aptitude – Programmerbay https://programmerbay.com A Tech Bay for Tech Savvy Thu, 14 Mar 2024 16:44:01 +0000 en-US hourly 1 https://wordpress.org/?v=6.5.5 https://programmerbay.com/wp-content/uploads/2019/09/cropped-without-transparent-32x32.jpg aptitude – Programmerbay https://programmerbay.com 32 32 Counting Figures Tricks with Triangle Examples https://programmerbay.com/counting-figures-problem-tricks/ https://programmerbay.com/counting-figures-problem-tricks/#respond Tue, 12 Mar 2024 06:09:49 +0000 https://www.programmerbay.com/?p=4385 Counting figures problems come under non-verbal reasoning in which one is required to identify the exact count of a shape formed within a design or picture like a circle, square, triangle and more. Such type of logical reasoning questions are frequently asked in different aptitude exams.

Counting figures sometimes sound too difficult if you don’t have an idea of how to solve them. In this article, we will be talking about tricks for counting figures problem.

counting figures

These are most repeatedly asked reasoning questions. In this, a shape or a figure would be given to you and your task is to determine the shape and count it down within that particular shape.
For example, consider the below figure:

countinng figure 4

They simply ask in the question, how many triangles are visible in the given figure? Initially, it might look easy but it is obviously not! Without knowing tricks you can’t easily figure out correct answer.

 

Types of questions with Triangle Counting Problem Examples

  • When a triangle  is divided  by  vertical lines

    • In such a case, we use can n (n+1)/2 where n is the number of triangles inside the main triangle

Q.  Find the number of triangles in the diagram

counting figures 1

Number of  triangles  inside the  main triangle   =   4

4(4+1)/2

= 20/2    =    10

 

  •  When a  triangle divided  by the horizontal lines

    • In such a case, count the number of horizontal lines that would give you the total number of triangles

Q.  Find the number  of figures  in the diagram

counting figure 2

Total number of horizontal lines = 3

So total possible triangles are 3

 

  • When a triangle has both vertical and horizontal lines

    • n(n+2)/2 (for vertical lines ) * number of horizontal lines

Q.  Find the number  of triangles in the diagram

counting figures 3

Number of triangles from vertical lines (ignoring horizontal lines) = 3 = 3(3+1)/2 = 6

Horizontal lines  = 3

= 6* 3

= 18

 

  • When a triangle has an inner triangle touching all of the edges of the outer one

    • In such a case, there always 4 figures are made and add 1 for the main triangle

Q.  Find the number  of triangles in the diagram

countinng figure 4

Starting from inner combination there are  = 4 triangle

count me

outer combination there are  = 4 triangle

count me 1

And for main  = 1

total = 9 triangles

 

  • When a triangle has a triangle touching all of the edges of outer one and also has lines from each vertex of the main triangle touching edges of the inner one

    • In this first, ignore all the lines coming from corners of the triangle
    • Now the triangle you see would  be similar to the previous case triangle ( touching all the edges of outer triangle)
    • Count the number of triangles
    • After that consider lines coming from edges, each line would make 2 triangles
    • Now add them all together

counting figure 5

Step 1.  If we ignore the lines coming from edges, the figure would look like

countinng figure 4

Step 2.  From the inner triangle, we will get 4, from outer one = 4, Main triangle = 1

Step 3. Total triangles = 9

Step 4. Now add lines which were removed previously, if each line creates 2 triangles then 3 lines would create = 3*2 =6 triangle

Step 5. Add them all. 9 + 6 = 15 triangles

 

  •  When a triangle has multiple triangles made on horizontal lines 

    • If you look closely from every edge there would equal number of triangles
    • Count triangles from the base
    • Add them in a consecutive manner where the result of the previous one would be used as input for the next one. i.e 1 , 1 +2 = 3, 3+3=6, 4+6 =10′. Add all the sums together.
    • Now after adding them all up, also consider second last sum again
    • Also add it

counting figure 6

Number triangles in each base = 3

Make a counting from 1 to 3

count me 3

Add them up = 1 + 3 + 6 = 10

Now also consider second last item = 3

Total triangle 10 + 3 = 13

 

Counting Figures Practice Questions

 

1. How many triangles are there in the given figure?

Screenshot from 2024 03 14 22 03 30

2. How many triangles are there in the given figure?

Screenshot from 2024 03 14 22 04 34

3.  Find the number of triangles in the given figure :

Screenshot from 2024 03 14 22 08 35

Frequently Asked Questions:

What is the Figure Counting Reasoning?

It comes under non verbal reasoning section where one requires to identify and count the exact number of shapes present in the given figure or design.

