Topic Note: Visual Ability

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Topic Note: Visual Ability

The idea behind this category is to enhance student’s visual abilities. We focus on two key skill sets

viz. 1) ability to visualize / imagine and 2) ability to spot things. The questions would either present a

situation where the student has to imagine / visualize a situation to answer the question or would

present them an image which the student needs to carefully observe and answer the given questions.

There are various types of questions in this category and some of these are given below:

SPATIAL SENSE

Spatial sense is an intuitive feel for shape and space. These kind of questions focus on developing and

enhancing the spatial sense for a child. They are provided with questions which test their spatial skills.

There are various examples of such questions. Some of these are given below:

One of the best way to solve such a question is to break down the question into various objects.

For instance, in a question involving various words, each letter can be considered as a separate

object. Similarly for an image like the following, the two arrows, the triangle inside the shape

, etc can be considered as separate objects.

Once the student classifies the objects, there are two important clues a student can use to solve

these kind of questions:

1) Study the relative position of various objects. Look at the relative position of various

objects in the question and also understand how that would change in the answer. This

would help eliminate a few options

2) Whether all objects which are present in the question, are included in the answer or not?

Mirror and Water Image

A lot of questions involve the student figuring out the right option which presents the mirror or water

image of a word.

Mirror Images

Mirrors follow a phenomenon called “Lateral Inversion” i.e. in such an image, the right side of the

object appears on the left side and vice - versa. A mirror - image is therefore said to be laterally inverted

and the phenomenon is called Lateral Inversion.

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Water Images

The reflection of an object, as seen in water, is called its water image. It is the inverted image obtained

by turning the object upside down. Unlike the mirror image where the left becomes right and vice-

versa, in case of a water image, top becomes bottom and vice versa

The above picture gives a very good way of understanding a mirror image and a water image. As can

be seen in the above diagram, the mirror image is like an image on a book open left and right. When

you close the book, the two images will super-impose. Similarly the water image is like a book opened

upside down. When you close the book, the images will super-impose.

Given below are few tables for mirror image and water image for the student’s reference. Please note

that these are only given as reference for the student to understand the concept and they are not

required (and should not) memorize these.

Mirror Images of Capital Alphabets

F

Mirror Image

F

Water Image


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Water Images of Capital Alphabets

Mirror Images of Numbers

Water Images of Numbers

Mirror Images of Small Alphabets


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Water Images of Small Alphabets

As you can see above, the mirror images follow the rule – left becomes right and right becomes

left; while the water images follow the rule – top becomes bottom and bottom becomes top.

Given the above fact, in case a mirror image or water image of a word is required, it becomes even

easier. As the word would appear in reverse in case of a mirror image and would appear upside down

(but in the same order) in the case of a water image. See the diagram below for reference

1. Which of the following options resemble the mirror image of NeL$0n125?

a. 521n0$LeN b. c. d.

Solution: As per the directions given earlier, lets assume that the various letters / symbols

are different objects. Clearly the first thing the student should look for is the order of the

words. As explained earlier, in case of a mirror image, left becomes right and vice versa. So in

this case the student should first look at options which have letters in the reverse order than

that given in NeL$0n125. So clearly option c and d are ruled out. Also given that in option a,

though the letters are in the reverse order, they are not really the mirror image (which is evident

by looking at any of the individual letter). So option (b) is the answer. Also on clearly

examining the option (b), a student can clearly see that it is the mirror image of the given word

WORD

Mirror Image

WORD

Water Image


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2. Which of the following options resemble the water image of NeL$0n125?

a. 521n0$LeN b. c. d.

Solution: First thing the student should look for is the order of the words. As explained earlier,

in case of a water image, the words are just turned upside down, while the order remains the

same. So in this case the student should first look at options which have letters in the same

order as that given in NeL$0n125. So clearly option c and d are possible answers. Also given

that in option c, though the letters are in the same order, they are not really the water image

(which is evident by looking at any of the individual letter). So option (d) is the answer. Also

on clearly examining the option (d), a student can clearly see that it is the water image of the

given word

3. Which of the following options resemble the mirror image of ?

Solution: First thing the student should look for is lateral inversion (left becoming right and

right becoming left). So in this case, if one looks only at the inner figure (excluding the arrow)

, one can clearly see that the answer will be from option c or d. Now looking at

arrows in both these options, only option (d) has arrows exhibiting lateral inversion. So option

(d) is the answer.

