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How many 3s

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How many 3s

by sandipgumtya » Sat Jul 04, 2015 11:06 pm
If we write numbers from 1 to 200,then how many times will the digit 3 be written?

A-20
B-38
C-40
D-42
E-44

OA is B.
But I am getting C as answer.
Experts Pl help.

Sandip Gumtya
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by Ian Stewart » Sun Jul 05, 2015 2:46 am
You have the right answer - we'd write '3' as a units digit exactly 20 times, and as a tens digit exactly 20 times, so we'd write the digit 40 times in total.

'38' is the answer to a different question: how many whole numbers between 1 and 200 contain the digit '3'? Because the answer to the previous question counts "33" and "133" twice, the answer to this question would be 40 - 2 = 38.

So perhaps the source was confused about what question they were asking - where is the question from?
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by theCEO » Sun Jul 05, 2015 3:00 am
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by sandipgumtya » Sun Jul 05, 2015 9:37 am
I think in 33 and 133 we need to count two 3s in each case.

Sandip.
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by sandipgumtya » Sun Jul 05, 2015 9:57 am
@ian:The qus is from prep4gmat.they have even provided explanation for ans.
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by sandipgumtya » Sun Jul 05, 2015 9:39 pm
Brent,Mitch need ur help.
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by blackiscorpio » Mon Jul 06, 2015 11:34 am
I think the answer should be 40. If we write number from 1 to 100 then each digit appears 20 times. So from 1 to 200 '3' should appear 40 times
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by Brent@GMATPrepNow » Mon Jul 06, 2015 12:28 pm
sandipgumtya wrote:If we write numbers from 1 to 200,then how many times will the digit 3 be written?

A-20
B-38
C-40
D-42
E-44
If we write the integers from 0 to 99 as TWO-DIGIT integers (00, 01, 02, 03, ....98, 99), then:
- we have 100 integers, each with 2 digits for a total of 200 digits.
1/10 of those digits are 0's, 1/10 of those digits are 1's, 1/10 of those digits are 2's, AND...
1/10 of those digits are 3's
So, the number of 3's = (1/10)(200) = 20

Next, if we write the integers from 100 to 199, we'll get another 20 3's

So, the number of 3's = 20 + 20 = [spoiler]40 = C[/spoiler]

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by Satya.Achanta » Mon Jul 13, 2015 9:13 am
If I am correct you counted 30 to 39 as 10 that includes 33 also, so it should be total 9 and same for 133 as well
-Satya Achanta
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