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. If n is a positive integer and n² is divisible by 120, which of the following MUST be an integer? 1. \frac{n}{24} II. \frac{n}{15} Ⅲ. 40 IV \frac{n}{60} A) I, III B) I only C) II only D) I, III, IV E) II, IV?
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. If n is a positive integer and n² is divisible by 120, which of the ...
To determine which of the given options must be an integer, we need to analyze the divisibility of n² by the different numbers involved.
Given that n² is divisible by 120, we can conclude that n² is divisible by all the prime factors of 120, which are 2, 3, and 5.
Now let's analyze each option:
I. n/24:
To determine if n/24 is an integer, we need to check if n is divisible by 24. Since 24 is divisible by 2 and 3, and n² is divisible by 2 and 3, we can conclude that n is divisible by 2 and 3, and hence n/24 is an integer.
II. n/15:
To determine if n/15 is an integer, we need to check if n is divisible by 15. Since 15 is divisible by 3 and 5, and n² is divisible by 3 and 5, we can conclude that n is divisible by 3 and 5, and hence n/15 is an integer.
III. 40:
40 is a fixed number and not dependent on n. It does not necessarily have to be an integer.
IV. n/60:
To determine if n/60 is an integer, we need to check if n is divisible by 60. Since 60 is divisible by 2, 3, and 5, and n² is divisible by 2, 3, and 5, we can conclude that n is divisible by 2, 3, and 5, and hence n/60 is an integer.
Based on the analysis, options I, II, and IV must be integers. Therefore, the correct answer is (D) I, III, IV
Given that n² is divisible by 120, we can conclude that n² is divisible by all the prime factors of 120, which are 2, 3, and 5.
Now let's analyze each option:
I. n/24:
To determine if n/24 is an integer, we need to check if n is divisible by 24. Since 24 is divisible by 2 and 3, and n² is divisible by 2 and 3, we can conclude that n is divisible by 2 and 3, and hence n/24 is an integer.
II. n/15:
To determine if n/15 is an integer, we need to check if n is divisible by 15. Since 15 is divisible by 3 and 5, and n² is divisible by 3 and 5, we can conclude that n is divisible by 3 and 5, and hence n/15 is an integer.
III. 40:
40 is a fixed number and not dependent on n. It does not necessarily have to be an integer.
IV. n/60:
To determine if n/60 is an integer, we need to check if n is divisible by 60. Since 60 is divisible by 2, 3, and 5, and n² is divisible by 2, 3, and 5, we can conclude that n is divisible by 2, 3, and 5, and hence n/60 is an integer.
Based on the analysis, options I, II, and IV must be integers. Therefore, the correct answer is (D) I, III, IV
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. If n is a positive integer and n² is divisible by 120, which of the following MUST be an integer? 1. \frac{n}{24} II. \frac{n}{15} Ⅲ. 40 IV \frac{n}{60} A) I, III B) I only C) II only D) I, III, IV E) II, IV?
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. If n is a positive integer and n² is divisible by 120, which of the following MUST be an integer? 1. \frac{n}{24} II. \frac{n}{15} Ⅲ. 40 IV \frac{n}{60} A) I, III B) I only C) II only D) I, III, IV E) II, IV? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about . If n is a positive integer and n² is divisible by 120, which of the following MUST be an integer? 1. \frac{n}{24} II. \frac{n}{15} Ⅲ. 40 IV \frac{n}{60} A) I, III B) I only C) II only D) I, III, IV E) II, IV? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . If n is a positive integer and n² is divisible by 120, which of the following MUST be an integer? 1. \frac{n}{24} II. \frac{n}{15} Ⅲ. 40 IV \frac{n}{60} A) I, III B) I only C) II only D) I, III, IV E) II, IV?.
. If n is a positive integer and n² is divisible by 120, which of the following MUST be an integer? 1. \frac{n}{24} II. \frac{n}{15} Ⅲ. 40 IV \frac{n}{60} A) I, III B) I only C) II only D) I, III, IV E) II, IV? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about . If n is a positive integer and n² is divisible by 120, which of the following MUST be an integer? 1. \frac{n}{24} II. \frac{n}{15} Ⅲ. 40 IV \frac{n}{60} A) I, III B) I only C) II only D) I, III, IV E) II, IV? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . If n is a positive integer and n² is divisible by 120, which of the following MUST be an integer? 1. \frac{n}{24} II. \frac{n}{15} Ⅲ. 40 IV \frac{n}{60} A) I, III B) I only C) II only D) I, III, IV E) II, IV?.
Solutions for . If n is a positive integer and n² is divisible by 120, which of the following MUST be an integer? 1. \frac{n}{24} II. \frac{n}{15} Ⅲ. 40 IV \frac{n}{60} A) I, III B) I only C) II only D) I, III, IV E) II, IV? in English & in Hindi are available as part of our courses for CAT.
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