Random Numbers
(CAT 1999)
There are 50 integers a1, a2 … a50, not all of them necessarily different. Let the greatest integer of these 50 integers be referred to as G, and the smallest integer be referred to as L. The integers a1 through a24 form sequence S1, and the rest form sequence S2. Each member of S1 is less than or equal to each member of S2.
1. All values in S1 are changed in sign, while those in S2 remain unchanged. Which of the following statements is true?
a. Every member of S1 is greater than or equal to every member of S2.
b. G is in S1.
c. If all numbers originally in S1 and S2 had the same sign, then after the change of sign, the largest number of S1 and S2 is in S1.
d. None of the above
2. Elements of S1 are in ascending order, and those of S2 are in descending order. a24 and a25 are interchanged. Then which of the following statements is true?
a. S1 continues to be in ascending order.
b. S2 continues to be in descending order.
c. S1 continues to be in ascending order and S2 in descending order.
d. None of the above
3. 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
a. 2^10
b. the smallest value of S2
c. the largest value of S2
d. (G – L)
For answers click here.
There are 50 integers a1, a2 … a50, not all of them necessarily different. Let the greatest integer of these 50 integers be referred to as G, and the smallest integer be referred to as L. The integers a1 through a24 form sequence S1, and the rest form sequence S2. Each member of S1 is less than or equal to each member of S2.
1. All values in S1 are changed in sign, while those in S2 remain unchanged. Which of the following statements is true?
a. Every member of S1 is greater than or equal to every member of S2.
b. G is in S1.
c. If all numbers originally in S1 and S2 had the same sign, then after the change of sign, the largest number of S1 and S2 is in S1.
d. None of the above
2. Elements of S1 are in ascending order, and those of S2 are in descending order. a24 and a25 are interchanged. Then which of the following statements is true?
a. S1 continues to be in ascending order.
b. S2 continues to be in descending order.
c. S1 continues to be in ascending order and S2 in descending order.
d. None of the above
3. 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
a. 2^10
b. the smallest value of S2
c. the largest value of S2
d. (G – L)
For answers click here.
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