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14 Oct 2015, 21:23
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (02:07) correct
29%
(01:52)
wrong
based on 184
sessions
History
Date
Time
Result
Not Attempted Yet
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: https://www.GMATinsight.com
(A) 900
(B) 648
(C) 720
(D) 252
(E) 729
Source: https://www.GMATinsight.com
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17 Oct 2015, 09:39
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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.
(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.
ENGRTOMBA2018
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Last visit: 01 Dec 2021
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Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
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15 Oct 2015, 04:50
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GMATinsight
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.
