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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 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.
Q. 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 is true?
- a)S1 continues to be in ascending order
- b)S2 continues to be in descending order
- c)Both (a) and (b)
- d)Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
There are 50 integers a1, a2 … a50, not all of them necessarily...
Assume S1 = {1, 2, 3,..., 24} and S2 = { 50, 49, 48, 47.. .., 25}.
Now even if we have interchanged 24 and 25, S1 continues to be in ascending order and S2 continues to be in descending order.
However, by choosing negative values of a24 and a25, we can show that S1 continues to be in ascending order, but S2 is no longer in descending order.
Most Upvoted Answer
There are 50 integers a1, a2 … a50, not all of them necessarily...
Let's assume that the sum of the integers is S. Then we know that:
a1 + a2 + ... + a50 = S
We also know that the sum of the even integers is:
a2 + a4 + ... + a50 = S/2
And the sum of the odd integers is:
a1 + a3 + ... + a49 = S/2
Now, we can subtract the sum of the odd integers from the sum of all the integers to get the sum of the even integers:
(a1 + a2 + ... + a50) - (a1 + a3 + ... + a49) = a2 + a4 + ... + a50 = S/2
We can also subtract the sum of the even integers from the sum of all the integers to get the sum of the odd integers:
(a1 + a2 + ... + a50) - (a2 + a4 + ... + a50) = a1 + a3 + ... + a49 = S/2
So, we have found that the sum of the even integers is half of the sum of all the integers, and the sum of the odd integers is also half of the sum of all the integers. Therefore, the sum of the even integers is equal to the sum of the odd integers.
a1 + a2 + ... + a50 = S
We also know that the sum of the even integers is:
a2 + a4 + ... + a50 = S/2
And the sum of the odd integers is:
a1 + a3 + ... + a49 = S/2
Now, we can subtract the sum of the odd integers from the sum of all the integers to get the sum of the even integers:
(a1 + a2 + ... + a50) - (a1 + a3 + ... + a49) = a2 + a4 + ... + a50 = S/2
We can also subtract the sum of the even integers from the sum of all the integers to get the sum of the odd integers:
(a1 + a2 + ... + a50) - (a2 + a4 + ... + a50) = a1 + a3 + ... + a49 = S/2
So, we have found that the sum of the even integers is half of the sum of all the integers, and the sum of the odd integers is also half of the sum of all the integers. Therefore, the sum of the even integers is equal to the sum of the odd integers.
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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 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.Q. Elements of S1are in ascending order and those of S2 are in descending order. a24 and a25 are interchanged then which of the following is true?a)S1continues to be in ascending orderb)S2 continues to be in descending orderc)Both (a) and (b)d)Cannot be determinedCorrect answer is option 'A'. 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 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.Q. Elements of S1are in ascending order and those of S2 are in descending order. a24 and a25 are interchanged then which of the following is true?a)S1continues to be in ascending orderb)S2 continues to be in descending orderc)Both (a) and (b)d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant 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 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.Q. Elements of S1are in ascending order and those of S2 are in descending order. a24 and a25 are interchanged then which of the following is true?a)S1continues to be in ascending orderb)S2 continues to be in descending orderc)Both (a) and (b)d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 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 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.Q. Elements of S1are in ascending order and those of S2 are in descending order. a24 and a25 are interchanged then which of the following is true?a)S1continues to be in ascending orderb)S2 continues to be in descending orderc)Both (a) and (b)d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
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.Q. Elements of S1are in ascending order and those of S2 are in descending order. a24 and a25 are interchanged then which of the following is true?a)S1continues to be in ascending orderb)S2 continues to be in descending orderc)Both (a) and (b)d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant 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 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.Q. Elements of S1are in ascending order and those of S2 are in descending order. a24 and a25 are interchanged then which of the following is true?a)S1continues to be in ascending orderb)S2 continues to be in descending orderc)Both (a) and (b)d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 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 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.Q. Elements of S1are in ascending order and those of S2 are in descending order. a24 and a25 are interchanged then which of the following is true?a)S1continues to be in ascending orderb)S2 continues to be in descending orderc)Both (a) and (b)d)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
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