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

110 111 271 300 304

any easy way to do this question? here is how i did it... let xyz be a 3-digit#, first, let Z=7, we have 10 options ( 0-9)for x and 10 options for y, then we get 10 x 10 =100, same logic is applied when y =7 and x = 7, we get 300 times. is it correct?

started using the same method, but got stuck in the middle of the road.

Bunuel, could you please clarify if slot method can be applied to this problem. Thanks in advance.

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

110 111 271 300 304

any easy way to do this question? here is how i did it... let xyz be a 3-digit#, first, let Z=7, we have 10 options ( 0-9)for x and 10 options for y, then we get 10 x 10 =100, same logic is applied when y =7 and x = 7, we get 300 times. is it correct?

started using the same method, but got stuck in the middle of the road.

Bunuel, could you please clarify if slot method can be applied to this problem. Thanks in advance.

Re: How many times will the digit 7 be written? [#permalink]
14 Jul 2014, 16:54

1

This post received KUDOS

Alternate solution:

Using probability of occurrence = desired outcomes / total outcomes, desired outcomes = probability x total outcomes.

total outcomes = 1000.

probability of occurrence - to simplify this, the question statement could be interpreted as "what is the probability that the digit 7 is picked at least once when 3 digits are chosen at random?"

probability of at least one 7 = 7 in first digit OR 7 in second digit OR 7 in third digit = 1/10 + 1/10 + 1/10 = 3/10

desired outcomes = probability x total outcomes = 3/10 x 1000 = 300.

Re: How many times will the digit 7 be written? [#permalink]
17 Jul 2014, 21:23

2

This post received KUDOS

The first time I did the question, my answer was C : 271 since I thought the question is "how many numbers from 0 - 1000, that contain the 7 digit". So I counted 77, 707,717,....,777,...797, 771, 772, 773,..., or 779 as one. That may be the reason why 23% of people who answered the question decided to pick answer C. That is really interesting question _________________

......................................................................... +1 Kudos please, if you like my post

Re: How many times will the digit 7 be written? [#permalink]
18 Jul 2014, 13:23

vad3tha wrote:

The first time I did the question, my answer was C : 271 since I thought the question is "how many numbers from 0 - 1000, that contain the 7 digit". So I counted 77, 707,717,....,777,...797, 771, 772, 773,..., or 779 as one. That may be the reason why 23% of people who answered the question decided to pick answer C. That is really interesting question

Yes, I made the same mistake.

gmatclubot

Re: How many times will the digit 7 be written?
[#permalink]
18 Jul 2014, 13:23