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Distance And Direction Reasoning Tricks with Example https://programmerbay.com/direction-problem-tricks/ https://programmerbay.com/direction-problem-tricks/#respond Sat, 15 Jul 2023 18:01:58 +0000 https://www.programmerbay.com/?p=4352 We will be discussing in this article about Direction sense. Questions of these types are easier than any other topics. In order to solve questions that come from the Direction Reasoning section, we have to first understand directions. These types of problems are more frequently asked questions in placements, job interviews and exams.

Distance and Direction Problem Basic Concept

Direction Reasoning tricks 1

  •  Direction problems revolve around two terms, Distance & Direction
  • There are 4 main directions: North, South, East, West
  • There are four cardinal directions: North-East, North-West, South-East, and South-West
  • The angle between major directions would be 90 degrees and between a major & a cardinal direction would be 90 degrees
  •  Making a left turn, would lead to a clockwise movement
  •  Making a right turn would lead to Anti-clockwise movement or turn
  •  In case of sunrise, if a person is facing east, then his should be toward the west
  • In the case of sunset, a person’s shadow would always be formed toward the east
  •  At noon, the sun positions vertically, therefore no shadow would be formed.

Screenshot from 2023 07 19 23 05 33

 

Screenshot from 2023 07 19 23 24 45

Here’s the direction reasoning trick, the below figure is used in almost every question of direction problem.

These are the 3 Types of Questions in Direction Reasoning

  •  Identify the direction of a walking person

Question. A man walks 5 km toward the south and then turns to the right. After walking 3 km he turns to the left and walks 5 km. Now in which direction is he from the starting place?

image 2020 12 06 131556

Answer: South -West

 

  • Identify the direction based on sunset or sunrise

    • Should Understand the concept of Shadow Direction reasoning to solve the related questions
      • In the case of sunrise, If a person is facing towards the east then his shadow would be formed to the west. In case of sunset, If a person is facing towards west then his shadow would be formed to the east.
      • In the case of sunrise, If a person is facing towards the north then his shadow would be formed to his left. In the case of sunset, If a person is facing towards north then his shadow would be formed to his right.
      • At noon, no shadow would be formed

Question. One evening before sunset Rekha and Hema were talking to each other face to face. If Hema’s shadow was exactly to the right of Hema, which direction was Rekha facing?

direction problem 2

Answer: South

 

Question. Reena starts walking early in the morning in the opposite direction to the sun. She then turns left and walks for 1 km and again takes a left turn. In which direction is she now?

1) West
2) North
3) East
4) South

Answer :

3) East

Screenshot from 2023 07 22 14 23 19

  • Find the nearest Distance

    • Should Understand the concept of Distance and Direction reasoning to solve the related questions
      • First, make lines as per directions in the question
      • You would end up with a right angle triangle
      • Apply Pythagoras theorem, (Hypotenuse)2 = (Base)2 + (Perpendicular)2

direction is here

Question. Suresh starting from his house goes 4 km in the East, then he turns to his right and goes 3 km. What minimum distance will be covered by him to come back to his house?

direction problem 3

(Hypotenuse)2 = (Base)2 + (Perpendicular)2

(Hypotenuse)2 = (3km)2 + (4km)2

(Hypotenuse)2 = 9km2 + 16km2

(Hypotenuse)2 = 25km2

Answer:  Hypotenuse = 5 km

  • A Direction Becomes equivalent or alias of Another Direction

In this type of question, a direction will become a new direction, based on that we need to find, what would be other directions become?

    • In this first, identify the relation between a given direction and its alias direction
    • The identification can be based on clockwise, degree, movement parameters
    • After identifying, use the same relation on the asked direction to get its alias

If North-East becomes North, then what will East become?
1) South-East
2) North-East
3) South-West
4) North-West

 

Screenshot from 2023 07 20 22 16 42

The answer will be North East

 Explanation:

1) The North-East becomes North. Considering the above picture, the movement is clockwise and shifts 45 degrees to become North direction.
2) Applying the same, East will become North East if we shift 45 degree and move further, clockwise.

  • Find Direction based on given degrees and turns

In this type of questions, degrees and the movement of a person are given. Based on that we need to find his final direction. The only thing one needs to consider, degree and facing position.

Question. A man is facing west and turns 45 degrees in the clockwise direction. He then turns another 180 degrees in the same direction and then 270 degree in anti clockwise direction. Which direction is he facing now?

