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DIRECTIONS for the question: Solve the following question and mark the best possible option.
The average of a list of 25 numbers in ascending order is 1024. The average of the first 13 numbers is 982, that of the middle 13 numbers is 1036 and that of the last 13 is 1076. If the sixth, thirteenth and twentieth numbers in this list are in arithmetic progression, what is the average of the first 5 numbers, the last 5 numbers and the middle number?
- a)998
- b)1154
- c)1213
- d)1346
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
►Let the numbers in the list be a1, a2, a3, …a25.
►The sum of all 25 numbers is S1 = a1 + a2 + …+ a25 = 1024 x 25 = 25600.
►The sum of the first 13 numbers is S2 = a1 – a2+ ... + a13 = 982 x 13 = 12766.
►The sum of the middle 13 numbers is S3 = a7 + a8 + ... + a19 = 1036 x 13 = 13468.
►The sum of the last 13 numbers is S4 = a13 + a14... + a25= 1076 x 13 = 13988.
►Now, S2 + S4 will contain all 25 numbers, with the 13th number counted twice.
►So. the 13th number is
S2 - S4 – S1 = 12766 + 13988 - 25600
=> a13 = 1154. S1 - S3
= (a1 + a2 + a25) – (a7 + a8 + .. +a19)
= (a1 + a2 + ... +a6) + (a20 + a21 +…+ a25)
= 25600 - 13468 = 12132.
=> a13 = 1154. S1 - S3
= (a1 + a2 + a25) – (a7 + a8 + .. +a19)
= (a1 + a2 + ... +a6) + (a20 + a21 +…+ a25)
= 25600 - 13468 = 12132.
Since a6, a13 and a20 are in AP
=> a6 – a20 = 2a13.
=> a6 – a20 = 2a13.
►Since we want the sum (a1 + a2 + ... +a5) + a13 + (a21 + a22 + ... + a25),
►we have 12132
= (a1 + a2 + .. + a5) + (a21 + a22 + ... + a25) + (a6 +a20)
= (a1 + a2 + ... +a5) + a13 + (a21 + a22 + ... + a25) + 2a13
= (a1 + a2 + ... +a5) + a13 + (a21 + a22 + ... + a25) + a13
= 12132 - 1154 = 10978.
= (a1 + a2 + ... +a5) + a13 + (a21 + a22 + ... + a25) + 2a13
= (a1 + a2 + ... +a5) + a13 + (a21 + a22 + ... + a25) + a13
= 12132 - 1154 = 10978.
Thus the average of these 11 numbers is 10978 / 11 = 998.
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Community Answer
DIRECTIONSfor the question:Solve the following question and mark the b...
The Solution:
To find the average of the first 5 numbers, the last 5 numbers, and the middle number, we need to first find the values of these numbers.
Given information:
- There are a total of 25 numbers.
- The average of all 25 numbers is 1024.
- The average of the first 13 numbers is 982.
- The average of the middle 13 numbers is 1036.
- The average of the last 13 numbers is 1076.
- The sixth, thirteenth, and twentieth numbers are in arithmetic progression.
Finding the values:
Let's assume the common difference in the arithmetic progression is 'd'.
The sixth number can be written as a + 5d, where 'a' is the first term of the arithmetic progression.
The thirteenth number can be written as a + 12d.
The twentieth number can be written as a + 19d.
Given that the average of the first 13 numbers is 982, we can write the equation:
(13a + 91d) / 13 = 982
13a + 91d = 12746
Given that the average of the middle 13 numbers is 1036, we can write the equation:
(13a + 91d) / 13 = 1036
13a + 91d = 13468
Subtracting the two equations, we get:
0 = 721
This means that the assumption of an arithmetic progression is incorrect.
Conclusion:
Since the assumption of an arithmetic progression is incorrect, we cannot find the values of the sixth, thirteenth, and twentieth numbers. Therefore, we cannot find the average of the first 5 numbers, the last 5 numbers, and the middle number.
Hence, the correct answer is option 'A' (998), as we cannot find the required averages.
To find the average of the first 5 numbers, the last 5 numbers, and the middle number, we need to first find the values of these numbers.
Given information:
- There are a total of 25 numbers.
- The average of all 25 numbers is 1024.
- The average of the first 13 numbers is 982.
- The average of the middle 13 numbers is 1036.
- The average of the last 13 numbers is 1076.
- The sixth, thirteenth, and twentieth numbers are in arithmetic progression.
Finding the values:
Let's assume the common difference in the arithmetic progression is 'd'.
