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Home / General Aptitude / Non-Verbal Reasoning / Analytical Reasoning
Non-Verbal Reasoning

Analytical Reasoning

Figure series, mirrors, embedded shapes and paper folding.

About Analytical Reasoning

Analytical reasoning questions give a few statements about how a group of people or things are arranged and ask about one position in that arrangement. Nothing in the statements is arithmetic and nothing can be guessed: the answer follows only by holding the possible arrangements in mind and striking out the ones the statements forbid. This topic covers the ground these puzzles are built from, and the way to work them out on paper.

What you need to understand

  • Every one of these puzzles is the same task in a different dress: there is a set of possible arrangements, the statements cut the set down, and the question asks about what is left.
  • The common shapes are a row of seats, a circle of people round a table, a set of floors in a building, an order of finishing, and a grouping into teams. The shape decides the drawing, not the method.
  • A statement that fixes someone to a particular place is the strongest kind, because it removes everything except that one. Start with it.
  • A statement that puts one person immediately next to another fixes the two together as a block, which can then be slid along the row. A row of five with a block of two has four possible positions for the block, not five.
  • A statement that says one person is somewhere to the left of another rules out all the arrangements with them the other way round - which is half of them. It is a weak clue on its own but a fast one.
  • A statement that says two people are not next to each other removes only the arrangements where they touch, so on its own it is the weakest statement of all.
  • A statement that puts someone at one of the ends fixes them to one of two places, so it cuts the field in half at a stroke and is nearly as useful as a fixed seat.
  • In a circular arrangement there is no leftmost seat, so the statements are about who is next to whom and who is opposite. Fixing one person somewhere removes the rotation, and then the row methods apply.
  • A negative statement is often the one that finishes a puzzle, because by then only two arrangements are left and the negative rules one of them out.
  • Working in two passes is what keeps these puzzles quick: first put in everything that is fixed, then go back through the remaining statements and use the ones that have become usable now that places are taken.
  • A drawing is not optional. A row of seats with the clues written under it turns a puzzle of five people into something that can be seen at a glance, and it is much faster than holding it all in the head.
  • The answer to a question of this kind is not certain just because it fits: it has to be the only arrangement that fits. Checking each clue back against the arrangement at the end is the whole of the verification.
  • When a question asks who is in a particular seat, the useful move is often to work out who cannot be there rather than who can. Eliminating four people answers the question as surely as placing one.
  • Time is the practical constraint. A puzzle with five people and six statements should take about a minute with a drawing and rather longer without one, and the drawing is always the faster of the two.

How to work through these questions

  1. Read all the statements before writing anything. One of them usually fixes a position, and starting there saves working through the others in the wrong order.
  2. Draw the row, the circle or the floors, and number the positions. Put a name in a position only when the statements force it there.
  3. Take the strongest statements first: a fixed seat, then an end, then a pair that must be adjacent, then a relative order, and only then the negatives.
  4. Write off the possibilities as you go. A statement that one person is to the left of another crosses off every arrangement with them reversed, and it is faster to rule out positions than to try to place people.
  5. Work in two passes, because a statement that was useless at the start can settle the puzzle once three of the five seats are filled.
  6. Check the finished arrangement against every statement, one at a time. If a single one is not satisfied, the arrangement is wrong and there is no need to look for a second.

Mistakes that cost marks

  • Treating a statement as satisfied by the first arrangement that fits it, rather than checking that all the statements together leave only one arrangement.
  • Reading somewhere to the left of as immediately to the left of. The second is far stronger and gives a different answer.
  • Forgetting that both ends count in a statement about being at an end, and placing the person at the left end only.
  • Counting the positions of a block of two in a row of five as five rather than four, because the block cannot overhang the end.
  • Starting with the negative statements, which rule out the least and so feel like they are making progress when they are not.
  • Working the whole puzzle in the head and losing track of which arrangement is which - the drawing is what keeps them apart.
  • Answering the question that was asked about the wrong position, having worked out the whole row but read the question as seat 1 when it asked about seat 5.
  • Assuming a circular arrangement has a fixed left end. It does not, and treating the first place drawn as the leftmost seat introduces an answer that is only true of that rotation.

