Question:
What is the number of triangles that can be formed whose vertices are the vertices of an octagon but have only one side common with that of the octagon?
What is the number of triangles that can be formed whose vertices are the vertices of an octagon but have only one side common with that of the octagon?
Show Hint
To calculate the number of triangles with one side common to the octagon, subtract the triangles that do not have a side common with the octagon from the total possible triangles.
Updated On: Mar 25, 2025
- 16
- 3
- 48
- 64
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The number of triangles that can be formed with vertices of an octagon is given by choosing 3 vertices from 8. The total number of triangles is:
\[
\binom{8}{3} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56.
\]
However, the triangles with one side common with the octagon must include two adjacent vertices. There are 8 sides in the octagon, so there are 8 such triangles.
The total number of triangles with one side common with the octagon is:
\[
56 - 53 = 3.
\]
Was this answer helpful?
0
0
Top Questions on Critical Reasoning
- Consider the following C program: \begin{verbatim} #include stdio.h void fX(); int main(){ fX(); return 0; } ____________________________ void fX(){ char a; if((a = getchar()) != '\n') fX(); if(a != '\n') putchar(a); } \end{verbatim} Assume that the input to the program from the command line is 1234 followed by a newline character. Which one of the following statements is CORRECT?
- GATE CS - 2024
- General Aptitude
- Critical Reasoning
- Read the following passage and answer the question that follows.
That’s how life plays out for all of us. We lose some. Like sportspersons, we too pack our gear and go to work. But unlike them, the gaze of the world is not upon us. Most of us do our business in anonymity, very few of us are emotionally wired to the outcomes of our day jobs. We don’t come back feeling like winners. Or losers. As sports fans we can summon empathy for those who stretch their bodies and minds to the limit in the pursuit of athletic excellence and provide such joys in the process.
But we will never experience the highs that are their reward. And we will never know the depth of their lows, which are their burden. Still, no one will know better than Rohit and Dravid that its already a new day. There might never be a World Cup win for them. But there are loved ones to go to. Life awaits still.
Which of the following statements BEST summarizes the above passage?- XAT - 2024
- Verbal and Logical Ability
- Critical Reasoning
- Read the following paragraph and answer the question that follows.
You may accumulate a vast amount of knowledge but it will be of far less value to you than a much smaller amount if you have not thought it over for yourself; because only through ordering what you know by comparing every truth with every other truth can you take complete possession of your knowledge and get it into your power.
Based on the above information, which of the following statements MUST be true?- XAT - 2024
- Verbal and Logical Ability
- Critical Reasoning
- Read the following passage and answer the question that follows.
How do we choose one discovery over any other? The physician Lewis Thomas made a choice. He bluntly asserts: “The greatest of all the accomplishments of 20th-century science has been the discovery of human ignorance.”
The science writer Timothy Ferris agrees: “Our ignorance, of course, has always been with us, and always will be. What is new is our awareness of it, our awakening to its fathomless dimensions, and it is this, more than anything else, that marks the coming of age of our species.” It is an odd, unsettling thought that the culmination of our greatest century of discovery should be the confirmation of our ignorance. How did such a thing come about?
Which of the following statements can be BEST concluded from the above passage?- XAT - 2024
- Verbal and Logical Ability
- Critical Reasoning
- Read the following paragraphs and answer the question that follows.
Paragraph 1: Here are some handy rules of thumb. Anyone who calls themselves a thought leader is to be avoided. A man who does not wear socks cannot be trusted. And a company that holds an employee-appreciation day does not appreciate its employees.
Paragraph 2: It is not just that the message sent by acknowledging staff for one out of 260-odd working days is a bit of a giveaway (there isn’t a love-your-spouse day ... for the same reason). It is also that the ideas are usually so tragically unappreciative. You have worked hard all year so you get a slice of cold pizza or a rock stamped with the words “You rock”?
Which of the following BEST describes the relationship of the first paragraph with the second paragraph?- XAT - 2024
- Verbal and Logical Ability
- Critical Reasoning
View More Questions
Questions Asked in ATMA exam
- A retailer purchases shirts from a distributor at the rate of 300 per shirt and puts the label of 450 on each shirt. If the retailer allows some discount and still make a profit of 23%, then what is the discount percentage offered by the shopkeeper?
- ATMA - 2021
- Percentage
- Read the following information carefully and answer the question that follows.
What is the ratio of sales in second quarter by Volvo to sales in first quarter by Mercedes?
- ATMA - 2021
- Data Interpretation
- Read the following information carefully and answer the question that follows.
How many trucks did Tata Motors sell in the complete year approximately?
- ATMA - 2021
- Data Interpretation
- 12 men and 6 women can complete a work in 10 days. 3 men and 6 women can complete this work in 25 days. How many men are required to complete this work in 5 days?
- ATMA - 2021
- Time and Work
- In a basketball team with 12 players, the average height of the players is 170 cm. Out of these players, the average height of 7 players is 166 cm. What is the average height of the remaining 5 players?
- ATMA - 2021
- Average
View More Questions