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The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is :
- a)1365
- b)1256
- c)1465
- d)1356
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The sum of all two digit positive numbers which when divided by 7 yiel...
= 7 × 90 + 24 = 654
Total = 654 + 702 = 1356
Most Upvoted Answer
The sum of all two digit positive numbers which when divided by 7 yiel...
Approach:
To find the sum of all two-digit positive numbers that yield a remainder of 2 or 5 when divided by 7, we need to first find all such numbers and then sum them up.
Finding the numbers:
- The first two-digit number that yields a remainder of 2 when divided by 7 is 16.
- The next number would be 16 + 7 = 23.
- Following this pattern, the numbers that yield a remainder of 2 when divided by 7 are 16, 23, 30, ..., 94.
- The first two-digit number that yields a remainder of 5 when divided by 7 is 19.
- The next number would be 19 + 7 = 26.
- Following this pattern, the numbers that yield a remainder of 5 when divided by 7 are 19, 26, 33, ..., 95.
Calculating the sum:
- We can see that the last number in the first sequence is 94 and in the second sequence is 95.
- To find the sum of all numbers, we can use the formula for the sum of an arithmetic series: Sn = n/2 * [2a + (n-1)d], where a is the first term, n is the number of terms, and d is the common difference.
- For the first sequence: a = 16, d = 7, n = (94-16)/7 + 1 = 14
- For the second sequence: a = 19, d = 7, n = (95-19)/7 + 1 = 14
- Calculating the sum for both sequences and adding them up will give us the final answer.
Therefore, the correct answer is option 'D' 1356.
To find the sum of all two-digit positive numbers that yield a remainder of 2 or 5 when divided by 7, we need to first find all such numbers and then sum them up.
Finding the numbers:
- The first two-digit number that yields a remainder of 2 when divided by 7 is 16.
- The next number would be 16 + 7 = 23.
- Following this pattern, the numbers that yield a remainder of 2 when divided by 7 are 16, 23, 30, ..., 94.
- The first two-digit number that yields a remainder of 5 when divided by 7 is 19.
- The next number would be 19 + 7 = 26.
- Following this pattern, the numbers that yield a remainder of 5 when divided by 7 are 19, 26, 33, ..., 95.
Calculating the sum:
- We can see that the last number in the first sequence is 94 and in the second sequence is 95.
- To find the sum of all numbers, we can use the formula for the sum of an arithmetic series: Sn = n/2 * [2a + (n-1)d], where a is the first term, n is the number of terms, and d is the common difference.
- For the first sequence: a = 16, d = 7, n = (94-16)/7 + 1 = 14
- For the second sequence: a = 19, d = 7, n = (95-19)/7 + 1 = 14
- Calculating the sum for both sequences and adding them up will give us the final answer.
Therefore, the correct answer is option 'D' 1356.
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The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is :a)1365b)1256c)1465d)1356Correct answer is option 'D'. Can you explain this answer?
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