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DIRECTIONS for questions: Select the correct alternative from the given choices.
The arithmetic mean of a set of numbers was calculated as 24. However, the frequency of one of the numbers was erroneously taken as 6, instead of 9. As a result, the arithmetic mean calculated was 5 less than the actual mean. If all the numbers in the set are integers, then which of the following could be the sum of all frequencies?
- a)40
- b)41
- c)42
- d)43
Correct answer is option 'C'. Can you explain this answer?
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DIRECTIONS for questions: Select the correct alternative from the giv...
Let the number whose frequency is taken erroneously be x.
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Let the sum of frequencies initially considered be k
=> The actual sum of frequencies = k + 3
Calculated mean = 24
=> calculated sum of all observations = 24k
Actual sum = 24k + 3x
Actual mean = 24k + 3x / k + 3 = 24 + 5 = 29
=> 24k + 3x = 29k + 87
=> 5k = 3x - 87
=> k = 3(x – 29) / 5
As both k and x are integers, x - 29 must be a multiple of 5 and k must be a multiple of 3.
=> k + 3 must be a multiple of 3.
Among the given options, only 42 is a multiple of 3.
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DIRECTIONS for questions: Select the correct alternative from the giv...
Question Analysis:
We are given that the arithmetic mean of a set of numbers was calculated as 24, but the frequency of one of the numbers was erroneously taken as 6 instead of 9. This resulted in the arithmetic mean being 5 less than the actual mean. We need to determine the sum of all frequencies.
Given:
Arithmetic mean (calculated) = 24
Arithmetic mean (actual) = 24 + 5 = 29
Frequency (erroneous) = 6
Frequency (actual) = 9
Solution:
To find the sum of all frequencies, we need to determine the sum of all numbers in the set. Let's assume the sum of all numbers in the set is S.
The arithmetic mean (calculated) is given by the formula:
24 = S / (frequency of all numbers)
The arithmetic mean (actual) is given by the formula:
29 = S / (frequency of all numbers)
Since the frequency of one number was erroneously taken as 6 instead of 9, the sum of all numbers in the set is:
S = 24 * (frequency of all numbers) = 29 * (frequency of all numbers + 3)
Let's find the values of (frequency of all numbers) that satisfy this equation, which will give us the possible values for the sum of all frequencies.
Calculating Possible Values:
We will start by assuming the frequency of all numbers as 1 and increment it until we find a value that satisfies the equation.
Assume the frequency of all numbers = 1:
S = 29 * (1 + 3) = 29 * 4 = 116
Assume the frequency of all numbers = 2:
S = 29 * (2 + 3) = 29 * 5 = 145
Assume the frequency of all numbers = 3:
S = 29 * (3 + 3) = 29 * 6 = 174
Assume the frequency of all numbers = 4:
S = 29 * (4 + 3) = 29 * 7 = 203
Assume the frequency of all numbers = 5:
S = 29 * (5 + 3) = 29 * 8 = 232
Assume the frequency of all numbers = 6:
S = 29 * (6 + 3) = 29 * 9 = 261
We can observe that the possible values for the sum of all frequencies are increasing by 29 each time. The only option among the given choices that is divisible by 29 is 42 (as 29 * 1 = 29 and 29 * 2 = 58).
Therefore, the sum of all frequencies could be 42.
Answer: c) 42
We are given that the arithmetic mean of a set of numbers was calculated as 24, but the frequency of one of the numbers was erroneously taken as 6 instead of 9. This resulted in the arithmetic mean being 5 less than the actual mean. We need to determine the sum of all frequencies.
Given:
Arithmetic mean (calculated) = 24
Arithmetic mean (actual) = 24 + 5 = 29
Frequency (erroneous) = 6
Frequency (actual) = 9
Solution:
To find the sum of all frequencies, we need to determine the sum of all numbers in the set. Let's assume the sum of all numbers in the set is S.
The arithmetic mean (calculated) is given by the formula:
24 = S / (frequency of all numbers)
The arithmetic mean (actual) is given by the formula:
29 = S / (frequency of all numbers)
Since the frequency of one number was erroneously taken as 6 instead of 9, the sum of all numbers in the set is:
S = 24 * (frequency of all numbers) = 29 * (frequency of all numbers + 3)
Let's find the values of (frequency of all numbers) that satisfy this equation, which will give us the possible values for the sum of all frequencies.
