Instructions

DIRECTIONS for the following questions: These questions are based on the situation given below: There are fifty integers $$a_1, a_2,...,a_{50}$$, not all of them necessarily different. Let the greatest integer of these fifty integers be referred to as $$G$$, and the smallest integer be referred to as $$L$$. The integers $$a_1$$ through $$a_{24}$$ form sequence $$S1$$, and the rest form sequence $$S2$$. Each member of $$S1$$ is less than or equal to each member of $$S2$$.

Question 42

Every element of S1 is made greater than or equal to every element of S2 by adding to each element of S1 an integer x. Then x cannot be less than:

Solution

For the least element L in $$S1$$ to be greater than the greatest element or equal to G in $$S2$$, the number that is added to L cannot be less than G - L.

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Every element of S1 is made greater than or equal to every element of S2 by adding to each element of S1 an integer x. Then x cannot be less than:

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