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Placement Aptitude (Quant, Logical, Verbal) Module 16

Non-verbal and spatial reasoning interview questions

Interview questions on non-verbal and spatial reasoning: warm-ups, then what each harder question tests and how a good answer starts.

16 questions: 4 warm-ups and 12 with model answers · Levels: Fresher

Warm-up questions

Short questions with short answers, each answered in full.

Fresher

Why should you compare the figures of a series one property at a time instead of as whole pictures?

Answered in the lesson Figure series, analogy and classification
Fresher

What is the difference between a mirror image and a water image of a figure, and what happens to a word written in capitals in each?

Answered in the lesson Mirror images and shape transformations
Fresher

A square sheet is folded in half three times and one hole is punched through every layer. How many holes appear when it is opened, and when can there be fewer?

Answered in the lesson Paper folding, cutting and pattern completion
Fresher

Why can two faces that appear together in one view of a die never be opposite, and how does that help with the options?

Answered in the lesson Cubes, dice and counting figures

Questions with model answers

What each question tests, the first step of a good answer and the follow-ups to expect.

Fresher

In a figure analogy, an upright arrow becomes an arrow pointing right. C is an upright L shape. Both the L turned a quarter turn clockwise and the L mirrored in a diagonal can be defended as D. Why, and how do you choose?
What it tests

Seeing that a symmetric element cannot tell a turn from a reflection, and using the options and the rest of the item to decide.

First step

An arrow is symmetric about its own length, so a quarter turn clockwise and a reflection in the diagonal from bottom left to top right both carry an upright arrow onto one pointing right. Apply each reading to the L and compare the two results with the options.
Follow-ups
- Which shape in A would have removed the doubt?
- What does each reading give for an upright flag?
- What do you do when both candidates are among the options?
From the lesson Figure series, analogy and classification
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In the answer:
- Model answer
- Follow-up answers
- Common mistakes
- Rubric
- Variants
- about 3 minutes
Fresher

Five figures: an outlined square, pentagon and triangle with two dots each, a filled hexagon with two dots and an outlined circle with three dots. Two figures each look like the odd one out. Which do you choose, and when is such an item really ambiguous?
What it tests

Counting how each property splits the set, weighing candidates by how many properties single them out, and deciding quickly.

First step

Count the split each property makes. The shading splits the five 4 to 1 with the hexagon alone; having straight sides splits them 4 to 1 with the circle alone; the number of dots splits them 4 to 1 with the circle alone again.
Follow-ups
- What if the circle had two dots like the others?
- How long should this decision take in a timed section?
- How would you rewrite the item so that only one answer survives?
From the lesson Figure series, analogy and classification
Model answer, Pro.
In the answer:
- Model answer
- Follow-up answers
- Common mistakes
- Rubric
- Variants
- about 3 minutes
Fresher

In a 3 × 3 figure matrix, the third figure of each row seems to be made from the first two. How do you tell an overlay from an overlay without the shared lines, or from the shared lines alone, and why do you test every complete row?
What it tests

Treating figures as sets of lines, testing the three ways of combining them on each row, and seeing when a row cannot tell the rules apart.

First step

Write each figure as the set of lines it contains. For each complete row work out the three candidates: every line of both figures, only the lines in both, and the lines in exactly one. Keep the rule that gives the third figure in every complete row.
Follow-ups
- Which kind of row cannot separate the overlay from the overlay without shared lines?
- What if the first row fits one rule and the second row another?
- How do the same rules work for shaded cells instead of lines?
From the lesson Figure series, analogy and classification
Model answer, Pro.
In the answer:
- Model answer
- Follow-up answers
- Common mistakes
- Rubric
- Variants
- about 3 minutes
Fresher

A wall clock shows 4:25. What does its mirror image show, why does subtracting from 11:60 work, and what happens to the rule at 12:10 and at 6:00?
What it tests

Reflecting both hands, turning the reflection into arithmetic on the dial, and handling the hour 12 and the times that stay fixed.

First step

Reflect each hand in the line through 12 and 6: a hand θ degrees clockwise from 12 moves to 360° − θ. The minute hand at 25 minutes, 150°, moves to 210°, which is 35 minutes.
Follow-ups
- Why is the mirror image of a clock always a real time?
- If the mirror shows 2:35, what does the clock show?
- At which times do a clock and its mirror image agree?
From the lesson Mirror images and shape transformations
Model answer, Pro.
In the answer:
- Model answer
- Follow-up answers
- Common mistakes
- Rubric
- Variants
- about 2 minutes
Fresher

A flag is turned a quarter turn clockwise and then reflected in an upright mirror. Is that the same as reflecting first and turning second? Show it with coordinates, and name the single move that each order equals.
What it tests

Writing moves as rules on coordinates, applying them in order, and recognising each result as a reflection in a diagonal.