  1. Man walks towards west
  2. He moves clockwise 45 degrees. Now he is facing towards North-West
  3. Again, he moves 180 degrees clockwise, that makes him positioned towards South-East
  4. Finally, he moves 270 degree anti clockwise, that makes him facing toward South-West

Answer is South-West

Screenshot from 2023 07 22 14 39 26

 

 

Below are some Mock Questions related to above example

1. A person walks 8 km, then he turned right & covered a distance of 3 km. After that, he turned left and covered a distance of 12 km. In the end, he was moving towards the north. From which direction, he started his journey?

1) North
2) East
3) South
4) West

2. If B is to north of A and C is to the east of B, in which direction is A with respect to C?

1) North-East
2) South-East
3) North-west
4) South-West

Answers:
1. South
2. South-west

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Calendar Problems Tricks And Shortcuts With Examples https://programmerbay.com/calendar-problems-tricks-and-shortcuts-with-examples/ https://programmerbay.com/calendar-problems-tricks-and-shortcuts-with-examples/#respond Tue, 11 Jul 2023 11:30:50 +0000 https://www.programmerbay.com/?p=4230 In this article, we will be aiming at various calendar problem’s tricks and concepts which is going to save your time while solving these types of questions.

Calendar Problem Concepts

First, let’s brush up basic concepts to which we already familiar with:

  • 1 week = 7 days
  • 1 year = 365 days or 366 days

A normal year has 365 days, consisting of 52 weeks and one extra day. On the other hand, a leap year has 366 days, consisting of 52 weeks and two extra days. A leap year always repeat after 4 years.

  • Normal year = 365 days = 52 weeks and 2 extra days
  • Leap year = 366 days = 52 weeks and 1 extra day (one extra days Occurs in the February Month = 29 days)

To check Whether a year is a leap year or not?

A year that consists of 366 days is known as a leap year. It is easy to know which year is a leap year. Let’s have a look:-

  1. If the given year is divisible by 4 and not divisible by 100 then it is a leap year. If the given year is divisible by 100 then we need to follow the second step to check whether it is a leap year or not.
    • For example, 2016 is a leap year, since it is divisible by 4 but not 100. however, for the year 2000, we find that it divisible by 4 but also by 100 too, in such cases we can’t say it is a leap year or not, for this we have to follow 2nd step.
  2. If the given year is divisible by 100, then it should also be divisible by 400 in order to be qualified as a leap year.
    • Since 2000 is also divisible by 400, it is a leap year.

Now lets come to the Calendar tricks you should know:

Week codes

CenturyCode
16006
17004
18002
19000
20006
21004
22002
23000

Month codes

  • For Normal years
MonthCode
January0
February3
March3
March6
May1
June 4
July 6
August 2
September 5
October 0
November 3
December5
  • For Leap years
MonthCode
January6
February2
March3
March6
May1
June 4
July 6
August 2
September 5
October 0
November 3
December5

Century codes

CenturyCode
16006
17004
18002
19000
20006
21004
22002
23000

Types Questions Asked from Calendar Problem

  • Directly Asking what day will be on a particular date

Case 1: For Normal or ordinary Year

These are the steps to solve:
1) Pick up last two digits from the given year
2) Divide it by 4 and take its quotient
3) Use date that is already given in the question
4) Use month code of the given month specified in the question
5) Use century code
6) Add altogether from 1 to all the way 5th step
7) Divide the sum by 7 and find its remainder
8) A reminder would represent the week code
Q. What was the day of the week on 11th, July 2019?
So,
The date is 11th, July 2019
Step 1. Take the last two digits from the given the year 2019 = 19
Step 2. Divide it by 4:
19 / 4 = Quotient = 11, Remainder 3
Step 3. Given date = 11
Step 4. Given Month = July and its month code is = 6
Step 5. Century Code 2000’s is = 6
Step 6. Total sum = 19+11+11+6+6 =53
Step 7. Divide it by 7
53/7 = Quotient = 7, Remainder = 4
Step 8. Week code 4 represents Thursday
So, Thursday is the answer.

