List of top Mathematics Questions on Integers

Ajosey buys some avocados. After bringing the avocados home, she finds two to be rotten and throws them away. Of the remaining avocados, she puts five-ninth in her fridge, and brings the rest to her hostel. She eats two avocados and puts the rest in her hostel's mess fridge. If her hostel mess fridge cannot hold more than five avocados, what is the maximum possible number of avocados bought by Ajosey?
Let T be the set of integers 3, 11, 19, 27, ... 451, 459, 467 and S be a subset of T such that the sum of no two elements of S is 470. In this case, the maximum possible number of elements in S will be how much?
P, Q and R are three consecutive odd numbers in ascending order. If the value of three times P is 3 less than two times R, find the value of R?
A test has 50 questions. A student scores 1 mark for a correct answer, –1/3 for a wrong answer, and –1/6 for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than:
How many integer solutions exists for the equation 11x + 15y = -1 such that both x and y are less than 100?
Find the remainder when: (1719 × 1721 × 1723 × 1725 × 1727) is divided by 18?