Non-Verbal Reasoning: Figure Series and Mirror Images

What does the name mean?

Non-verbal questions use shapes, figures and pictures instead of words.

You solve them by looking carefully, not by reading.

Which types come up most?

Mirror and water images, dice and cubes, counting shapes, and figure series.

Each type has its own short rule.

What skill do they test?

They test whether you can see how a figure changes: flipped, turned, or repeated.

Patience and a quick sketch help more than speed.

What is a figure series?

A row of figures changes step by step. You find the next figure.

Each step may turn, flip, add a part or remove a part.

How do you find the rule?

Compare the first two figures. Name what changed in one short phrase.

Then check that the same change takes figure two to figure three.

What if two changes happen together?

Track each change on its own. A shape may turn while a dot moves.

Predict both before you look at the options.

Why this works: each change repeats on its own schedule, so you can read them one at a time.

Can you see a series solved?

A dot sits at top-left, then top-right, then bottom-right, then bottom-left.

It moves one corner clockwise each step. So the next place is top-left.

Why this works: after four steps the dot has been to every corner, so the cycle starts again.

What is the difference?

A mirror image flips left and right, like a mirror held beside the object.

A water image flips top and bottom, like a reflection in still water below.

Which letters look the same?

In a mirror, these stay the same: A, H, I, M, O, T, U, V, W, X, Y.

In water, these stay the same: B, C, D, E, H, I, K, O, X.

Can you see it solved?

How many letters of MOTHER look the same in a mirror? M, O, T and H do. E and R do not.

So the answer is 4. In water, only O, H and E stay the same, which gives 3.

Why this works: each letter is checked on its own against the list, and then we count the ones that pass.

Can you try another word?

How many letters of TOMATO look the same in a mirror? T, O, M, A, T and O all do, so the answer is 6.

In water, only O stays the same, and it appears twice. So the answer is 2.

Why this works: T, M and A are symmetric left to right, but not top to bottom.

How do you get a mirror time?

Subtract the time from 12:00. Treat 12:00 as 11:60 if you need to borrow.

The result is the time the mirror shows.

Can you see it solved?

A clock shows 3:25. Its mirror image shows 12:00 minus 3:25, which is 8:35.

Why this works: the hands keep the same angle from the 12-to-6 line, but on the other side.

Can you try another time?

A clock shows 4:10. In a mirror it shows 12:00 minus 4:10, which is 7:50.

To borrow, think of 12:00 as 11:60. Then 11:60 minus 4:10 is 7:50.

Why this works: each hand reflects across the 12-to-6 line, so the sum of the two times is 12:00.

Why does this work?

A mirror flips the dial left to right, so each hand reflects around the 12-to-6 line.

A water image flips the dial top to bottom. That rarely gives a real clock time, so exams mostly ask the mirror kind.

What is the key idea?

Faces that touch the same corner can be seen together. Faces opposite each other can never be seen together.

So two faces shown in one view are never opposite.

Can you see it solved?

View 1 shows 2, 3 and 5. View 2 shows 2, 4 and 5. Two faces are common, which are 2 and 5.

So the two remaining faces, 3 and 4, must lie opposite each other.

Why this works: the faces seen together in one view all meet at one corner, so none of them are opposite.

Can you read opposite faces from a net?

In the net, 1 and 6 are two squares apart in a column, so they are opposite.

2 and 5 are also two squares apart in the column. 3 and 4 are two squares apart in the row.

Why this works: faces that are one square apart meet at an edge, and faces two apart sit across the cube.

What if only one face is common?

Fix that face as an anchor. Then turn the second view in your mind to match the first.

The face that stays hidden opposite the anchor is the answer.

Can you solve a one-common-face case?

View 1 shows 1, 2 and 3. View 2 shows 1, 4 and 5. Only 1 is common.

Faces 2 and 3 are both next to 1. Faces 4 and 5 are also next to 1.

So the face opposite 1 must be 6, the only face never seen with 1.

Why this works: opposite faces are never seen together, so the missing face must be the opposite.

How do you count squares?

In an n by n grid, add up n squared, then (n – 1) squared, and so on down to one.

For a 2 by 3 grid, there are 6 small squares and 2 bigger ones. That is 8.

Why this works: a 2 by 2 square fits in two positions across, and there is only one row for it.

Can you count a 3 by 3 grid?

Squares: 9 small, 4 of size 2 and 1 of size 3. That is 9 + 4 + 1 = 14.

Rectangles: 3 x 4 / 2 = 6 for each direction, and 6 x 6 = 36.

Why this works: every rectangle is chosen by two lines across and two lines down.

How do you count rectangles?

In an m by n grid, the count is (m x (m + 1) / 2) times (n x (n + 1) / 2).

For a 2 by 4 grid, 3 times 10 gives 30.

Why this works: 2 rows give 3 ways to pick the top and bottom, and 4 columns give 10 ways to pick the sides.

How do you count triangles?

Count by size. First the small ones, then those made of two or more.

Check each count so that no shape is counted twice.

What mistakes cost marks?

Mixing up mirror and water images.

Forgetting that large shapes also count in grid questions.

How do you stay quick?

Learn the two letter lists by heart. Use the 12:00 subtraction trick for clocks.

Sketch dice and grids in the margin, not in your head.

How should you practise?

Do three questions of each type a day. Check every answer against the rule.

Then try the quiz below and read every explanation.