NeL$0n125

NeL$0n125


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PAPER FOLDING

These questions involve the process of selecting a figure which would closely resemble the pattern

that would form when a transparent sheet carrying designs on either side of a dotted line is folded

along the line. In these questions it is important to divide the figure into two or more parts and then

understand how each of these parts will appear in the folded sheet. In some cases, these questions could

also involve asking student the number of vertices which the paper will have after being folded on a

particular line.

Some examples of these type of questions are as follows:

4. Find out from amongst the four alternatives as to how the pattern would appear when the

transparent sheet is folded at the dotted line.

Solution: Let’s assume that the given transparent sheet has 2 halves – one each on either side

of the dotted line. And also let’s name the key points in the diagram as A, B, C and so on.

Now, the part which is not folded should stay as is in the resultant picture. Thus in this case

part 1 will stay as is in the resultant picture and part two will overlap on part 1. Part 1 staying

as is means there has to be a straight line connecting points A and E in the final answer. Also

on overlapping part 2 on part 1, pt. C will come on top of pt. A and D on top of F. Thus there

has to be a line connecting B and F in the resultant figure.

So the result figure has one line connecting pt. A to E and another one connecting Pt. B to F.

So the answer is option D.

5. Find out from amongst the four alternatives as to how the pattern would appear when the

transparent sheet is folded at the dotted line.

+

Part 1 Part 2

A B

EF

A B C

DEF

B C

DE


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Solution: Let’s assume that the given transparent sheet has 2 halves – one each on either side

of the dotted line and let’s name the key points in the diagram as A, B, C and so on.

Clearly Part 1 should stay as is and Part 2 would overlap on Part 1. In option B, part 1 seems

to have changed. So option B cannot be the answer. Also option A does not seem to have any

overlap of part 2, so option A also does not seem to be the answer.

So the possible answer is from option C or D. Both option C and D seem to be very similar,

except the location of point C and point D on the overlapping portion. An important clue here

is that pt D is currently closer to the dotted line compared to point C. So clearly that should

be the case in the overlapping figure too. So option D is the answer.

These explanations may look very detailed and complicated right now. But as a child

practices these questions, he would be able to carry out most of these calculations in the

mind itself. We are just trying to provide a systematic way for the child to think.

6. The paper sheet given below is folded along the given dotted line(s) in the sequence as mentioned.

First fold is made along the dotted line 1, then along dotted line 2 and so on. How many edges

would the resultant paper sheet, after the folds, have?

a) 5 b) 6 c) 7 d) 8

Transparent Sheet Response Figures

A B C D

A

B

C

D

E

F

Part 1 Part 2


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Answer: Option c. In these type of questions, a common mistake is to miss or double count a

particular side or corner. The best way to avoid this mistake is to keep marking the side/corner

which has been counted. Also remember that number of sides will always be equal to the number

of corners.

PAPER CUTTING

In these type of questions, we study the problem relating to the analysis of a pattern that is formed

when a folded piece of paper have been cut in a definite design.

In these type of questions, a set of three figures showing a manner in which the piece of paper has

been folded, is given. In each of the first two figures, a dotted line together with an arrow on it has

been given. The dotted line is the reference line along which the paper has to be folded and the

arrow indicates the direction of the fold. Thus, these two figures indicate the sequence in which

the paper is folded. In this third figure, there are marks showing the position and the nature of the

cut made in the folded sheet. The student has to select one of the figures from the set of four

alternative figures which would most closely resemble the pattern when the paper is unfolded.

It is important to note that the cut made would reflect on all the folds.

7. Consider the following figure marked X, Y and Z, showing one fold in X, another one in Y and a

cut in Z. From amongst the options, A, B, C and D, select the option that most closely resembles

the unfolded position after cut in step Z.

Solution: Clearly the cut would show on all the four triangles in which the paper is folded. So

the option is option C or D. In all these questions, it is important to note the relative

positioning of objects / figures. In this case, if you note the difference between option C and

D is the positioning of the smaller squares (on left and right side) relatively to the larger square.

