During the holidays, João and Ana decided to do physical activities together, but the exercises they chose have different routines. João exercises every 4 days, while Ana exercises every 6 days. Today, they started their exercises together.

The theater group of a school needed to reorganize its rehearsal schedule based on the availability of the students. The dance, music, and theater performances take place every 10, 15, and 20 days, respectively. From a certain day when all three groups meet, what will be the next day when they can all meet again? What is the minimum number of days that will pass for this to happen?

In a cooking contest, two participants need to cook different dishes, but both need to use the oven. The first dish needs 15 minutes in the oven and the second dish needs 10 minutes. They need to rotate the use of the oven so that both can finish their dishes at the same time, without any of the dishes staying in the oven longer than necessary. What is the minimum possible time for both dishes to be finished at the same time, considering that the time in the oven is counted from the moment the dish is placed in it?

Two cyclists start from point A and ride on a circular track of 10 km. The first cyclist completes a lap every 45 minutes, while the second cyclist completes a lap every 36 minutes. After 7 hours, at what time will both cyclists be back at point A and what distance will the second cyclist have covered by then? Consider that the cyclists maintain a constant pedaling pace and that neither of them stops during the journey for rest or any other activity.

A student from CMRJ, when asked about the number of math textbook exercises he had solved, replied: 'I don't know, but counting by 2, there is a remainder of 1; counting by 3, there is a remainder of 1; counting by 5, there is also a remainder of 1; but counting by 11, there is no remainder; furthermore, the total number of exercises is greater than 100 and less than 200.' So, the number of exercises solved is such that the sum of the digits of its numeral is equal to:

To solve this question, we must use the Chinese Remainder Theorem, as the student provides information about the remainder of the number of exercises when divided by 2, 3, 5, and 11. Let's analyze the given information: 1. Counting by 2, there is a remainder of 1: this means the number of exercises is odd (in the form n = 2k + 1). 2. Counting by 3, there is a remainder of 1: this means the number of exercises leaves a remainder of 1 when divided by 3 (in the form n = 3k + 1). 3. Counting by 5, there is a remainder of 1: this means the number of exercises leaves a remainder of 1 when divided by 5 (in the form n = 5k + 1). 4. Counting by 11, there is no remainder: this means the number of exercises is divisible by 11 (in the form n = 11k). Additionally, the total number of exercises is greater than 100 and less than 200. Now, we must find a number that satisfies all these conditions. Since 2, 3, 5, and 11 are pairwise coprime, we can look for a common multiple of 2, 3, and 5 and then add 1. The least common multiple of 2, 3, and 5 is 30, so the number we are looking for is in the form n = 30k + 1. We need to find a value of k that makes n divisible by 11 and is in the range of 100 to 200. Testing some values of k: k = 4: n = 30*4 + 1 = 121, which is divisible by 11 and is in the desired range. Therefore, the number of exercises solved is 121. The sum of the digits of this numeral is 1 + 2 + 1 = 4, which is the correct answer among the provided alternatives.

Question bank: LCM Problems

Access these and thousands of other questions, create assignments, projects, and lesson plans in minutes.

Why are Teachy's Question Banks the most complete available?

Complete platform:

Custom filters:

Focus on students:

Time for what matters:

Access anywhere: