Thinking with visuals
Lesson Objective
Earlier, in the previous lesson you tried problems with numbers. In this lesson you will learn how to solve various visual and thinking questions with logical analysis and thinking. This topic deals with the graphical representation of a problem and solving them based on representation. This is a self-paced class.
Why is solving visual and thinking questions important?
The way you will use to solve such questions will enhance your creative thinking and will also increase your level of commitment to approach any problem fearlessly. Also it helps in visualization along with objects and image recognition.
About the lesson
Here, basically we will be dealing with various types of visual, logical and reasoning problems, which will ask you to think deeper and make this lesson very exciting and interesting. Happy learning!!
Are you looking for some hints?
Then here it is…
Now, hurry up to solve 🔥
1. Picture equations:
What are they?
These are the equations consisting of images of different objects as variables and you have to figure out how much value that particular image object holds or equates to.
How do we think and approach such questions?
At the first glance, it seems to be a mathematical problem, which is asking you to solve some equations. Now, you all might have studied how to solve multivariable equations during your school days, try to follow the same thinking pattern.
Example 1: Find the missing part.
- 3R
- 2R
- R
- 4R
How to approach
If you thought of replacing the colored boxes with appropriate variables then you are on the right path! Just assign a unique English character to the same type of object. In example 1, we are taking the blue box as ‘B’, the red box as ‘R’ and the green box as ‘G’.
- You can choose any variable name as per your choice but a great tip is using appropriate variables as this will help you develop the same practice when developing programs in the future. Write down the equations you have obtained by replacing the colored boxes with alphabets and proceed to solve them in the same manner you always have done algebra.
- After you get the values for all variables, substitute those values into the object image to which that variable is pointing.
Find the missing part
- 3R
- 2R
- R
- 4R
Check the Solution!
Detailed solution:
B = 2R — (1)
G - B = R
G = R + B
G = R + 2R (from (1))
→ G = 3R
Follow up
Now try to solve the remaining examples on your own. We hope you understand the concept involved in solving such problems. It is an essential skill in solving a coding problem.
Follow up Questions
Problem statement 1: Find the missing value
- 141
- 143
- 146
- 149
Check the Solution!
Ans: C(146)
Detailed solution:
3A = 42 => A = 14
2B + A x A = 208
2B = 208 - 196
2B = 12
B = 6
C x C + 2B = 112
C x C = 100
C = 10
B + A x C = 146
Problem statement 2: Find the missing value
- 10
- 12
- 14
- 16
Check the Solution!
Ans: C(14)
Detailed Solution:
3A = 30 => A = 10
A + 2B = 18
2B = 8 => B = 4
B - 2C = 2 => C = 1
C + A + B = 14
Problem statement 3: Find the missing value
- 54
- 52
- 51
- 38
Check the Solution!
Ans: C(51)
Detailed Solution:
3A = 45 => A = 15
2B + A = 23 => B = 4
B + 2C = 10 => C = 3
C + B + B x D = 2 + 3 + 3 x 11 = 51
We suggest you explore further and try solving the vast variety of similar problems available on the internet. Let’s move further and on to the next topic.
2. Inductive Reasoning:
What is it?
Here you will get 2 images and you have to visualise the common trend they are following. After viewing the images and analysing some trends between them, you have to choose from the options which among the 4 given images follow the same analogy or same trend.
Where to start and how do we deal with such problems:
At the first glance, it looks like an intuitive problem. You have to scan both the images on the left side and try to visualise the similarity between them. They may or may not have all the same elements in a row, column or diagonal etc. So, there are various possible similarities between them but try to find a more intuitive and generalised similarity between the images.
Example 1:
How to approach:
There are often multiple ways of approaching a problem. Here, you can see two such approaches given below. Feel free to come up with alternative approaches and see if you reach the same conclusion.
- By taking the reference of objects in the figure.
- By looking at various objects at different columns and rows.
(The above two methods guarantee the correct result)
- Check for the same type of elements and their positions in both the figures. Try to figure out if this can help you get a generalised pattern between the two images.
- Try to pay attention to the type of objects that are present in the same column,row or diagonal in both the figures. Are they following any noticeable patterns?
Now, in the first example, by following strategy 2, we will get the answer as you can see there are similar types of objects on the main diagonal in both the figures. So, kudos you got it right.
This is the best strategy to use when encountered with solving implementation base brute force questions.
Follow up:
Now try to solve the remaining examples on your own. Learning by doing is the most effective way to grasp and retain such concepts. These are the kind of aptitude questions you may face in your placement and internship interviews.
Follow up Questions:
Question 1:
Check the Hint!
Hint: Observe that images on LHS both have their first two columns as a constant shape and colour.
Question 2:
Check the Hint!
When you observe the LHS, you can find that the 2nd and 3rd row are the same.
Question 3:
Check the Hint!
When you observe the LHS, you can notice that the last 2 rows have their extreme ends to be the same.
3. Paper cutting:
What is it?
These are various step by step images that show a paper is folded and cut to achieve the final pattern shown in the last image. Now, your task is to figure out what the unfolded paper would look like from the 4 options.
Where to start and how do we deal with such problems
At the first glance it appears to be a pattern based problem. This problem will teach you how a question that appears complex can be solved by making some very detailed and minute observations . Among all the given options you will see a square which represents the unfolded paper after it has been folded and cut. Try to visualise its folding and analyse which of the four options represent the final pattern.
Example 1:
How to approach:
The best way to solve this question is to take in consideration the rightmost half of a square for each of the options one by one. Observe that if you cut the square vertically in the middle and then cut the right half of the square horizontally in the middle once again, does it look exactly like the last step shown in the question? If so, then there you have your correct answer! But be careful, you have to visualize each fold and cut being made, sometimes more than one option way look right.
Solution:
Let’s see example 1 now. First visualize the right half of the paper after cutting and visualise that you have cut it horizontally. Now, the third figure will give you the most the same image as shown in the last step of the question. So yes, that is the correct answer.
(This problem will enhance the level of your visualisation as it is in an important skill to master while coding complex questions).
Now try to solve the remaining examples on your own.
Follow up
Question 1: Choose a figure which would most closely resemble the unfolded form of figure.
Check the Hint!
The paper is folded twice, so the small square will appear on all the 4 quadrants of the circle.
Check the Solution!
The answer is option 1.
Question 2: Choose a figure which would most closely resemble the unfolded form of figure.
Check the Hint!
The bottom right corner circle will remain the same, top left circle will be unfolded to form 3 more circles
Check the Solution!
The answer is option 3.
Question 3: Choose a figure which would most closely resemble the unfolded form of figure.
Check the Hint!
Those 2 small circles will appear on all the corners.
Check the Solution!
The answer is option 4.
And if you think we are done with Visuals, here is what we wanted to say.
