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If t is a positive integer and 8t is divisible by 96, what will be the remainder when t3 is divided by 108?
- a)0
- b)5
- c)10
- d)15
- e)Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If t is a positive integer and 8t is divisible by 96, what will be the...
Given: 108 = 22 × 33
Since 8t is divisible by 96, we may write
8t = 96k, where k is a positive integer
- 23t = 25 × 3× k
- t = 22 × 3× k
- t3 = 26 × 33 × k3
- t3 = ( 22 × 33 )( 24 × k3)
- t3 = 108( 24 × k3)
This shows that t3 is completely divisible by 108, implying that the remainder is 0.
Answer: Option (A)
Most Upvoted Answer
If t is a positive integer and 8t is divisible by 96, what will be the...
To find the remainder when t^3 is divided by 108, we need to first determine the possible values of t that satisfy the condition 8t is divisible by 96.
Given that 8t is divisible by 96, we can write the equation as 8t = 96k, where k is a positive integer.
Simplifying this equation, we get t = 12k.
So, t can be any positive integer multiple of 12.
To find the remainder when t^3 is divided by 108, we can substitute t = 12k into the expression t^3.
t^3 = (12k)^3 = 1728k^3.
Now, we need to find the remainder when 1728k^3 is divided by 108.
Dividing 1728 by 108, we get a quotient of 16 and a remainder of 0.
Therefore, the remainder when 1728k^3 is divided by 108 is also 0.
Since the remainder is 0, the correct answer is option A) 0.
Given that 8t is divisible by 96, we can write the equation as 8t = 96k, where k is a positive integer.
Simplifying this equation, we get t = 12k.
So, t can be any positive integer multiple of 12.
To find the remainder when t^3 is divided by 108, we can substitute t = 12k into the expression t^3.
t^3 = (12k)^3 = 1728k^3.
Now, we need to find the remainder when 1728k^3 is divided by 108.
Dividing 1728 by 108, we get a quotient of 16 and a remainder of 0.
Therefore, the remainder when 1728k^3 is divided by 108 is also 0.
Since the remainder is 0, the correct answer is option A) 0.
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If t is a positive integer and 8t is divisible by 96, what will be the remainder when t3 is divided by 108?a)0b)5c)10d)15e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If t is a positive integer and 8t is divisible by 96, what will be the remainder when t3 is divided by 108?a)0b)5c)10d)15e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If t is a positive integer and 8t is divisible by 96, what will be the remainder when t3 is divided by 108?a)0b)5c)10d)15e)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?.
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