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# Each item sold at a market is labelled with a 2-, 3-, or 4- digit code

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Intern
Joined: 11 Oct 2017
Posts: 22
Each item sold at a market is labelled with a 2-, 3-, or 4- digit code  [#permalink]

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09 Nov 2017, 18:19
2
00:00

Difficulty:

25% (medium)

Question Stats:

74% (02:11) correct 26% (01:57) wrong based on 120 sessions

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Each item sold at a market is labelled with a 2-, 3-, or 4- digit code where each digit is selected from the digits 1 through 9, inclusive. If the digits may be repeated and if the same digits used in a different order represent a different code, how many different items at the market can be labeled with a unique code?

A. 216
B. 504
C. 3,024
D. 3,600
E. 7,371

Math Expert
Joined: 02 Aug 2009
Posts: 7444
Re: Each item sold at a market is labelled with a 2-, 3-, or 4- digit code  [#permalink]

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09 Nov 2017, 19:35
3
1
Each item sold at a market is labelled with a 2-, 3-, or 4- digit code where each digit is selected from the digits 1 through 9, inclusive. If the digits may be repeated and if the same digits used in a different order represent a different code, how many different items at the market can be labeled with a unique code?

A. 216
B. 504
C. 3,024
D. 3,600
E. 7,371

2-digit code = 9*9
3-digit code = 9*9*9
4-digit code = 9*9*9*9

total = $$9*9+9*9*9+9*9*9*9=9*9(1+9+9*9)=81*(1+9+81)=81*91$$

no more calculations required ..
UNIT's digit will be 1*1=1 and only choice with units digit as 1 is E
ans E
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Joined: 07 Jun 2017
Posts: 171
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
Re: Each item sold at a market is labelled with a 2-, 3-, or 4- digit code  [#permalink]

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09 Nov 2017, 23:19
9∗9+9∗9∗9+9∗9∗9∗9=9∗9(1+9+9∗9)=81∗(1+9+81)=81∗91

answer should be E , the only answer has last digit 1
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Re: Each item sold at a market is labelled with a 2-, 3-, or 4- digit code  [#permalink]

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14 Nov 2017, 07:20
Each item sold at a market is labelled with a 2-, 3-, or 4- digit code where each digit is selected from the digits 1 through 9, inclusive. If the digits may be repeated and if the same digits used in a different order represent a different code, how many different items at the market can be labeled with a unique code?

A. 216
B. 504
C. 3,024
D. 3,600
E. 7,371

The number of 2-digit codes is 9 x 9 = 9^2, the number of 3-digit codes is 9 x 9 x 9 = 9^3, and the number of 4-digit codes is 9 x 9 x 9 x 9 = 9^4, so the total number of codes is:

9^2 + 9^3 + 9^4 = 9^2(1 + 9 + 9^2) = 81(91) = 7371

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Re: Each item sold at a market is labelled with a 2-, 3-, or 4- digit code  [#permalink]

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23 Nov 2018, 08:53
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Re: Each item sold at a market is labelled with a 2-, 3-, or 4- digit code   [#permalink] 23 Nov 2018, 08:53
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