Case 2: For Leap Year

1) Follow all 7 Steps as mentioned in an ordinary year and must follow week table of Leap year mentioned above.
Q. What was the day of the week on 26th, January 2016?
So,
The date is 26th, January 2016
Step 1. Take the last two digits from the given the year 2016 = 16
Step 2. Divide it by 4:
16 / 4 = Quotient = 4, Remainder 0
Step 3. Given date = 26
Step 4. Given Month = January and its month code is = 6
Step 5. Century Code for 2000’s is = 6
Step 6. Total sum = 16+4+26+6 +6=58
Step 7. Divide it by 7
58/7 = Quotient = 8, Remainder = 2
Step 8. Week code 1 represents Tuesday
So, Tuesday is the answer.
  • Directly Asking which day will be after the given number of days from the mentioned day

Step to solve it:

Step 1. Divide the given number of days by 7 and find the remainder

Step 2. Add the given remainder to corresponding week code, and the resultant code will be our answer

 

Q. If today is Thursday then after 15 days, the day will be?

Step 1. 15/7 = Quotient 2, Remainder 1

Step 2. Thursday = 4, 4+1 = 5 , refers to Friday

  • Can ask which would be the very first mentioned day in a given month of a year

Need to perform a basic addition operation

 

Q. When will be the first Friday fall in the month of July 2019?

On 1st July 2019, the day will be Monday by using the method mentioned in the above example. On 5th July will be first Friday

  • In this, date along with day will be given and using that day as a base, you need to figure out what will be the day for the asked date

    Just find an extra or odd day in between the years and add extra days only if February of that month covers. In a leap year, there are 2 extra days and in Normal year there is only one odd day

 

Q If 26th May 2018 falls Saturday then What day will be on 26th May 2019

Between this, Only a single February falls which is in the year 2019. So we add only odd days of 2019, skipping 2018

Day on 26th May 2018 = Saturday = 6

Odd days in the year 2019 is = 1

6+1= 7

So, 26th May 2019 falls on Sunday.

Below are some practise question for Calendar Problem:

Question. What would be the day on 25th January 1950?
Answer Wednesday

Question. If the day on 4th October 2018 was Thursday, then what will be the day on 2nd February 2019?
Answer Saturday

Question. What will be the day on 20th May 2030?

Answer Monday

Question. When will be the first Sunday fall in the month of July 2024?

Answer 6th July 2024

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Dice Problems Tricks And Shortcuts With Examples https://programmerbay.com/dice-problems-tricks-and-shortcuts-with-examples/ https://programmerbay.com/dice-problems-tricks-and-shortcuts-with-examples/#respond Thu, 10 Sep 2020 07:17:26 +0000 https://programmerbay.com/?p=5057 Basic Concepts to Solve Dice Problems

You should keep in mind that a cube has 6 faces. Each face has 4 adjacent faces and 1 opposite face. If you want to solve cube based problems, it’s good to advise that you should learn something about the cube and its faces.

Tricks:

If you are not able to think about the 3D cube, you can just open up the cube and create a 2D image and write down the given data on that image.

Example: Two positions of a cubical block are shown. When 5 is at the top which number will be at bottom?

dice1

Solution: We first notice the common face i.e. 3.
Then we will write down the adjacent faces, that are, 1,4,2,6.
Since we require the face opposite to 5, there is only 1 face which is not adjacent to 3, i.e. 5.
So the face opposite to 5, at the bottom, is 3.

Example: From the four positions of a dice given below, find the color which is opposite to yellow?

dice2

Solution: Since, we need to find the face opposite to yellow, we need to only find 4 adjacent faces, and the non-adjacent one is opposite to yellow.
From cube 1, orange and blue is adjacent to yellow.
From cube 3, red and blue is adjacent to yellow.
From cube 4, rose and red is adjacent to yellow.
From above 3, we can conclude that, orange, blue, red and rose are adjacent faces.
Hence, Violet is opposite to yellow.

Example: You are given three positions of dice then which face is opposite to the face with alphabet B?

dice3

Solution: Sometimes, these questions will get tricky to solve. So we will make a 2D image for this and solve accordingly.
From first 2 cubes, we can see that common face is F.
So put F at center.
From cube 1, if D is at right face then A is placed below.
From cube 2, if E is at upper face then C is at left face.
Fill the remaining block with B which is left.

dice4

You can see that F and B are non-adjacent, hence opposite to each other.

Example: In above dice example, what are the pair of opposite faces?
Solution: Creating a 2D image by solving given example.

dice5

We know that, each face has 4 adjacent faces and 1 non-adjacent face which is opposite to it.
Similar thing is applied for 2D image.
Hence, we can conclude that opposite pair of faces are: C-D, E-A and F-B.

Example: Here 4 positions of a dice are shown. Which sign will be opposite to “ * “ ?

dice6

Solution: We will start from finding the 4 adjacent faces of *
From cube 3 and 4, we find #, @ as adjacent faces
In cube 1, we can see that ^ is adjacent to both # and @.
Also, 2 adjacent sides together can be adjacent to 2 more faces only if they are opposite to each other.
Hence, ^ is opposite to *

This article is contributed by Shushank Mittal.

