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Re: GMAT CLUB - PS. (Dont agree with OE -but agree with OA) [#permalink]

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21 Aug 2008, 12:18

I figured it like this: (and I realize there is a formula for this too, but I'm not sure what it is).

This method took me about 90 seconds to complete.

Answer: 300

Units Digit: 10-7's per 100 numbers * 10 groups of 100 from 1 - 1000 = 100 Tens Digit: 10-7's in the 70's section of each group of 100 so 10*10 = 100 Hundreds digit: 100-7's from 700 to 799, so 100 again

Total = 300.

Am I forgetting anything?

x2suresh wrote:

How many times will the digit 7 be written when listing the integers from 1 to 1000?

110 111 271 300 304

This problem is from GMACLUB test. I agree with answer but not the explanation.

Let see how others will tackle this problem.

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Re: GMAT CLUB - PS. (Dont agree with OE -but agree with OA) [#permalink]

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21 Aug 2008, 12:52

When counting the times a certain number appears, this might be a more scientific method of counting.

If you're counting units digits, you know that any single number will appear in the units digit column 1 time out of 10. If you're counting 1 to n, then multiply the number of times that digit appears out of 10 * n/10: Example: looking for # of 5s in the units column from 1 to 600. There will be a 5 in each group of 10. So take 600 (the 1 to 600) and divide 600 by 10, for 60. There will be 60-5's in the units column from 1 to 600.

Tens column: You see there will be 10-5's in the tens column per group of 100. Divide the last number by the size of the group. 600 / 100 = 6 groups, so 60-50s in the tens digit.

Hundreds column: You know there will be 5's here only in 500-599. So that's 100 numbers per group of 1000. Since we don't go all the way to 1000, we know that's 1. so It's 100*1. what's the total? 60+60+100 = 220.

LOL....I'm not sure this makes it any easier!!

hibloom wrote:

I got D with similar counting method and took about 90 sec But I would love to know some shorter method

_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Re: GMAT CLUB - PS. (Dont agree with OE -but agree with OA) [#permalink]

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21 Aug 2008, 13:10

x2suresh wrote:

zoinnk wrote:

x2suresh wrote:

How many times will the digit 7 be written when listing the integers from 1 to 1000?

110 111 271 300 304

This problem is from GMACLUB test. I agree with answer but not the explanation.

Let see how others will tackle this problem.

For every 100 numbers, 7 appears 10 times (x07, x17, x27, x37, x47, x57, x67, x77, x87, x97) --> Do you belieive 7 appeared 10 times or 11 times here. Don't worry your answer is correct.. Here you treated x77 (7 in the 10th place ignored.. and reconsider when "Ten digit calculations" ) 10*10 = 100

Tens digit: For every 100 numbers, 7 appears 10 times (x70, x71, x72, x73, x74, x75, x76, x77, x78, x79) 10*10 = 100

Hundreds digit: 7 appears in the hundreds digit in every number from 700-799 799-700+1 = 100

Total 7s: 100+100+100 = 300

I ignored the 7 in the tens place for that part of the calculation because i was just counting the 7s in the ones digit.

Re: GMAT CLUB - PS. (Dont agree with OE -but agree with OA) [#permalink]

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21 Aug 2008, 13:14

Hi Allen and Zoink,

Agree with both of you.. Now I agree with OE approach too.. OE is also explained similar to your approach. ( You ignored the x77 tenth digit 7 when counting unit digit calculations and reconsider this 7 when tenth digit calucations.. see zoink reply)

My approach was:

7 occur only once. (7XX, X7X,XX7) = "7 is one of the digit" * "select other than 7" * "select other than 7" * (no of ways 7 can appear ) = 1*9*9* 3 =243 7 occur twice (77X,7X7,X77) = "7 is two of the digit" * "select 3rd one other than 7" * ( Each number 7 written twice)