Question

Let X be the set of first 100 natural numbers. Sets S1 and S2 are subsets of X such that each of them has more than zero elements and no common element. If the maximum number of elements in S1 = x1, in S2 = y1 and minimum no. of elements in S1 = x2, in S2 = y2 then:
If |x1 - y1| and |x2 - y2| are at their minimum possible values then which of the following is true?

• A. |x1 - x2| > |y1 - y2|
• B. |x1 - x2| = |y1 - y2|
• C. |x1 - x2| < |y1 - y2|
• D. |x1 - x2| < |y1 - y2|

Answer 1

The correct option is B

|x1 - x2| = |y1 - y2|

The minimum possible value of |y1 - y2| = 1 - 1 = 0. The minimum possible value of |x1 - x2| = 99 - 99 = 0. So, |x1 - x2| = |y1 - y2|.

Hence, option (b) is correct.