1. When 310 is divided by a two-digit positive integer K, the remainder is 37. What is the sum of all possible values of K?

2. N is a positive integer. When N is divided by 3, the remainder is 2. When N is divided by 4, the remainder is 3. What is the remainder when N is divided by 12?

EDIT: TYPO!!!

It's When N is divided by 3, the remainder is **2**

3. The zoo transferred 131 birds to the safari park over the course of many days.

The zookeeper planned to send the same number of birds each day, except that there might be fewer on the last day when he would send whatever was left. However, he mistakenly thought that there were 113 birds in total instead of 131, which caused the transfer to take 3 more days than he anticipated. Interestingly, the number of birds transferred during the last day was the same as he had originally planned.

How many birds were transferred during the last day?

4. Duncan found a set of positive integers less than 50 such that no two of them sum to a multiple of 7. What is the largest number of integers in Duncan's collection?

sudsw12 Jan 10, 2019

#1**+1 **

2. Rewriting this, we have: \(3x+3=4y+3, \frac{3x}{4}=y.\) Now, plugging a value of \(x\) that will leave \(y\) are a non-negative integer, is \(x=4.\) Answer is 3? I might be wrong...

tertre Jan 10, 2019

#2**+2 **

2. N is a positive integer. When N is divided by 3, the remainder is 3. When N is divided by 4, the remainder is 3. What is the remainder when N is divided by 12?

If some number is divided by 3 how can the remainder be 3?

Melody Jan 10, 2019