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

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CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
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GMAT: INSIGHT
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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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14 Oct 2015, 20:23
1
6
00:00

Difficulty:

35% (medium)

Question Stats:

72% (02:08) correct 28% (01:42) wrong based on 85 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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15 Oct 2015, 03:50
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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

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

P.S.: GMAT options are usually in either descending or ascending order.
Intern
Joined: 29 Mar 2015
Posts: 22
Re: In how many no. between 100 and 1000 at least one of their digits is 7  [#permalink]

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17 Oct 2015, 08:39
1
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.
Intern
Joined: 11 Dec 2016
Posts: 15
Location: India
GMAT 1: 720 Q48 V42
GPA: 3.44
Re: In how many no. between 100 and 1000 at least one of their digits is 7  [#permalink]

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11 Feb 2019, 12:18
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.
Re: In how many no. between 100 and 1000 at least one of their digits is 7   [#permalink] 11 Feb 2019, 12:18
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