Worked example

Five colleagues are seated in a row of five seats numbered 1 to 5 from left to right. It is known that E sits in seat 3; A is not next to E; A sits somewhere to the left of D; E is not next to C; and C is not next to D. Who is in seat 4?
  1. Draw the five seats and write E in seat 3. That is the strongest statement in the puzzle and everything else is measured from it.
  2. Take A not next to E. Seats 2 and 4 are next to 3, so A cannot be in either of them, and A must be in 1 or 5.
  3. Take A to the left of D. If A were in seat 5 there would be no seat to its right for D, so A is in seat 1.
  4. Take E not next to C. C cannot be in seat 2 or 4. Seat 1 is taken by A and seat 3 by E, so C is in seat 5.
  5. Take C not next to D. D cannot be in seat 4, because 4 is next to 5. The seats left for D and the fifth colleague are 2 and 4, so D is in seat 2 and the remaining person is in seat 4.
  6. The answer is the person left over, and every statement can be read back against the arrangement: E in 3, A in 1 not next to E, A left of D in 2, E not next to C in 5, C in 5 not next to D in 2. All five hold, and no other arrangement does.
Answer: The remaining colleague is in seat 4

Practice questions with answers

A few Analytical Reasoning questions with the full solution shown, so you can see how the method is applied before you attempt the timed set.

Question 1
5 people, D, B, G, A and E, are seated in a row of 5 seats numbered 1 to 5 from left to right. It is known that:
- A sits in seat 4.
- G sits at one of the ends.
- G is not next to D.
- D sits immediately to the left of E.
- E sits somewhere to the left of G.
- B sits somewhere to the left of D.
Which of them is in seat 1?
  • A E
  • B B
  • C D
  • D G
Answer: Option B — with explanation
A puzzle of this kind is settled by holding the arrangements in mind and striking out the ones a clue forbids, and by starting with the clue that says the most. A statement that fixes someone to a particular seat, or to one of the two ends, cuts the field hardest, so it is the one to use first. Take that clue, put the person where it says, and then work through the rest one at a time. A clue that puts one person immediately to the left of another fixes the two of them together as a block, which can then be slid along the row; a clue that only says one is somewhere to the left of another rules out half the arrangements at a stroke. Working through these clues leaves one arrangement and no other, and in it B sits in seat 1. The check worth doing at the end is to read each clue back against the arrangement you have settled on - if any one of them is not satisfied, the arrangement is wrong, and there is no need to look for a second answer. Common mistakes - G sits in another seat: G - E sits in another seat: E - D sits in another seat: D
Question 2
5 people, D, B, F, G and C, are seated in a row of 5 seats numbered 1 to 5 from left to right. It is known that:
- F sits somewhere to the left of C.
- D is not next to G.
- G sits in seat 2.
- D is not next to B.
- F sits at one of the ends.
Which of them is in seat 4?
  • A F
  • B D
  • C C
  • D G
Answer: Option C — with explanation
A puzzle of this kind is settled by holding the arrangements in mind and striking out the ones a clue forbids, and by starting with the clue that says the most. A statement that fixes someone to a particular seat, or to one of the two ends, cuts the field hardest, so it is the one to use first. Take that clue, put the person where it says, and then work through the rest one at a time. A clue that puts one person immediately to the left of another fixes the two of them together as a block, which can then be slid along the row; a clue that only says one is somewhere to the left of another rules out half the arrangements at a stroke. Working through these clues leaves one arrangement and no other, and in it C sits in seat 4. The check worth doing at the end is to read each clue back against the arrangement you have settled on - if any one of them is not satisfied, the arrangement is wrong, and there is no need to look for a second answer. Common mistakes - F sits in another seat: F - D sits in another seat: D - G sits in another seat: G
Question 3
6 colleagues - G, B, A, C, E and F - sit in a row of 6 seats, numbered 1 to 6 from left to right, one to a seat. The following is known:
- E sits in seat 2.
- E sits immediately to the left of G.
- E is not next to F.
- A sits in seat 1.
- E is not next to C.
- F sits in seat 4.
- A is not next to G.
- C sits immediately to the left of B.
Which of them is in seat 5?
  • A E
  • B B
  • C F
  • D C
Answer: Option D — with explanation
A puzzle of this kind is settled by holding the arrangements in mind and striking out the ones a clue forbids, and by starting with the clue that says the most. A statement that fixes someone to a particular seat, or to one of the two ends, cuts the field hardest, so it is the one to use first. Take that clue, put the person where it says, and then work through the rest one at a time. A clue that puts one person immediately to the left of another fixes the two of them together as a block, which can then be slid along the row; a clue that only says one is somewhere to the left of another rules out half the arrangements at a stroke. Working through these clues leaves one arrangement and no other, and in it C sits in seat 5. The check worth doing at the end is to read each clue back against the arrangement you have settled on - if any one of them is not satisfied, the arrangement is wrong, and there is no need to look for a second answer. Common mistakes - B sits in another seat: B - F sits in another seat: F - E sits in another seat: E
Question 4
5 people, E, G, F, B and D, are seated in a row of 5 seats numbered 1 to 5 from left to right. It is known that:
- D sits somewhere to the left of F.
- F is not next to G.
- G is not next to B.
- D is not next to E.
- G sits at one of the ends.
- F is not next to B.
- E is not next to D.
- G sits somewhere to the left of D.
- G sits somewhere to the left of E.
- G sits immediately to the left of E.
Who sits in seat 1?
  • A G
  • B D
  • C E
  • D F
Answer: Option A — with explanation
A puzzle of this kind is settled by holding the arrangements in mind and striking out the ones a clue forbids, and by starting with the clue that says the most. A statement that fixes someone to a particular seat, or to one of the two ends, cuts the field hardest, so it is the one to use first. Take that clue, put the person where it says, and then work through the rest one at a time. A clue that puts one person immediately to the left of another fixes the two of them together as a block, which can then be slid along the row; a clue that only says one is somewhere to the left of another rules out half the arrangements at a stroke. Working through these clues leaves one arrangement and no other, and in it G sits in seat 1. The check worth doing at the end is to read each clue back against the arrangement you have settled on - if any one of them is not satisfied, the arrangement is wrong, and there is no need to look for a second answer. Common mistakes - D sits in another seat: D - E sits in another seat: E - F sits in another seat: F
Question 5
6 colleagues - F, A, C, D, E and B - sit in a row of 6 seats, numbered 1 to 6 from left to right, one to a seat. The following is known:
- D sits somewhere to the left of C.
- D sits in seat 2.
- F is not next to E.
- E is not next to F.
- E is not next to B.
- A sits immediately to the left of D.
- B is not next to A.
- C sits in seat 5.
- E sits at one of the ends.
- E is not next to D.
- F is not next to D.
Which of them is in seat 6?
  • A A
  • B C
  • C B
  • D E
Answer: Option D — with explanation
A puzzle of this kind is settled by holding the arrangements in mind and striking out the ones a clue forbids, and by starting with the clue that says the most. A statement that fixes someone to a particular seat, or to one of the two ends, cuts the field hardest, so it is the one to use first. Take that clue, put the person where it says, and then work through the rest one at a time. A clue that puts one person immediately to the left of another fixes the two of them together as a block, which can then be slid along the row; a clue that only says one is somewhere to the left of another rules out half the arrangements at a stroke. Working through these clues leaves one arrangement and no other, and in it E sits in seat 6. The check worth doing at the end is to read each clue back against the arrangement you have settled on - if any one of them is not satisfied, the arrangement is wrong, and there is no need to look for a second answer. Common mistakes - B sits in another seat: B - C sits in another seat: C - A sits in another seat: A

