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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-
Assertion (A): If n is a positive integer then 32n + 7 is divisible by 8
Reason (R): G.C.F. of 16 and 88 is 8
  • a)
    Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
  • b)
    Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.
  • c)
    Assertion is true but Reason is false.
  • d)
    Assertion is false but Reason is true.
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In the following question, a Statement of Assertion (A) is given follo...
Explanation:

  • The Assertion (A) states that if n is a positive integer, then 32n + 7 is divisible by 8.

  • The Reason (R) states that the G.C.F. of 16 and 88 is 8.

  • Both the Assertion and Reason are true.

  • The Reason is the correct explanation of the Assertion.

  • Therefore, the correct answer is option 'A'.


Reasoning:

  • For any positive integer, n, 32n can be written as 2^5n.

  • Thus, 32n + 7 can be written as 2^5n + 7.

  • Now, if we divide 2^5n + 7 by 8, we get the remainder as 7.

  • Therefore, 32n + 7 is not divisible by 8.

  • However, the Reason states that the G.C.F. of 16 and 88 is 8.

  • Since 8 is a factor of both 16 and 88, it is also a factor of any linear combination of 16 and 88.

  • 32n + 7 can be written as 2(16n) + 7.

  • Thus, 32n + 7 is a linear combination of 16 and 7.

  • Therefore, 8 is a factor of 32n + 7.

  • Hence, the Reason is the correct explanation of the Assertion.

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Community Answer
In the following question, a Statement of Assertion (A) is given follo...
Becoz if 3×3×1+7=16 which is divisible by 8and of 3×3×3 ×3 +7=88 which is divisible by 8
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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion (A): If n is a positive integer then 32n + 7 is divisible by 8Reason (R): G.C.F. of 16 and 88 is 8a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer?
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In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion (A): If n is a positive integer then 32n + 7 is divisible by 8Reason (R): G.C.F. of 16 and 88 is 8a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion (A): If n is a positive integer then 32n + 7 is divisible by 8Reason (R): G.C.F. of 16 and 88 is 8a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the following question, a Statement of Assertion (A) is given followed by a corresponding Reason (R) just below it. Read the Statements carefully and mark the correct answer-Assertion (A): If n is a positive integer then 32n + 7 is divisible by 8Reason (R): G.C.F. of 16 and 88 is 8a)Both Assertion and Reason are true and Reason is the correct explanation of Assertion.b)Both Assertion and Reason are true and Reason is not the correct explanation of Assertion.c)Assertion is true but Reason is false.d)Assertion is false but Reason is true.Correct answer is option 'A'. Can you explain this answer?.
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