Knowee
Questions
Features
Study Tools

The organizers of a gymnastics event wish to arrange the participants in neatrows. They try rows of 2, 3, 4, 5, 6, 7 and 8, but in each case there is one gymnastleft over. There are fewer than 1000 gymnasts in all. How many are there? Explainyour reasoning

Question

The organizers of a gymnastics event wish to arrange the participants in neatrows. They try rows of 2, 3, 4, 5, 6, 7 and 8, but in each case there is one gymnastleft over. There are fewer than 1000 gymnasts in all. How many are there? Explainyour reasoning

🧐 Not the exact question you are looking for?Go ask a question

Solution

The problem is asking for the smallest number that leaves a remainder of 1 when divided by 2, 3, 4, 5, 6, 7, and 8. This is equivalent to finding the least common multiple (LCM) of these numbers and adding 1.

Step 1: Find the LCM of 2, 3, 4, 5, 6, 7, and 8.

The LCM of 2, 3, 4, 5, 6, 7, and 8 is 840. This is because 840 is the smallest number that all these numbers can divide into evenly.

Step 2: Add 1 to the LCM.

Adding 1 to 840 gives 841.

So, there are 841 gymnasts. This number leaves a remainder of 1 when divided by 2, 3, 4, 5, 6, 7, and 8, and is less than 1000, which fits the conditions of the problem.

This problem has been solved

Similar Questions

A gymnastics competition has 9 gymnasts. How many different top-4 rankings are possible?

During the morning assembly in a school, students stand in the playground in a fixed pattern of rows. Each row consists of students of only one particular class.1) There are four more rows of Class 10 students than of Class 5 students.2) The number of rows of Class 6 students is one less than of Class 10 students.3) One of the classes has the maximum number of rows, i.e., seven.4) There are two rows of Class 5 students.5) There are two more rows of Class 8 students than of Class 5 students.6) The number of rows of Class 9 students is less than that of Class 7 students.Analyze this information and answer the question given below.Which of the following is the total number of rows of Class 10 students? 4 5 6 7 8Mark for Later

In men's artistic gymnastics, what is the maximum number of athletes that can compete in a team event?

An event has 24 adults and 42 children. The event planner wants to make each table identical, with the same combination of adults and children and no people left over. What is the greatest number of tables the planner can set up?

Suppose that a group of 27 students are going to pose for a class photo.They are to be arranged in three rows with 10 in the front row, 6 in the middle row and 11 in the back row.The photographer selects which students go in each row.In how many different ways can the class now be arranged for the photo?

1/1

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.