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Missing Number Series Tricks With Examples https://programmerbay.com/missing-term-in-series/ https://programmerbay.com/missing-term-in-series/#respond Thu, 10 Sep 2020 07:17:24 +0000 https://programmerbay.com/?p=5056 Concept:

Generally, you are given a series having some numbers and a missing number.

Finding that number is sometimes easy if the series contains the multiples of the same number or based on simple addition or subtraction, but sometimes there is a pattern you need to find out to identify the missing number.

Missing Number Series Tricks:

To find out the missing number, you need to identify the pattern between the given series.

Check that the series is only increasing/ decreasing or both. Then check the difference between 2 numbers, all these will help you to find the pattern.

If you can’t see any pattern, there are few common patterns that are widely used in these type of questions like:

Common Number Series Patterns

Perfect Squares: 196, 225, 256, 289, 324
Perfect Cubes: 343, 512, 729, 1000
Geometric Series: 7, 21, 63, 189
Arithmetic Series: 17, 21, 25, 29, 33
Increasing Difference: 2, 5, 9, 14, 20

Types of Missing Number Problems and Tricks

Equation-Based Problem

Example: 10, 22, 46, 94, 190, ?

Solution: You can see that the numbers are always increasing, hence there will be a case of addition or multiplication. We also notice that next number is somewhat greater than twice the previous number.
Hence the pattern can be: 2x + 2 for the next number

Increasing alternate difference

Example: 3, 4, 8, 10, 13, 16, 18, ?

Solution: You can see that the numbers are always increasing, hence there will be a case of addition or multiplication. Let’s just see the difference between every term.
Taking alternative terms,
3, 4 i.e. 3 + 1
8, 10 i.e. 8 +2
13, 16 i.e. 13 + 3
Remaining alternative terms,
4, 8 i.e. 4 + 4
10, 13 i.e. 10 + 3
16, 18 i.e. 16 + 2

Explanation:

You can notice that alternatively the difference is increasing and simultaneously decreasing for next alternative terms. Hence the next term would be 18 + 4 i.e. 22

Square or cubes

Example: 1, 8, 9, 64, 25, 216, ?

Solution: Here the numbers are increasing and decreasing both, hence subtraction / division can also be presented.

Here, you can see that every number is either square or cube of some number. Hence just write down their possibilities.
12 or 13, 23, 32, 82 or 43, 52, 63
Here we can notice that terms are in the order of being square of first number, then cube of the next.
Hence the series can be written as,
12, 23, 32, 43, 52, 63, 72 i.e. 49

Example: 1, 2, 6, 24, ?

Solution: Here, the numbers are increasing with large margins, hence it is possible that there can be multiplication.
We can write the series as: 1×1, 1×2, 2×3 and 6×4
Here, we can notice that the equation can be (previous term x n) where n is incrementing by 1.
Hence the next term can be 24×5 i.e. 120

This article is contributed by Shushank Mittal.

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Verbal Reasoning Tricks With Examples https://programmerbay.com/verbal-reasoning-problem-and-tricks/ https://programmerbay.com/verbal-reasoning-problem-and-tricks/#respond Thu, 10 Sep 2020 07:17:20 +0000 https://programmerbay.com/?p=5055 Verbal Reasoning does not have any particular concept. It targets the ability of an individual to understand and interpret the information from the given set of data.

Tricks to Solve Verbal Reasoning 

Verbal Reasoning type of questions is mostly based on your ability to extract data. So, there might be a passage and some questions based on it, for which you need to answer in True or False or Cannot Say.
The most important thing to keep in mind is time. Sometimes the passage is large and a number of questions are less, so time for solving each question will be more. Hence, you need to keep in mind about the time.


Example:
Even though the minimum age for obtaining a driving license has increased in recent years a substantial increase in car sales over the corresponding years has resulted in a staggering rise in fatal car accident numbers. As the latest figures show, fatal car accidents are especially prevalent among young drivers who have less than five years of driving experience. Last winter 50 percent of all fatal road accidents involved drivers with up to five years driving experience and an additional 15 percent were drivers who had between six to eight years of experience. The interim figures of the current year show that the massive advertisement campaign ‘fighting accidents’ has resulted in some improvements but the truth is that the number of younger drivers involved in fatal accidents is intolerably high. Fatal car accidents are more prevalent amongst young drivers with six to eight years of experience than older drivers with similar experience.


Solution: Cannot Say.
Given data only mentions experience, not age. Although the main idea of the passage is that younger drivers are generally more likely to be involved in fatal car accidents, we cannot say that all relatively inexperienced drivers are young.

The considerable increase in car sales is the reason behind the sharp increase in fatal car accidents.


