is smaller than YY > X
X is between Y and ZY > X > Z or Z > X > Y

Practice questions

Easy
  1. 1A is taller than B and B is taller than C. Who is the shortest?
  2. 2Rani is older than Seema and Seema is older than Tara. Who is the youngest?
  3. 3In P > Q > R, who is in the middle?
Medium
  1. 4A > B, C > A, B > D. Who is the second biggest?
  2. 5Five students : X is shorter than Y but taller than Z. W is taller than Y. V is shorter than Z. Who is the third tallest?
  3. 6In a race A reached after C but before B. D reached before C. Who was last?
Challenging
  1. 7A is taller than B, B is taller than C, D is shorter than C, E is taller than A. Who is in the middle?
  2. 8In a group of 7 people, Mani is third from the tallest. How many people are shorter than him?
Show answers (try them yourself first)
  1. 1A > B > C. The shortest is C.
  2. 2Rani > Seema > Tara. The youngest is Tara.
  3. 3The middle one is Q.
  4. 4C > A > B > D. The second is A.
  5. 5W > Y > X > Z > V. The third is X.
  6. 6In order D, C, A, B. Last is B.
  7. 7E > A > B > C > D. The middle one is B.
  8. 87 − 3 = 4 people.

Mixed questions : adding, removing and checking

From daily life

In a queue some new people come and stand, some people leave. Does our place change then? Some numbers change and some stay the same. The trick of this part is to see carefully which one changes.

Simple definition

When people come or go, the total changes. If the change is on your left, the number from the left changes; if the change is on your right, the number from the right changes. The other side stays the same.

Which number changes

Where the change happenedNumber from leftNumber from right
People came on our leftGoes upDoes not change
People on our left went awayGoes downDoes not change
People came on our rightDoes not changeGoes up
1
Rule 1

If people come on the left, the number from the left goes up by that many.

  • E.g. 12th from the left. 3 people came on the left. Now 12 + 3 = 15th.
2
Rule 2

When people come or go, the total goes up or down by the same number.

  • E.g. If 2 leave from 40, now 40 − 2 = 38.
3
Rule 3

If the total is known, boys and girls : girls = total − boys.

  • E.g. 17 boys among 28 people. Girls 28 − 17 = 11.
4
Rule 4

After finding the answer, check it the other way round with "L + R − 1 = total".

  • E.g. 12 and 9 gave total 20. Check : 12 + 9 − 1 = 20, correct.
Example 1 · easy

In a row of 24 children there are 15 boys. 3 more girls come and stand in the row. How many girls are there now and how many in all?

  1. Girls earlier 24 − 15 = 9. 3 more : 12 girls.
  2. Total 24 + 3 = 27.
Example 2 · medium

In a row of 25, Mohit is 10th from the front. 4 people come and stand in front of him. What is his number from the back now?

  1. Now from the front 10 + 4 = 14th. Total 25 + 4 = 29.
  2. From the back 29 + 1 − 14 = 16th. (The number from the back is the same as before : 25 + 1 − 10 = 16.)
Example 3 · exam type

In a row Sunita is 8th from the left and Tina is 10th from the right. There are 6 people between them. How many are in the row? How many are left if Tina goes away?

  1. Tina is 8 + 6 + 1 = 15th from the left.
  2. Total 15 + 10 − 1 = 24. After Tina goes 24 − 1 = 23.
Remember

Only the number of the side where the change happened changes. The other side stays the same.

Common mistake

Thinking the number from the back also changes when people come in front. The number from the back does not change.

Shortcut

Memory clue : "Where the change is, there the number changes."

Shortcut

At the end always check with L + R − 1 = total.

Spot the difference

QuestionWhat changes
5 people came on the leftNumber from left + 5, total + 5
5 people left from the endTotal − 5, number from left same
Boys and girls askedGirls = total − boys

Practice questions

Easy
  1. 1In a row of 28 there are 17 boys. How many girls are there?
  2. 212th from the left. 3 people come and stand on the left. What is his number from the left now?
  3. 32 people leave from 40. How many remain?
Medium
  1. 4In a row of 30, Anil is 11th from the front. 5 people come in front. What are his numbers from the front and from the back now?
  2. 5From a row of 22 students the last 5 leave. What is the number from the back of the one who was 14th from the front?
  3. 6In a row of 35, Rahul is 20th from the left. How many people are to his right?
Challenging
  1. 7In a row Pooja is 14th from the left and Qasim is 11th from the right. There are 7 people between them. How many are in the row?
  2. 8In a row of 26, Kavya is 9th from the front and Lata is 8th from the back. How many people are between them? How many are between them after 4 more people come between them?
Show answers (try them yourself first)
  1. 128 − 17 = 11.
  2. 212 + 3 = 15th.
  3. 340 − 2 = 38.
  4. 4From the front 11 + 5 = 16th. From the back the same as before : 30 + 1 − 11 = 20th.
  5. 5The total is now 22 − 5 = 17. The 14th from the front is 17 + 1 − 14 = 4th from the back.
  6. 6To the right 35 − 20 = 15 people.
  7. 7Qasim is 14 + 7 + 1 = 22nd from the left. Total 22 + 11 − 1 = 32.
  8. 8Lata is 26 + 1 − 8 = 19th from the front. Between them 19 − 9 − 1 = 9 people. After 4 more come 9 + 4 = 13 people.

Quick revision of the whole lesson

TypeMemory clue
Place in a rowLeft + right − 1 = total
RankTop + bottom − 1 = total; above = rank − 1
ExchangeNew place = the other's old place
ComparingAll arrows in one direction
Adding, removingWhere the change is, there the number changes
People between twoDifference − 1

🎯 Most important points for the exam

  • Total = number from left + number from right − 1. The same for rank.
  • Other side = total + 1 − number from this side.
  • People between two = bigger number − smaller number − 1 (both from the same side).
  • After an exchange the new number = the other's old number; the total stays the same.
  • In comparing questions write all statements in one direction (bigger > smaller) and join the chain.
  • Only the number on the side where people came or went changes.
🧠 Study mantra

"Count, subtract one; check at the end."