As shown in figure Z, the sides of both smaller bigger squares are parallel which will be the

case for all the four squares. So the option in this case is option C.


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8. Consider the following figure marked X and Y, showing one fold in X and a cut along the red

highlighted portion as shown in figure Y. From amongst the options, A, B, C and D, select the

option that most closely resembles the unfolded position after cut in step Y.

Answer: Option D.

CUBES AND DICE

There are various kinds of questions which can be formed in this category. Most of them relate to

spatial positioning of various objects and a student’s ability to understand spatial positioning of

objects.

Counting the number of cubes / blocks in the given figure In this type of questions, the student is presented with a 3-D diagram of cubes or blocks and is

required to count the number of cubes in the overall diagram. The best way to solve a question like

this is to divide the diagram into various columns and count the number of cubes in each

column.

9. Count the number of blocks in the figure given below:

Solution: The above figure can be divided into 4 columns. 1 column has 2 blocks while 3

remaining columns have 1 block each. So the answer is (3X1) + (1X2) = 5


Parallel sides


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Solution: The above figure can be divided into 6 columns. 1 column has 3 blocks, while 2 have

2 blocks each and the remaining 3 columns have 1 block each. So the answer is (3X1) + (2X2)

+ (1X3) = 10.

Couple of more complicated ones are as follows:


Solution: The above figure can be divided into 22 columns. 9 columns have 5 blocks each,

while 7 have 4 blocks each, 5 have 3 blocks each and the remaining 1 column has 1 block. So

the answer is (9X5) + (7X4) + (5X3) + (1X1) = 89.


Solution: The above figure can be divided into 25 columns. 21 columns have 2 blocks each,

while 4 have 1 block each. So the answer is (21X2) + (4X1) = 46.


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Colouring a stack of cubes

In these questions, one or more side of a cube / stack of cubes is painted and student is asked a questions

based on that. The best way to solve such questions is to pick each of the face of the cube and solve

for them one after the other.

13. A cube whose two adjacent faces are coloured is cut into 64 identical small cubes. How many of

these small cubes does not have even a single face coloured?

Solution: As shown in the adjacent diagram, let’s assume that the

upper and right hand side face of the cube are coloured. (Please note

you can take any two adjacent faces of the cube to be coloured

and it won’t really make a difference). And on the front face let’s

show the 16 cubes which will be forming there (64 cubes will be

obtained on dividing each side into 4 parts. Thus dividing the length

and breadth of the cube into 4, the front face will end up becoming a

face for a total of 16 cubes).

The given cube can now be considered similar to the earlier

problem of counting the number of cubes. One can consider the

given cube as comprising 16 columns with each column having 4 cubes.

Now one can see that the smaller cubes which have faces shown with dots, will not have any

face coloured. And each of these 9 colulmns having a dot willl have four cubes each. So the

total number of cubes without any coloured face is (9X4)=36.

14. A cube is painted green on all the four adjacent surfaces and red on two opposite sides i.e. top and

bottom and is cut into 27 smaller cubes. Please find out the number of cubes which have

1) No face painted

2) One face red and exactly one face green

3) One face red and 2 face green

4) Two adjacent faces green and no red face

5) Only one face painted in red

6) Only one face painted green


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Solution: As shown in the diagram below, let’s divide the cube into smaller cuboids having

only one column depth. So the three cuboids /panels will look as follows:

In the above panels, all four sides are coloured green, and the bottom side of the “Bottom Panel

is coloured red”.

Using the above picture it is very easy to answer all the questions:

No face painted – only one which is the centre cube in the “Middle Panel”

One face red and exactly one face green – four on the top face (highlighted by dot in the

below diagram) and similar four on the bottom face. So total 8.

One face red & 2 face green – four corner cubes on both top and bottom face. So total 8

Two adjacent faces green and no red face – the four corner faces in the middle cube. So

total 4.

Only one face painted in red – The centre cube in top and bottom panel. So total 2.

Only one face painted green – 4 cubes highlighted by dots in the centre panel. So total 4.

