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# In how many no. between 100 and 1000 exactly Two of the digits is 5?

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In how many no. between 100 and 1000 exactly Two of the digits is 5?  [#permalink]

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14 Oct 2015, 21:45
3
3
00:00

Difficulty:

5% (low)

Question Stats:

82% (01:46) correct 18% (01:53) wrong based on 90 sessions

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In how many no. between 100 and 1000 exactly Two of the digits is 5?

(A) 648
(B) 512
(C) 252
(D) 225
(E) 26

Source: http://www.GMATinsight.com

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Re: In how many no. between 100 and 1000 exactly Two of the digits is 5?  [#permalink]

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15 Oct 2015, 05:13
2
GMATinsight wrote:
In how many no. between 100 and 1000 exactly Two of the digits is 5?

(A) 648
(B) 512
(C) 252
(D) 225
(E) 26

Source: http://www.GMATinsight.com

Tricky. +1

Realise that the asked arrangements = 55X , 5X5 where X can be anything from 0 to 9 excluding 5 and Y55 where Y $$\neq$$5 or 0

Scenarios possible =

55X = 1*1*9 = 9
5X5 = 1*9*1 = 9
Y55 = 8*1*1 = 8

Total = 9+9+8=26

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Re: In how many no. between 100 and 1000 exactly Two of the digits is 5?  [#permalink]

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15 Oct 2015, 05:52
We have here 2C3=3 combinations because there are always two 5's
55x:1*1*9+
5x5:1*1*9+
x55:8*1*1 because we must have a 3 digit number, means first digit must be >0, so we have 8 options for that digit (1,2,3,4,6,7,8,9)
26 Ways to do that.
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Re: In how many no. between 100 and 1000 exactly Two of the digits is 5?  [#permalink]

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15 Oct 2015, 06:00
GMATinsight wrote:
In how many no. between 100 and 1000 exactly Two of the digits is 5?

(A) 648
(B) 512
(C) 252
(D) 225
(E) 26

Source: http://www.GMATinsight.com

It's simple can be solved by elimination of answer choices.

Option A and B are too large, not possible. Even C & D are large to have correct choice.

Ans : E

Alternatively
X55 --- 8 possibility
5X5 --- 9 possibility
55X --- 9 possibility

8+9+9=26

Ans E
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Re: In how many no. between 100 and 1000 exactly Two of the digits is 5?  [#permalink]

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16 Jan 2019, 22:10
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Re: In how many no. between 100 and 1000 exactly Two of the digits is 5?   [#permalink] 16 Jan 2019, 22:10
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