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How many 3s ?

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by Whitney Garner » Wed Oct 17, 2012 6:36 am
sohailmbaprep wrote:Q) How many times would 3 appear in all the numbers from 255 to 432 (both inclusive) ?
How can i find that ?
Hi sohailmbaprep!

Just to verify, are you asking how many multiples of 3 are in this list, OR if we factored every number in this list, how many 3s would we have total?

For example, if I had the list from 1 - 30 inclusive. The multiples of 3 would just be:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30 = 10 total multiples.

BUT, if I wanted to know how many 3s are in this if I completely factor each number, I would have to remember that #s like 9 and 18 have two-3s each (because they are divisible by 9), and 27 would have three-3s (because it is 3^3).

:)
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by AIM TO CRACK GMAT » Wed Oct 17, 2012 8:31 am
sohailmbaprep wrote:
Q) How many times would 3 appear in all the numbers from 255 to 432 (both inclusive) ?
How can i find that ?


255-432

1) 263,273,283,293- 4 tyms 3 is repeated
403, 413,423,430,431,432- 6 times 3 is repeated... therefore= 6+4= 10 times repeated...

2)300-399= 3 appears 100 times only in the hundreds column
330-339= 3 appears 10 times only in tens column
303-393= 3 appears 10 times in the units column

we calculated all the 3s from 100s, 10s and units... 100+10+10 and 10 from Step 1= 130... so 3 appears 130 times in 255 to 432... i hope it is clear...
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