Solution: False.
In the last line, we can see that ‘fighting accidents’ has resulted in some improvements which mean that increasing car sales doesn’t directly increase car accidents.

The advertising campaign called ‘fighting accidents’ has failed to reduce the number of car accidents.
Solution: False.
In the last line, we can see that ‘fighting accidents’ has resulted in some improvements which contradict the statement.

This article is contributed by Shushank Mittal.

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Statement and Argument Reasoning Tricks with Example https://programmerbay.com/argument-statement-problem-and-tricks/ https://programmerbay.com/argument-statement-problem-and-tricks/#respond Thu, 10 Sep 2020 06:09:16 +0000 https://programmerbay.com/?p=5053 Argument Statements are always one of the most complicated topics in aptitude as arguments vary from person to person but we need to provide the general solution hence we also need to look at keywords before identifying the strong or weak argument.
There will be normally 2 arguments for a statement and you need to identify the existence of each statement. Generally, there are 4 options to select with.
If the only argument I am strong
If only argument II is strong
If neither I nor II is strong
If both I and II are strong.

Tricks to Solve Statement and Argument Reasoning:

Some statements are based on general facts and figures while some have straight arguments. Moreover, you can look for keywords like only that makes a statement’s existence to be weak. This makes the argument to have lesser importance in the statement.
Don’t go with Yes or No, they are just to confuse, don’t have any existence for the argument.

Statement: Should the crackers be completely banned in India?
Arguments.
I: Yes, the use of child labors in the manufacturing of firecrackers is very high.
II: No, the jobs of thousand workers will be hindered.
Solution: We all know that child labor is illegal and not good. So will accept the statement that crackers should be banned.
But, because of crackers, there are lots of people getting food who work once a year for survival. So, this is a contradicting argument.
Since both, the arguments are equally strong. Answer is D

Statement: Should there be a world government?
Arguments:
Yes. It will help in eliminating tensions among the nations.
No. Then, only the developed countries will dominate the government.
Solution: Here, you can see that in the first argument, there is a possibility that there will be peace but no surety of it, hence making it a weak argument.
Whereas, the second argument is a fact that I will encourage the power to lead others.
Hence answer is B

Statement: Should school education be made free in India?
Arguments:
Yes. This is the only way to improve the level of literacy.
No. It would add to the burden on economy of India.
Solution: Here, we see that only is used that makes the argument weak. In the second argument, it’s a general fact that education plays an important role in managing the economy of the country and if it’s been made free for all, it will have a big impact on the economy.
Hence, the answer is B.

Statement: Should foreign films be banned in India?
Arguments:
Yes. They depict an alien culture which adversely affects our values.
No. Foreign films are of a high artistic standard.

Solution: We all know that alien culture might have adverse effect but is extremely good in expanding our thinking, hence the first argument is not strong enough. Moreover, the second statement agrees that they have a high artistic standard, hence it is not strong enough too.
Answer is C

This article is contributed by Shushank Mittal.

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Simplification Problems and Tricks With Examples https://programmerbay.com/simplification-problem-tricks/ https://programmerbay.com/simplification-problem-tricks/#respond Thu, 10 Sep 2020 05:55:36 +0000 https://programmerbay.com/?p=5051 In this article, we’ll be going to discuss simplification concept, tricks and related questions that are often asked in quantitative aptitude test. 

Concept:

Simplification mostly deals with the questions that are based on either VBODMAS rule or general simplification. If an equation is given with certain mathematical relations, you need to solve them according to the VBODMAS rule.

Tricks:

You should remember the VBODMAS rule thoroughly and first start by solving all the brackets. Sometimes there are various kinds of brackets, so you need to solve them in a particular order that they are implemented on. Most of the cases, ( ) gets solved first.

image 2021 01 02 201219
Figure : VBODMAS Full Form

Some Important points :

  • From left to right, always multiplication & Division expression must be performed first, and then Addition & Subtraction.

For example,

5*2+3-4/2

first, multiplication and division will be done,

= 10+3-2 i.e ( 5*2 = 10, 4/2 = 2 )

Now, perform addition and subtraction = 11

  • Multiplication & Division are of same priorities and Addition & Subtraction are of same priorities

 

  • There can be a situation where multiple types of brackets might exist in the expression to complex it, in order to avoid confusion one should know the order to remove the brackets:

() -> must be solved first,
{} -> then after curly braces
[] -> lastly Rectangular bracket

 

Simplification Problem Examples

Example: 1035 ÷ [(3/4) of (71+65) – 63/4]
Solution: We will start by solving the brackets first: 1035 ÷ [(3/4) of 136 – 63/4]
Now, we will solve of condition inside the bracket: 1035 ÷ [102 – 63/4]
Solving the bracket we get: 1035 ÷ (345/4)
It’s difficult to solve this, so we will reciprocate the equation inside the bracket and replace ÷ by *
Hence, 1035*(4/345) will give us 12

Example: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs.4000.What will be the total price of 12 chairs and 3 tables?

