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What is the sum of the first 100 positive odd numbers?
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25 Nov 2016, 01:48

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This one is about pattern recognition. Set up a table as follows:

Number Sum 1 1 3 4 5 9 7 16 9 25

Now as you see, the sum always equals the perfect square of the number of odd integers that you want to sum. So the sum of the first 5 odd integers is 5^2 = 25. The pattern continues. Thus, the sum of the first 100 odd integers will be equal to 100^2 = 10,000. The correct answer is (D).

Re: What is the sum of the first 100 positive odd numbers?
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25 Nov 2016, 05:01

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Top Contributor

MathRevolution wrote:

What is the sum of the first 100 positive odd numbers?

A. 5,000 B. 7,500 C. 8,000 D. 10,000 E. 12,000

Before answering any GMAT quant problem, always check the answer choices first Here, the answer choices are somewhat spread apart, which means we can be somewhat aggressive in our estimations.

Nice formula: 1 + 2 + 3 . . . + n = (n)(n + 1)/2

Let's use the above formula to find the sum of the first 200 integers (including odds AND evens) 1 + 2 + 3 . . . + 199 + 200 = (200)(200 + 1)/2 = (200)(201)/2 = (100)(201) = 20,100 So, the sum of the first 200 integers is 20,100 HALF of those integers are ODD and HALF are even. So, this sum includes the sum of the first 100 ODD integers and the sum of the first 100 EVEN integers. So, the sum of the first 100 ODD integers is APPROXIMATELY 20,100/2 20,100/2 = 10,050 So, the sum of the first 100 ODD integers ≈ 10,050 Answer choice D is the only one that's close to 10,050 so it must be the correct answer.

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19 Jul 2018, 20:56

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