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How many four-digit numbers have at least one digit repeating?

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Manager
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Joined: 17 Jan 2017
Posts: 61
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How many four-digit numbers have at least one digit repeating?  [#permalink]

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New post 11 May 2018, 12:14
5
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (01:51) correct 36% (01:36) wrong based on 46 sessions

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How many four-digit numbers have at least one digit repeating?
A. 3000
B. 4464
C. 4500
D. 4536
E. 5000

Source: ExpertsGlobal
Director
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Joined: 02 Oct 2017
Posts: 735
Re: How many four-digit numbers have at least one digit repeating?  [#permalink]

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New post 11 May 2018, 14:21
1
2
Total no of 4 digit numbers- number of 4 digit when no digit repeat

Total Number of 4 digit number=9000 (from 1000-9999)

No digit repeat in 4 digit number=9*9*8*7(first 9 as zero can't come in thousand place as it will no longer be 4 digit number
One digit has already choosen for thousand place so 9 digit choice left for hundred place

Similarly 8 and 7 for ten and unit place

=9000-9*9*8*7
=4464

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Joined: 29 Dec 2017
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Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33
GMAT 2: 690 Q47 V37
GMAT 3: 710 Q50 V37
GPA: 3.25
WE: Marketing (Telecommunications)
Re: How many four-digit numbers have at least one digit repeating?  [#permalink]

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New post 11 May 2018, 20:35
push12345 wrote:

=9000-9*9*8*7
=4464



Everething is perfect, but I would add a shortcut to save some time:

9*9*8*7 = 81*56 = ....6
9000 - ....6= .....4

The only one option with 4 as a unit digit is 4464. Answer (B)
GMAT Club Bot
Re: How many four-digit numbers have at least one digit repeating? &nbs [#permalink] 11 May 2018, 20:35
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How many four-digit numbers have at least one digit repeating?

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