Solution:
Given that Price ( 10C = 4T ) i.e. 5C = 2T
Now, Price ( 15C + 2T ) = 4000
Using 5C = 2T, we get, 6T + 2T =4000 i.e. T = 500
Hence C=200
Since price of 1 chair is Rs.200 and table is Rs.500.
Therefore, the price of 12 chairs and 3 tables will be Rs.3900.

Example:
(469 + 174)2 – (469 – 174)2 = ?
(469 x 174)

Solution: This type of questions seems to be difficult in first reading but are based on simple tricks. Don’t get hyper after looking into squares of big numbers.
This numerator can be written in the form of (a+b)2 – (a-b)2 = 4ab
Therefore, 4ab/ab = 4
We don’t even need to look at the numbers. Just need to find the pattern and the general mathematical formulae that is used in these equations.

Example: (7 x 7)3 ÷ (49 x 7)3 x (2401)2
Solution: Again, we have big numbers with powers but it seems common that 7 is repeating a lot of times.
So, there is a possibility that 2401 can be equal to some power of 7.
After solving we can see that 2401 is square of 49 which itself is square of 7,
74 = 2401
Therefore we can write the equation as: (7 x 7)3 ÷ (72 x 7)3 x (74)2
(72)3 ÷ (73)3 x (74)2 = 76 ÷ 79 x 78
We know that Xa ÷ Xb = Xa-b and Ya x Yb = Ya+b
Therefore, 76 ÷ 79 x 78 = 76-9+8 = 75

This article is contributed by Shushank Mittal.

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Seating Arrangement Problems Tricks And Shortcuts With Examples https://programmerbay.com/seating-arrangement-problems-tricks-and-shortcuts-with-examples/ https://programmerbay.com/seating-arrangement-problems-tricks-and-shortcuts-with-examples/#respond Wed, 09 Sep 2020 16:52:19 +0000 https://programmerbay.com/?p=5038 Seating Arrangement questions don’t have any kind of formula or structure. These are totally based on your presence of mind, whether you can elaborate on the given conditions and prepare an outcome.

Tricks

There is no hidden trick to solve it, but what you can do is mark an empty space until any event occurs and try to fill all the spaces one by one according to the given conditions. After solving each condition, just go through all of them and the answer will be visible to you.


If you are given some kind of set and only 1 or 2 questions, then try to skip the question as this will take some time to get solve. Try to solve it only if consists of more than 3 or 4 questions.

Seating Arrangement : Single Row Problem

Example: Eleven friends M, N, O, P, Q, R, S, T, U, V and W are sitting in the first row of the stadium watching a cricket match.
T is to the immediate left of P and third to the right of U.
V is the immediate neighbor of M and N and third to the left of S.
M is the second to the right of Q, who is at one of the ends.
R is sitting next to the right of P and P is second to the right of O.

Solution:
Given that there are 11 friends,
U _ _ T P This can be possible in 2 ways : MVN_S or NVM_S You might think that it has 2 cases but not, as Q is at one of the end but also given that M is at the right which means Q is at the let end i.e. Q _M _ _ _ _ _ _ _
O_PR or ORP
Now we need to combine all 4 things:
By examining 1 and 4, we know that ORP is not possible, hence eliminate it.
Therefore, it will be like U_OTPR.
By examining 2 and 3, we know that NVM_S is not possible, hence eliminate it.
Therefore, it will be like Q MVN_S _ _ _
Now we can conclude that the solution can be: QWMVNUSOTPR.
Q.1. Who is sitting in the center of the row?

  1. N
  2. O
  3. S
  4. U

Q.2. Which of the following people are sitting to the right of S?

  1. OTPQ
  2. OTPR
  3. UNVM
  4. UOTPR

Q.3. Which of the following statements is true with respect to the above arrangement?

  1. There are three persons sitting between P and S
  2. W is between M and V.
  3. N is sitting between V and U
  4. S and O are neighbors sitting to the immediate right of T

Q.4. Who are the immediate neighbors of T?

  1. O, P
  2. O, R
  3. N, U
  4. V, U

Q.5. If Q and P, O and N, M and T, and W and R interchange their positions then which of the following pairs of friends are sitting at the ends?

