What is the sum of all three-digit positive integers that are multiples of 7?
Answer and explanation
Correct answer: B. 70336
- Step 1: Find smallest three-digit multiple of 7: 100 / 7 = 14.28... => 15 * 7 = 105.
- Step 2: Find largest three-digit multiple of 7: 999 / 7 = 142.71... => 142 * 7 = 994.
- Step 3: The numbers form an arithmetic progression with a = 105, d = 7, l = 994.
- Step 4: Number of terms: n = (994 - 105) / 7 + 1 = 889 / 7 + 1 = 127 + 1 = 128 terms.
- Step 5: Sum formula: S_n = (n / 2) (a + l) = (128 / 2) (105 + 994) = 64 * 1099 = 70,336.
Answer
70336.
Why not the others: '70000' is a rounded estimate; '65432' miscounts the number of terms as 119; '72450' uses 132 terms.
Practise more Algebra, Trigonometry and Probability.
Free questions with an explanation for every one, and full timed Qatar Senior Secondary Certificate (Thanaweya) mock tests.
More Algebra, Trigonometry and Probability questions
- What is the modulus and principal argument of the complex number z = -1 + i * sqrt(3)?
- Using De Moivre's Theorem, evaluate (cos(pi/6) + i sin(pi/6))^6.
- In the binomial expansion of (2x - 1/x)^8, what is the term independent of x (the constant term)?
- Solve the trigonometric equation 2 cos^2(x) - cos(x) - 1 = 0 on the interval [0, 2pi).
- A committee of 4 students is to be selected at random from 6 boys and 5 girls. What is the probability that the committee contains exactly 2…
- Solve the system of linear equations using Cramer's Rule:
2x + 3y = 8
5x - y = 3