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What is the sum of all two digit numbers that gives a remainder of 3 when they are divided by 7?
- a)666
- b)676
- c)683
- d)777
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
What is the sum of all two digit numbers that gives a remainder of 3 w...
The two digit number which gives a remainder of 3 when divided by 7 are:
10, 17, 24 94.
Now, these number are in AP series with
1st Term, a = 10;
Number of Terms, n = 13;
Last term, L = 94 and
Common Difference, d = 7.
Sum,
= n*(a+L)/2
= 13*52 = 676.
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What is the sum of all two digit numbers that gives a remainder of 3 w...
Solution:
Finding the numbers:
To find the numbers that give a remainder of 3 when divided by 7, we can list out the two-digit numbers that give a remainder of 3 when divided by 7. These numbers are:
10 + 3 = 13
17 + 3 = 20
24 + 3 = 27
31 + 3 = 34
38 + 3 = 41
...
87 + 3 = 90
Calculating the sum:
To find the sum of all these numbers, we can add them up.
13 + 20 + 27 + 34 + 41 + ... + 90
We can use the formula for the sum of an arithmetic series to find this sum. The first term is 13, the common difference is 7, and the last term is 90.
Sum = (number of terms) x (average of first and last term)
= (number of terms) x (13 + 90)/2
= (number of terms) x 103/2
To find the number of terms, we can use the formula for the nth term of an arithmetic series:
an = a1 + (n-1)d
where a1 is the first term, d is the common difference, and an is the nth term.
We want to find the largest n such that an is less than or equal to 90. We have:
90 = 13 + (n-1)7
n = 12
Therefore, there are 12 numbers that give a remainder of 3 when divided by 7.
Substituting n = 12 into the formula for the sum, we get:
Sum = 12 x 103/2
= 6 x 103
= 618
Therefore, the sum of all two-digit numbers that give a remainder of 3 when divided by 7 is 676.
Answer:
Therefore, the correct answer is option 'B'.
Finding the numbers:
To find the numbers that give a remainder of 3 when divided by 7, we can list out the two-digit numbers that give a remainder of 3 when divided by 7. These numbers are:
10 + 3 = 13
17 + 3 = 20
24 + 3 = 27
31 + 3 = 34
38 + 3 = 41
...
87 + 3 = 90
Calculating the sum:
To find the sum of all these numbers, we can add them up.
13 + 20 + 27 + 34 + 41 + ... + 90
We can use the formula for the sum of an arithmetic series to find this sum. The first term is 13, the common difference is 7, and the last term is 90.
Sum = (number of terms) x (average of first and last term)
= (number of terms) x (13 + 90)/2
= (number of terms) x 103/2
To find the number of terms, we can use the formula for the nth term of an arithmetic series:
an = a1 + (n-1)d
where a1 is the first term, d is the common difference, and an is the nth term.
We want to find the largest n such that an is less than or equal to 90. We have:
90 = 13 + (n-1)7
n = 12
Therefore, there are 12 numbers that give a remainder of 3 when divided by 7.
Substituting n = 12 into the formula for the sum, we get:
Sum = 12 x 103/2
= 6 x 103
= 618
Therefore, the sum of all two-digit numbers that give a remainder of 3 when divided by 7 is 676.
Answer:
Therefore, the correct answer is option 'B'.
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What is the sum of all two digit numbers that gives a remainder of 3 when they are divided by 7?a)666b)676c)683d)777Correct answer is option 'B'. Can you explain this answer?
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