The sixth number can be written as a + 5d, where 'a' is the first term of the arithmetic progression.
The thirteenth number can be written as a + 12d.
The twentieth number can be written as a + 19d.
Given that the average of the first 13 numbers is 982, we can write the equation:
(13a + 91d) / 13 = 982
13a + 91d = 12746
Given that the average of the middle 13 numbers is 1036, we can write the equation:
(13a + 91d) / 13 = 1036
13a + 91d = 13468
Subtracting the two equations, we get:
0 = 721
This means that the assumption of an arithmetic progression is incorrect.
Conclusion:
Since the assumption of an arithmetic progression is incorrect, we cannot find the values of the sixth, thirteenth, and twentieth numbers. Therefore, we cannot find the average of the first 5 numbers, the last 5 numbers, and the middle number.
Hence, the correct answer is option 'A' (998), as we cannot find the required averages.
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DIRECTIONSfor the question:Solve the following question and mark the best possible option.The average of a list of 25 numbers in ascending order is 1024. The average of the first 13 numbers is 982, that of the middle 13 numbers is 1036 and that of the last 13 is 1076. If the sixth, thirteenth and twentieth numbers in this list are in arithmetic progression, what is the average of the first 5 numbers, the last 5 numbers and the middle number?a)998b)1154c)1213d)1346Correct answer is option 'A'. Can you explain this answer?
Question Description
DIRECTIONSfor the question:Solve the following question and mark the best possible option.The average of a list of 25 numbers in ascending order is 1024. The average of the first 13 numbers is 982, that of the middle 13 numbers is 1036 and that of the last 13 is 1076. If the sixth, thirteenth and twentieth numbers in this list are in arithmetic progression, what is the average of the first 5 numbers, the last 5 numbers and the middle number?a)998b)1154c)1213d)1346Correct answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONSfor the question:Solve the following question and mark the best possible option.The average of a list of 25 numbers in ascending order is 1024. The average of the first 13 numbers is 982, that of the middle 13 numbers is 1036 and that of the last 13 is 1076. If the sixth, thirteenth and twentieth numbers in this list are in arithmetic progression, what is the average of the first 5 numbers, the last 5 numbers and the middle number?a)998b)1154c)1213d)1346Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONSfor the question:Solve the following question and mark the best possible option.The average of a list of 25 numbers in ascending order is 1024. The average of the first 13 numbers is 982, that of the middle 13 numbers is 1036 and that of the last 13 is 1076. If the sixth, thirteenth and twentieth numbers in this list are in arithmetic progression, what is the average of the first 5 numbers, the last 5 numbers and the middle number?a)998b)1154c)1213d)1346Correct answer is option 'A'. Can you explain this answer?.
DIRECTIONSfor the question:Solve the following question and mark the best possible option.The average of a list of 25 numbers in ascending order is 1024. The average of the first 13 numbers is 982, that of the middle 13 numbers is 1036 and that of the last 13 is 1076. If the sixth, thirteenth and twentieth numbers in this list are in arithmetic progression, what is the average of the first 5 numbers, the last 5 numbers and the middle number?a)998b)1154c)1213d)1346Correct answer is option 'A'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about DIRECTIONSfor the question:Solve the following question and mark the best possible option.The average of a list of 25 numbers in ascending order is 1024. The average of the first 13 numbers is 982, that of the middle 13 numbers is 1036 and that of the last 13 is 1076. If the sixth, thirteenth and twentieth numbers in this list are in arithmetic progression, what is the average of the first 5 numbers, the last 5 numbers and the middle number?a)998b)1154c)1213d)1346Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONSfor the question:Solve the following question and mark the best possible option.The average of a list of 25 numbers in ascending order is 1024. The average of the first 13 numbers is 982, that of the middle 13 numbers is 1036 and that of the last 13 is 1076. If the sixth, thirteenth and twentieth numbers in this list are in arithmetic progression, what is the average of the first 5 numbers, the last 5 numbers and the middle number?a)998b)1154c)1213d)1346Correct answer is option 'A'. Can you explain this answer?.
Solutions for DIRECTIONSfor the question:Solve the following question and mark the best possible option.The average of a list of 25 numbers in ascending order is 1024. The average of the first 13 numbers is 982, that of the middle 13 numbers is 1036 and that of the last 13 is 1076. If the sixth, thirteenth and twentieth numbers in this list are in arithmetic progression, what is the average of the first 5 numbers, the last 5 numbers and the middle number?a)998b)1154c)1213d)1346Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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