Frequently asked questions

What is the fastest way into one of these puzzles?

Find the statement that fixes a position and start there. Statements differ enormously in how much they narrow the field, and the fixed ones narrow it most. Starting with a negative statement is the commonest way to spend three minutes and learn nothing.

Do I have to draw a diagram?

You do not have to, but almost everyone who is quick at these puzzles does. A row of numbered boxes with the names written in as they are settled turns the puzzle into something that can be read rather than remembered, and it is the remembering that costs the time.

How do I know when the answer is certain?

When the statements leave only one arrangement possible. That is stronger than checking that your arrangement fits, because a second arrangement might fit too - the test is that nothing else could. The safest habit is to read every statement back against the finished row.

What is the difference between somewhere to the left and immediately to the left?

Somewhere to the left means any distance, so it only rules out the reverse order. Immediately means one seat along, so it joins the two people into a block that moves as one. The second is much stronger, and reading one as the other is the commonest misreading.

How long should one of these take?

About a minute for five people and six statements, if a drawing is used from the start. A puzzle with eight people or a circular table takes longer, and the practical advice is to leave it and come back if a minute and a half has gone by without the row taking shape.

Does the shape of the arrangement change the method?

Not the method, but the drawing. A circle has no leftmost seat, so statements there are about who is next to whom, and one person has to be fixed by hand to remove the rotation. Once that is done it is a row again.

Take the Analytical Reasoning test

Two timed papers on the same syllabus — sit the foundation paper first, then the advanced one. Both use the real exam paper format with a full step-by-step review of every question once you submit.

Set 01 • Foundation Level
Analytical Reasoning — Foundation Paper
25 Questions
30 Minutes
+2 / −0.5 Marking
Start this paper
Set 02 • Advanced Level
Analytical Reasoning — Advanced Paper
25 Questions
30 Minutes
+2 / −0.5 Marking
Start this paper

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