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In the set of positive integers from 1 to 500, what is the s

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by BTGmoderatorDC » Mon Dec 17, 2018 10:32 pm

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In the set of positive integers from 1 to 500, what is the sum of all the odd multiples of 5?

A. 10,000
B. 12,500
C. 17,500
D. 22,500
E. 25,000

OA B

Source: Magoosh
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by [email protected] » Tue Dec 18, 2018 8:11 am
Hi All,

We're asked for the sum of all the ODD multiples of 5 from 1 to 500. This question is essentially about Arithmetic and can be solved with 'bunching.'

There are 100 multiples of 5 between 1 and 500: 1(5)..... (100)(5), but the question asks for only the ODD multiples of 5 (meaning that we should NOT include 10, 20, 30, etc.). Half of those 100 multiples are EVEN and half are ODD, so we know that there will be 50 numbers to consider.

If we 'bunch' the smallest and largest, we get:
5 + 495 = 500

Then the next smallest and next largest....
15 + 485 = 500

We can 'pair up' terms in this way, which will give us 25 'pairs' of 500...
(25)(500) = 12,500

Final Answer: B

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by Scott@TargetTestPrep » Sun Mar 03, 2019 6:35 pm
BTGmoderatorDC wrote:In the set of positive integers from 1 to 500, what is the sum of all the odd multiples of 5?

A. 10,000
B. 12,500
C. 17,500
D. 22,500
E. 25,000

OA B

Source: Magoosh
The odd multiples of 5 from 1 to 500 are 5, 15, 25, ..., 495.

Because this is an evenly-spaced set, the average of these multiples of 5 is (495 + 5)/2 = 250.

The number of these multiples of 5 is (495 - 5)/10 + 1 = 50.

So the sum is 250 x 50 = 12,500.

Answer: B

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