What is 40% of the sum of the first 175 natural numbers?
Answer and explanation
Correct answer: 6160
First calculate the sum of the first 175 natural numbers using Sₙ = n(n + 1)/2. Thus S₁₇₅ = 175 × 176 / 2 = 175 × 88 = 15400. Next, express 40% as 40/100 = 2/5. Therefore, 40% of the required sum is (2/5) × 15400 = 2 × 3080 = 6160. Hence option C is correct. Another check is that 20% of 15400 is 3080, so 40% must be twice that amount, or 6160. Options A, B, and D do not result from applying 2/5 to 15400; they may come from an incorrect sum or percentage calculation. The order of operations matters: find the complete natural-number sum first, then calculate its percentage.
Frequently asked questions
What is the correct answer to this question?
6160
Why is this the correct answer?
First calculate the sum of the first 175 natural numbers using Sₙ = n(n + 1)/2. Thus S₁₇₅ = 175 × 176 / 2 = 175 × 88 = 15400. Next, express 40% as 40/100 = 2/5. Therefore, 40% of the required sum is (2/5) × 15400 = 2 × 3080 = 6160. Hence option C is correct. Another check is that 20% of 15400 is 3080, so 40% must be twice that amount, or 6160. Options A, B, and D do not result from applying 2/5 to 15400; they may come from an incorrect sum or percentage calculation. The order of operations matters: find the complete natural-number sum first, then calculate its percentage.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sum of first n natural numbers.
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