Constructing Cubes

RED Colour

Top Panel Middle Panel Bottom Panel

Middle Panel

Top / Bottom Panel

Middle Panel


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In these types of questions, the child is given a sheet of paper cut in a specific shape / design and he is

asked to identify the cube of cuboid that will be formed by folding such a sheet. Conversely the student

may also be asked to identify the type of figure that will be formed when a particular cube or cuboid

is unfolded. An unfolded cube or cuboid may take various shapes in 2D form. Some of these shapes

are as given below. In these type of questions, the relative position of various faces is important to

understand and that will help a child find the answer.

15. Choose the box that is similar to the box formed from the given sheet of paper (X)?

Answer: Both 1 and 4


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CONSTRUCTION OF SQUARES AND TRIANGLES

These questions deal with the problems of construction of squares by combination of three parts after

selecting them from the list of five different alternatives numbered from A to E. To solve these

problems, select a piece which contains a right angle between two adjacent outer edges. Then try

to fit another piece in its hollow spaces. If you can't, select another piece. Repeat the procedure

with different sets of such pieces. Finally with the two pieces fitting into each other, find the third

piece which fits into the other two selected ones, to get a completed square.

16. Given below are five alternative figures marked A, B, C, D or E followed by four options marked

(a), (b), (c) and (d). Select the answer that depicts three of the alternative figures which when fitted

together will form a complete square.

Solutions: Given that we have to form a square, the first thing to be done is to find a figure

which has a right angle in it. The only figure with a right angle is C. And figure B and D fit

into it as shown below to form a complete square.

So the answer is option (c)

17. Given below are five alternative figures marked A, B, C, D or E followed by four alternative

answers marked (a), (b), (c) and (d). Select the answer that depicts three of the alternative figures

which when fitted together will form a complete square.


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Solutions: Answer is (c), as shown below:

VISUAL RECOGNITION

This sub-topic assesses and enhances a child’s ability to spot things in a given image / figure. There

could be various types of questions in this. Some of which are given below:

COUNTING THE NUMBER OF GEOMETRICAL FIGURES

In this type of question, the student is presented a picture and he is required to calculate the number of

a particular type of geometrical figure (eg. Circle, rectangle, etc) which can be formed in that picture.

The most common mistake which people do in such problems is that they may miss one or two

such geometric figures or double count some of them. It’s very important to proceed in a

systematic way to be able to solve this problem correctly. A very good way to solve this problem

is to name every important point in the diagram (typically one of the vertices or an intersection

point of lines) as A, B, C and so on, and then write down the vertices which make a geometrical

figure. This way you can always avoid double counting. In some lower grade questions, this may

not be required. Let’s take some examples:

18. Count the number of triangle in the figure given below?


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Solution: As explained earlier, let’s put a name to each of the vertices / important points in

the above diagram. As a result it will look as follows:

Now let’s write down the various triangles which can be formed in this figure. We will go in

a systematic way, starting from the smallest one and heading to the largest one.

Smallest triangles: ABC, ACD, ADE

Medium sized triangles / Triangle which include a triangle in itself: ABD and ACE

Largest Triangle: ABE

So in all 6 triangles are there in the above figure.

19. Count the number of squares in the figure given below?

Answer: As discussed earlier, let’s name the important points as shown in the diagram below

and then proceed in a systematic manner. To begin with let us start with the smallest square.

A

B C D E

A B C D

E F G H

I J K L

M N O P


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Smallest squares – these are 9 in number: AEFB, FBCG, CGHD, IEFJ, FJKG, KGHL,

MIJN, JNOK, OKLP

Squares of 2x2 block – these are 4 in number: AIKC, BJLD, EMOG, FNPH

Square of 3x3 block – only one – AMPD

Thus there are a total of 14 squares.

There is also a short trick to find the number of squares or triangles in such a

symmetrical figure.

Check the dimensions of the symmetrical in terms of number of blocks – in this case

it is 3x3. So the number of squares in this figure would be 12 + 22 + 32 = 1 + 4 + 9

While the number of rectangles would be 13 + 23 + 33 = 1 + 8 + 27 = 36; you can

check this out for yourself.

Similarly in a 4x4 square, number of squares would be 12 + 22 + 32 + 42 = 1 + 4 + 9

+ 16 = 30 and number of rectangles would be 13 + 23 + 33 + 43 = 1 + 8 + 27 + 64 =

100

This way a student can also find the number of squares / rectangles on a chess

board i.e. 8x8 dimension.

