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In how many no. between 100 and 1000 at least one of their digits is 7

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In how many no. between 100 and 1000 at least one of their digits is 7  [#permalink]

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New post 14 Oct 2015, 21:23
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7
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A
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D
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Difficulty:

  35% (medium)

Question Stats:

71% (02:10) correct 29% (01:49) wrong based on 137 sessions

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In how many no. between 100 and 1000 at least one of their digits is 7?

(A) 900
(B) 648
(C) 720
(D) 252
(E) 729

Source: http://www.GMATinsight.com

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In how many no. between 100 and 1000 at least one of their digits is 7  [#permalink]

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New post 15 Oct 2015, 04:50
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GMATinsight wrote:
In how many no. between 100 and 1000 at least one of their digits is 7?

(A) 900
(B) 648
(C) 720
(D) 252
(E) 729

Source: http://www.GMATinsight.com


We have 900 3-digit numbers between 100 and 1000.

So # of numbers with atleast 1 7-digit = total - no 7 digits = 900 - 8*9*9 = 900-648=252

D is the correct answer.

P.S.: GMAT options are usually in either descending or ascending order.
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Re: In how many no. between 100 and 1000 at least one of their digits is 7  [#permalink]

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New post 17 Oct 2015, 09:39
2
Let's count the number of occurrences with only one 7:

(1) 7XX: 1 * 9 * 9 = 81
(2) X7X: 8 * 1 * 9 = 72
(3) XX7: 8 * 9 * 1 = 72

81 + 72 + 72 = 225

At this point we can already see that the answer must be D since the choice are very dispersed.

Anyways, let's count number of occurrences with two 7s:

(1) 77X: 1 * 1 * 9 = 9
(2) X77: 8 * 1 * 1 = 8
(3) 7X7: 1 * 9 * 1 = 9

9 + 8 + 9 = 26

Number 777 is missing. So the total becomes

225 + 26 + 1 = 252

GMATinsight I feel that the question would become more interesting (and I think also more realistic) if the answer choices are less dispersed. Maybe something you can think about.
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Re: In how many no. between 100 and 1000 at least one of their digits is 7  [#permalink]

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New post 11 Feb 2019, 13:18
1
My solution.

there are 19 numbers containing atleast one seven from 100 to 200. The same will be true for the eight following hundreds sequences except the 700-800 sequence. The 700 - 800 sequence contains 100 numbers that has atleast one seven in it .
So the total no of digits can be calculated as 8*19 + 100 = 252. Ans D

Give a kudos if this solution helped you.
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Re: In how many no. between 100 and 1000 at least one of their digits is 7  [#permalink]

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New post 18 Feb 2019, 00:16
1
GMATinsight wrote:
In how many no. between 100 and 1000 at least one of their digits is 7?

(A) 900
(B) 648
(C) 720
(D) 252
(E) 729

Source: http://www.GMATinsight.com


Method 1:

From 100-199 there are 19 numbers with atleast one of their digits 7 {107, 117, 127, 137, 147, 157, 167, 177, 187, 197}

Likewise every 100 numbers except series 700-799 will have 19 numbers with one of their digits 7

so total such numbers = 19*8

from 700-799, all 100 numbers will have one of their digits 7 hence total required numbers = 19*8+100 = 252

Method 2:

Total Three digit numbers from 100-1000 = 900

Total three digit numbers without use of digit 7 = 8*9*9 = 648

Total Numbers with one of the digits 7 = 900 - 648 = 252

Answer: Option D
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Re: In how many no. between 100 and 1000 at least one of their digits is 7   [#permalink] 18 Feb 2019, 00:16
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