First step

Put the centre of the turn at the origin, with x to the right and y upwards. A quarter turn clockwise sends (x, y) to (y, −x), and the mirror along the y-axis sends (x, y) to (−x, y). Apply them in each order to one point, such as (1, 2).
Follow-ups
- Which pairs of moves do give the same result in either order?
- How can the order of labelled corners rule out an option?
- What do two mirrors at 45° to each other make?
From the lesson Mirror images and shape transformations
Model answer, Pro.
In the answer:
- Model answer
- Follow-up answers
- Common mistakes
- Rubric
- Variants
- about 3 minutes
Fresher

Why does the water image of an analogue clock never show a real time, and how should you answer an item that asks what a clock reads in water?
What it tests

Reflecting hand angles, checking the twelve-to-one relation between the hands, and reading an ambiguous image from its options.

First step

Write the hand angles t minutes after 12: the minute hand at 6t degrees and the hour hand at t/2. On a real clock the minute angle is twelve times the hour angle, give or take whole turns. Reflect both angles with θ → 180° − θ and test that relation.
Follow-ups
- What are the two readings of 3:10 in water?
- Which reading does the shortcut 18:30 − t give?
- Is a clock seen upside down any different?
From the lesson Mirror images and shape transformations
Model answer, Pro.
In the answer:
- Model answer
- Follow-up answers
- Common mistakes
- Rubric
- Variants
- about 2 minutes
Fresher

A 4 by 4 sheet is folded left half over right, then left half over right again, and punched at row 1, column 4. Where are the holes, and what goes wrong if you undo the first fold first?
What it tests

Recording each fold's mirror line on the packet it was made on, unfolding in reverse order, and checking the number of holes.

First step

Write down each fold's line as it is made. The first runs down the sheet's middle, between columns 2 and 3. The second runs down the middle of the packet that is left, columns 3 and 4, so it lies between columns 3 and 4.
Follow-ups
- How many holes should there be, and why?
- Where are the holes if the second fold is top down and the punch is at row 4, column 4?
- Which pairs of folds give the same holes in either order?
From the lesson Paper folding, cutting and pattern completion
Model answer, Pro.
In the answer:
- Model answer
- Follow-up answers
- Common mistakes
- Rubric
- Variants
- about 2 minutes
Fresher

A 64 cm paper strip is folded in half three times, to 8 cm, and cut straight across 3 cm from the end where its two loose ends lie. How many pieces fall out, and how long is each?
What it tests

Counting layers, turning one cut on the packet into its points on the strip by reflection, and checking that the lengths add up.

First step

Three folds make 8 layers, so the cut crosses the strip at 8 points and leaves 9 pieces. Pieces at the strip's ends are 3 cm long; a piece that runs round a fold has twice the distance from the cut to that fold.
Follow-ups
- How long are the pieces if the cut is 3 cm from the other end of the packet?
- What changes if the strip is folded four times instead?
- Why do the pieces come in only three lengths?
From the lesson Paper folding, cutting and pattern completion
Model answer, Pro.
In the answer:
- Model answer
- Follow-up answers
- Common mistakes
- Rubric
- Variants
- about 2 minutes
Fresher

Three quarters of a square tile pattern are drawn and the bottom-right quarter is missing. When do you complete it by mirroring and when by turning, how do you tell which, and can the two rules give the same answer?
What it tests

Testing the visible quarters for mirror and turning symmetry, applying the rule that passes, and knowing when both rules agree.

First step

Compare the top-right quarter with the top-left quarter twice: once mirrored left to right and once turned a quarter turn clockwise. Whichever matches is the pattern's rule; check it on the bottom-left quarter too.
Follow-ups
- What does the missing quarter look like under each rule for a turning pattern?
- Why do both rules give the same quarter for a pattern with two lines of symmetry?
- What if neither test matches?
From the lesson Paper folding, cutting and pattern completion
Model answer, Pro.
In the answer:
- Model answer
- Follow-up answers
- Common mistakes
- Rubric
- Variants
- about 2 minutes
Fresher

Two views of one die show top 2, front 1, right 5 and top 2, front 4, right 3. Which face is opposite 1, why does reading the views clockwise work, and what goes wrong if you assume that opposite faces add up to 7?
What it tests

Reading two views from their shared face, knowing why the reading is valid, and not importing the rule of a standard die.