Calculating Possible Values:
We will start by assuming the frequency of all numbers as 1 and increment it until we find a value that satisfies the equation.
Assume the frequency of all numbers = 1:
S = 29 * (1 + 3) = 29 * 4 = 116
Assume the frequency of all numbers = 2:
S = 29 * (2 + 3) = 29 * 5 = 145
Assume the frequency of all numbers = 3:
S = 29 * (3 + 3) = 29 * 6 = 174
Assume the frequency of all numbers = 4:
S = 29 * (4 + 3) = 29 * 7 = 203
Assume the frequency of all numbers = 5:
S = 29 * (5 + 3) = 29 * 8 = 232
Assume the frequency of all numbers = 6:
S = 29 * (6 + 3) = 29 * 9 = 261
We can observe that the possible values for the sum of all frequencies are increasing by 29 each time. The only option among the given choices that is divisible by 29 is 42 (as 29 * 1 = 29 and 29 * 2 = 58).
Therefore, the sum of all frequencies could be 42.
Answer: c) 42
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DIRECTIONS for questions: Select the correct alternative from the given choices. The arithmetic mean of a set of numbers was calculated as 24. However, the frequency of one of the numbers was erroneously taken as 6, instead of 9. As a result, the arithmetic mean calculated was 5 less than the actual mean. If all the numbers in the set are integers, then which of the following could be the sum of all frequencies?a) 40b) 41c) 42d) 43Correct answer is option 'C'. Can you explain this answer?
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DIRECTIONS for questions: Select the correct alternative from the given choices. The arithmetic mean of a set of numbers was calculated as 24. However, the frequency of one of the numbers was erroneously taken as 6, instead of 9. As a result, the arithmetic mean calculated was 5 less than the actual mean. If all the numbers in the set are integers, then which of the following could be the sum of all frequencies?a) 40b) 41c) 42d) 43Correct answer is option 'C'. 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 DIRECTIONS for questions: Select the correct alternative from the given choices. The arithmetic mean of a set of numbers was calculated as 24. However, the frequency of one of the numbers was erroneously taken as 6, instead of 9. As a result, the arithmetic mean calculated was 5 less than the actual mean. If all the numbers in the set are integers, then which of the following could be the sum of all frequencies?a) 40b) 41c) 42d) 43Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONS for questions: Select the correct alternative from the given choices. The arithmetic mean of a set of numbers was calculated as 24. However, the frequency of one of the numbers was erroneously taken as 6, instead of 9. As a result, the arithmetic mean calculated was 5 less than the actual mean. If all the numbers in the set are integers, then which of the following could be the sum of all frequencies?a) 40b) 41c) 42d) 43Correct answer is option 'C'. Can you explain this answer?.
DIRECTIONS for questions: Select the correct alternative from the given choices. The arithmetic mean of a set of numbers was calculated as 24. However, the frequency of one of the numbers was erroneously taken as 6, instead of 9. As a result, the arithmetic mean calculated was 5 less than the actual mean. If all the numbers in the set are integers, then which of the following could be the sum of all frequencies?a) 40b) 41c) 42d) 43Correct answer is option 'C'. 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 DIRECTIONS for questions: Select the correct alternative from the given choices. The arithmetic mean of a set of numbers was calculated as 24. However, the frequency of one of the numbers was erroneously taken as 6, instead of 9. As a result, the arithmetic mean calculated was 5 less than the actual mean. If all the numbers in the set are integers, then which of the following could be the sum of all frequencies?a) 40b) 41c) 42d) 43Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONS for questions: Select the correct alternative from the given choices. The arithmetic mean of a set of numbers was calculated as 24. However, the frequency of one of the numbers was erroneously taken as 6, instead of 9. As a result, the arithmetic mean calculated was 5 less than the actual mean. If all the numbers in the set are integers, then which of the following could be the sum of all frequencies?a) 40b) 41c) 42d) 43Correct answer is option 'C'. Can you explain this answer?.
Solutions for DIRECTIONS for questions: Select the correct alternative from the given choices. The arithmetic mean of a set of numbers was calculated as 24. However, the frequency of one of the numbers was erroneously taken as 6, instead of 9. As a result, the arithmetic mean calculated was 5 less than the actual mean. If all the numbers in the set are integers, then which of the following could be the sum of all frequencies?a) 40b) 41c) 42d) 43Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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