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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 is 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.
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)
    210
  • b)
    the smallest value of S2
  • c)
    the largest value of S2
  • d)
    (G- L)
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
There are 50 integers a1, a2,........, a50, not all of them necessaril...
The smallest integer of the series is 1 and greatest integer is 50. If each element of S1 is made greater of equal to every element of S2, then the smallest element 1 should be added to (50 - 1) = 49. Hence option (G-L) is the correct answer.
As this is a variable based question: the word "ANY" can be used.
Let the series of integers a1,a2,.......,a50 be 1,2,3,4,5,.......,50.
S1=1,2,3,4,.........24, S2=25,26,27,..........50.
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Community Answer
There are 50 integers a1, a2,........, a50, not all of them necessaril...
To understand why the correct answer is option 'D', let's analyze the given conditions step by step.

Step 1: Finding the greatest and smallest integers
We are given 50 integers a1, a2, ..., a50. The greatest integer among them is referred to as G, and the smallest integer is referred to as L.

Step 2: Dividing the integers into two sequences
The integers a1 through a24 form sequence S1, and the remaining integers a25 through a50 form sequence S2.

Step 3: Adding an integer x to each element of S1
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.

Step 4: Finding the minimum value of x
We need to determine the minimum possible value of x.

Now, let's analyze the options one by one:

Option A: 210
If x = 210, then the minimum value in S1 would be L + 210, and the maximum value in S2 would be G. However, since every element of S1 is made greater than or equal to every element of S2, the maximum value in S1 must be greater than or equal to the maximum value in S2. Thus, x cannot be less than 210.

Option B: the smallest value of S2
The smallest value of S2 might be smaller than the smallest value of S1 after adding x. Therefore, it is possible for x to be less than the smallest value of S2.

Option C: the largest value of S2
Similar to option B, the largest value of S2 might be smaller than the smallest value of S1 after adding x. Therefore, it is possible for x to be less than the largest value of S2.

Option D: (G - L)
The difference between G and L is the maximum possible difference that can exist between any two integers in the given set. By adding (G - L) to each element of S1, we ensure that the maximum value in S1 is at least as large as the maximum value in S2. Hence, x cannot be less than (G - L).

Therefore, the correct answer is option 'D' (G - L).
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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 is 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.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)210b)the smallest value of S2c)the largest value of S2d)(G- L)Correct answer is option 'D'. Can you explain this answer?
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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 is 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.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)210b)the smallest value of S2c)the largest value of S2d)(G- L)Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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 is 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.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)210b)the smallest value of S2c)the largest value of S2d)(G- L)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 is 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.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)210b)the smallest value of S2c)the largest value of S2d)(G- L)Correct answer is option 'D'. Can you explain this answer?.
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