First step

The views share only the 2, so they show two diagonally opposite corners of the face 2. Read each view clockwise from the 2, round the corner from the top to the right to the front: 2, 5, 1 and 2, 3, 4.
Follow-ups
- Why must two corners that share exactly one face be diagonal on it?
- What can you say if the views share two faces instead?
- How would a third view confirm the answer?
From the lesson Cubes, dice and counting figures
Model answer, Pro.
In the answer:
- Model answer
- Follow-up answers
- Common mistakes
- Rubric
- Variants
- about 2 minutes
Fresher

A 4 × 5 × 6 block painted on the outside is cut into 120 unit cubes. How many have exactly three, two, one and no painted faces? Show a check that the four counts are right.
What it tests

Counting corners, edge interiors, face interiors and the core of a cuboid, and checking the total.

First step

Strip one cube from every side: the unpainted core is 2 × 3 × 4 = 24 cubes. The 8 corners have three painted faces whatever the size of the block.
Follow-ups
- How many cubes lie on the edges but not at the corners?
- What changes if the block is 1 × 5 × 6?
- Which counts change if the bottom face is left unpainted?
From the lesson Cubes, dice and counting figures
Model answer, Pro.
In the answer:
- Model answer
- Follow-up answers
- Common mistakes
- Rubric
- Variants
- about 2 minutes
Fresher

How many rectangles, squares included, does a 3 by 5 grid of small squares contain, and how many of them are squares? Give a method that cannot miss or repeat one.
What it tests

Fixing a rectangle by its pair of horizontal and pair of vertical grid lines, and counting squares size by size.

First step

A rectangle is decided by its top and bottom lines and its left and right lines. The grid has 4 horizontal lines and 6 vertical ones, so count the pairs of each.
Follow-ups
- How many of the rectangles are not squares?
- How many rectangles contain the grid's top-left small square?
- What does the method give for a chessboard?
From the lesson Cubes, dice and counting figures
Model answer, Pro.
In the answer:
- Model answer
- Follow-up answers
- Common mistakes
- Rubric
- Variants
- about 2 minutes

The lessons of this module

Figure series, analogy and classification Free core, Pro depth: 8 of 30 minutes free
Mirror images and shape transformations Free core, Pro depth: 10 of 30 minutes free
Paper folding, cutting and pattern completion Free core, Pro depth: 8 of 25 minutes free
Cubes, dice and counting figures Free core, Pro depth: 11 of 30 minutes free

All Placement Aptitude (Quant, Logical, Verbal) interview questions · The Placement Aptitude (Quant, Logical, Verbal) track

Warm-up questions

Why should you compare the figures of a series one property at a time instead of as whole pictures?

What is the difference between a mirror image and a water image of a figure, and what happens to a word written in capitals in each?

A square sheet is folded in half three times and one hole is punched through every layer. How many holes appear when it is opened, and when can there be fewer?

Why can two faces that appear together in one view of a die never be opposite, and how does that help with the options?

Questions with model answers

In a figure analogy, an upright arrow becomes an arrow pointing right. C is an upright L shape. Both the L turned a quarter turn clockwise and the L mirrored in a diagonal can be defended as D. Why, and how do you choose?

Five figures: an outlined square, pentagon and triangle with two dots each, a filled hexagon with two dots and an outlined circle with three dots. Two figures each look like the odd one out. Which do you choose, and when is such an item really ambiguous?

In a 3 × 3 figure matrix, the third figure of each row seems to be made from the first two. How do you tell an overlay from an overlay without the shared lines, or from the shared lines alone, and why do you test every complete row?

A wall clock shows 4:25. What does its mirror image show, why does subtracting from 11:60 work, and what happens to the rule at 12:10 and at 6:00?

A flag is turned a quarter turn clockwise and then reflected in an upright mirror. Is that the same as reflecting first and turning second? Show it with coordinates, and name the single move that each order equals.

Why does the water image of an analogue clock never show a real time, and how should you answer an item that asks what a clock reads in water?

A 4 by 4 sheet is folded left half over right, then left half over right again, and punched at row 1, column 4. Where are the holes, and what goes wrong if you undo the first fold first?

A 64 cm paper strip is folded in half three times, to 8 cm, and cut straight across 3 cm from the end where its two loose ends lie. How many pieces fall out, and how long is each?

Three quarters of a square tile pattern are drawn and the bottom-right quarter is missing. When do you complete it by mirroring and when by turning, how do you tell which, and can the two rules give the same answer?

Two views of one die show top 2, front 1, right 5 and top 2, front 4, right 3. Which face is opposite 1, why does reading the views clockwise work, and what goes wrong if you assume that opposite faces add up to 7?

A 4 × 5 × 6 block painted on the outside is cut into 120 unit cubes. How many have exactly three, two, one and no painted faces? Show a check that the four counts are right.

How many rectangles, squares included, does a 3 by 5 grid of small squares contain, and how many of them are squares? Give a method that cannot miss or repeat one.