CAT Exam Model Paper 7 with solutions for free online practice

Question : 13 of 60

Marks: +1, -0

A is the set of the first 100 natural numbers. What is the minimum number of elements that should be picked from A to ensure that atleast one pair of numbers whose difference is 10 is picked?

Validate

Solution:

Let’s divide the first 100 natural numbers in five sets of 20 numbers each:
{1, 2, 3....20}, {21, 22, 23....40}.................{81, 82, 83.......100}. If we pick the first ten numbers from each set we will not get any pair of two numbers whose difference is 10.
However, if we pick just one more number from any of the sets, it would have a difference of 10 with one of the numbers which has already been picked.
So the answer is

10 × 5 + 1 =51.

Go to Question:

Prev Question

Next Question