As an interesting exercise, a student should try and think why this shortcut always

works. Try and derive this relationship.

20. Count the number of triangle in the figure given below?

Solution: As explained earlier, let’s put a name to each of the vertices / important points in

the above diagram. As a result it will look as follows:

Now let’s list down the various triangles:

A

C

DE F G

M

H

B

J K

L

I


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Three big triangles: ACH, BDF, MEG

Smaller triangle at the intersection: BCJ, IEF, LKH, JKI

So 7 triangles in total.

SPOTTING THE EMBEDDED FIGURE

In these questions, the question provides a figure which is embedded in one of the four answer

figures which the student is required to spot. There is no specific approach to do this, but to just

observe the given pictures closely

21. In each of the following questions, figure (x) is embedded in any one of the four alternative figures

(a), (b), (c) or (d). Find the alternative which contains figure (x) embedded in it.

Answer: (a)

22. In each of the following questions, figure (x) is embedded in any one of the four alternative figures

(a), (b), (c) or (d). Find the alternative which contains figure (x) embedded in it.

Answer: (c)

COMPLETION OF INCOMPLETE PATTERN

In these type of problems, a figure or a matrix containing a set of figures following a particular

sequence or pattern is given, in which a part, generally a quarter is left blank. This problem figure is

followed by four alternative figures. The student is required to choose the one which best fits into the

blank space of problem figure so as to complete the original pattern. The given figures typically

follow a symmetrical sequence and understanding the symmetry is key to solve such problems.

Typically the left out figure is a replica (just turned around a bit) of an existing quadrant.

In this case also, a student can look at some of the objects and their relative position to determine

which of the options is the answer.

23. Select a figure from the four alternatives, which when placed in the blank space of fig (x) would

complete the pattern.


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Answer: Option (a). In this case one important thing to look at is that the missing piece should

complete the circle in the image in the question. That means it should have an arc bent upwards.

Clearly this is only possible in option (a). So option (a) is the answer.

24. Select a figure from the four alternatives, which when placed in the blank space of fig (x) would

complete the pattern.

Answer: Option (d). In this case, there are 2-3 key things to look at 1) the image should complete

the circle – possible in all the four options. 2) the image inside the circle should complete the star

– and thus have sharp corners. Only option d has an image which has sharp corners for the image

inside the circle. So clearly option (d) is the answer.

DOT PLACEMENT

The problems on Dot Placement involve a cluster of three of more geometrical figures – usually

triangle, circle and rectangles, having one or more dots placed at any point inside the cluster. The

cluster is followed by a set of four alternative figures each composed of a cluster of same type of

figures. Now for each dot, the student has to observe the region in which it is enclosed, i.e. to which

of the geometrical figures this region is common. Then the student should look for such a region in the

four alternatives. Once the student has found it for one dot, he/she should repeat the procedure for

other dots too. Some examples are given below to explain the structure.

In these type of questions, the student should focus on one dot at a time and it is important to

make sure the exact figures which are overlapping in the region and look for the same

combination in the answer figures. If done systematically these questions are not difficult to

solve.

25. From amongst the figures marked (1), (2), (3) and (4), select the figure which satisfies the same

conditions of placement of the dot as in figure (x).


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Solution: Let’s look at each dot one after the other given in the figure (x). Let’s look at dot 1 in

the circle. This dot is coming on the overlap of a circle and a triangle. Now look at the four

options and try to find out which options have a region where only circle and a triangle overlap.

All four figures 1, 2, 3 and 4 have a region where a circle and a triangle overlap. So the answer

can be anyone of the four. These regions are highlighted by the red circle in the following

diagram:

Now let’s look at the second dot. The second dot appears on a region which is an overlap of a

triangle and a square. Now let’s look at option 1, 2, 3 and 4 and see which of these have a region

which has the overlap of only a square and a triangle. Clearly it looks like only option 1 has a

region which is an overlap of only a triangle and a square (highlighted in green in the following

figure). So option 1 is the answer.



Answer: Option (3)


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Answer: Option (4)


Topic Note: Visual Ability

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