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How many numbers between 500 and 1000 are divisible by 13?
- a)36
- b)37
- c)38
- d)39
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
How many numbers between 500 and 1000 are divisible by 13?a)36b)37c)38...
500 = 13 × 38 + 6 [∵ 13 × 38 = 494]
⇒ First number divisible by 13 = 13 × 39 = 507
1000 = 76 × 13 + 12 [∵ 76 × 13 = 988]
⇒ Last number divisible by 13 in the given interval = 13 × 76
⇒ Number of multiples = 76 – 39 + 1 = 38 [1 is added ∵ 507 is also included]
∴ There are 38 numbers between 500 and 1000 that are divisible by 13
1000 = 76 × 13 + 12 [∵ 76 × 13 = 988]
⇒ Last number divisible by 13 in the given interval = 13 × 76
⇒ Number of multiples = 76 – 39 + 1 = 38 [1 is added ∵ 507 is also included]
∴ There are 38 numbers between 500 and 1000 that are divisible by 13
Most Upvoted Answer
How many numbers between 500 and 1000 are divisible by 13?a)36b)37c)38...
500 = 13 × 38 + 6 [∵ 13 × 38 = 494]
⇒ First number divisible by 13 = 13 × 39 = 507
1000 = 76 × 13 + 12 [∵ 76 × 13 = 988]
⇒ Last number divisible by 13 in the given interval = 13 × 76
⇒ Number of multiples = 76 – 39 + 1 = 38 [1 is added ∵ 507 is also included]
∴ There are 38 numbers between 500 and 1000 that are divisible by 13
1000 = 76 × 13 + 12 [∵ 76 × 13 = 988]
⇒ Last number divisible by 13 in the given interval = 13 × 76
⇒ Number of multiples = 76 – 39 + 1 = 38 [1 is added ∵ 507 is also included]
∴ There are 38 numbers between 500 and 1000 that are divisible by 13
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Community Answer
How many numbers between 500 and 1000 are divisible by 13?a)36b)37c)38...
Identifying the numbers divisible by 13 between 500 and 1000
To find out the numbers between 500 and 1000 that are divisible by 13, we need to determine the first and last numbers in the given range that are divisible by 13.
Finding the first number
To find the first number divisible by 13 in the range of 500 to 1000, we need to divide 500 by 13.
500 ÷ 13 = 38 with a remainder of 6
Since the remainder is not 0, the next multiple of 13 after 500 is 13 * 38 + 13 = 499 + 13 = 512.
Finding the last number
To find the last number divisible by 13 in the range of 500 to 1000, we need to divide 1000 by 13.
1000 ÷ 13 = 76 with a remainder of 12
Since the remainder is not 0, the last multiple of 13 before 1000 is 13 * 76 - 13 = 988.
Calculating the total numbers
To find out how many numbers are divisible by 13 between 512 and 988, we subtract the first number (512) from the last number (988) and divide by 13.
(988 - 512) ÷ 13 = 476 ÷ 13 = 36
Therefore, there are 38 numbers between 500 and 1000 that are divisible by 13. So, the correct answer is option C) 38.
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How many numbers between 500 and 1000 are divisible by 13?a)36b)37c)38d)39Correct answer is option 'C'. Can you explain this answer? for Defence 2025 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about How many numbers between 500 and 1000 are divisible by 13?a)36b)37c)38d)39Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many numbers between 500 and 1000 are divisible by 13?a)36b)37c)38d)39Correct answer is option 'C'. Can you explain this answer?.
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