  1. P and Q
  2. Q and R
  3. P and W
  4. W and R

Seating Arrangement: Round Table Problem

Example: P, Q, R, S, T, U and V are seven friends and are sitting in a circle facing the center of the circle.
V is second to the left of S and is the neighbor of T and U.
S is not a neighbor of R or T.
P is a neighbour of Q and R.
Solution: Given that there are 7 friends sitting in a round table facing each other.
There can be 2 cases: TVUS or UVTS
UVTS can be eliminated. Hence TVUS
There can be 2 cases: QPR or RPQ
From 2 and 3 we can conclude that RPQ is not possible as s does not have R as a neighbour.
Hence the final conclusion should be:

Q.6. Which of the following is correct?

  1. Q is between P and S.
  2. S is between U and P.
  3. T is to the immediate right of V.
  4. U is to the immediate left of V.

Q.7. Which has the pair with the second person sitting to the immediate right of the first person?

  1. QU
  2. VU
  3. TR
  4. PT

Q8. Which of the following will be S’s position after T and S interchange their places?

  1. Neighbour of V and R
  2. To the immediate left of R
  3. To the immediate right of U
  4. Neighbour of R and P

Q9. What is the position of R?

  1. Second to the left of Q
  2. Third to the right of U
  3. To the immediate left of P
  4. None of these

Q. 10 Which of the following has the second person sitting between the first and third persons?

  1. SPQ
  2. VRT
  3. QRP
  4. VUS

Answers:
4
2
3
1
3
1
2
1
4

 

This article is contributed by Shushank Mittal.

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Boat and Stream Problems Tricks And Shortcuts With Examples https://programmerbay.com/boat-and-stream-problems-tricks-and-shortcuts-with-examples/ https://programmerbay.com/boat-and-stream-problems-tricks-and-shortcuts-with-examples/#respond Tue, 28 Jul 2020 15:04:22 +0000 https://www.programmerbay.com/?p=4387 At the time of attempting an aptitude test,  you may have seen the questions from boat and stream. These are some of the topics in which your concepts should be clear in order to solve them quickly. In this article, we will see how to deal with this type of questions.

boat 1626516 640

You should know this formula:

Speed = Distance/ Time

Basic Concepts of Boat and Stream Problems

Let’s see the basic concept of Boat and Stream problem.

Boat and Stream Problems

Still Water: When no flow is visible in the water

  • Speed of a boat in still water= (Upstream + downstream)/2

Stream: In this topic, it simply means the continuous flow of water

  • Speed of a boat in stream= (downstream – Upstream )/2

The stream can be of two types

Downstream: Direction with the stream. [ When a boat is moving in the same direction as water flows]

  • Speed= Speed of boat + Stream

Upstream: Direction opposite to stream. [ When a boat is moving in the opposite direction as water flows]

  • Speed of Boat = Speed of boat – Stream

Types of Questions Asked from Boat and Stream Problems

  • When Speed of the boat need to find first

    • Apply the formula considering the type of stream

Q. A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.

Boat’s speed = 13km/hr
Stream’s Speed = 4 km

Speed of boat = 13 km/hr + 4 km/hr
= 17 km/hr

Distance = 68 km

Time = Distance / speed
= 68/17
= 4 hours

  • When Speed of the stream is missing

Q. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

speed of the motorboat = 15 km/hr
Speed of stream = x
Speed of motorboat in downstream = (15 + x)
Speed of motorboat in upstream = (15 – x)

Distance = 30 km
Total time taken = 9/2 hr ( converted time 4 hours 30 min in hours)

Time = Distance/Speed

Time required to go all the way in downstream = distance/ speed = 30 /(15+x)
Time required to come back all the way in upstreaam = distance/ speed = 30 /(15-x)

Downstream time + upstream time = total time
30/(15+x) +30/(15-x) = 9/2

((15 -x)*30 + 30(15+x))/(15+x)(15-x) = 9/2
(450 – 30x + 450 +30x)/ 225 -x2 = 9/2                                   [ (a+b)(a-b) =a2-b2)
900/225-x2 = 9/2
1800 = 2025 – 9x2 [ Since all are multiples of 9, dividing all by 9 to get standerd form)

200 = 225 = x2
x2 = 225 – 200
x2 = 25
x =5

  • Finding Speed of a boat in still water

Q. In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is

Speed of boat in downstream = 11 km/hr
Speed of boat in upstream = 5 km /hr

Speed of a boat in still water (U + D ) /2

(11+5)/2 = 16/2 = 6 km/hr

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