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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, 17:19
1
00:00

Difficulty:

35% (medium)

Question Stats:

70% (02:12) correct 30% (02:05) wrong based on 89 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: 7035
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, 18:35
1
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 07 Jun 2017
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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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09 Nov 2017, 22:19
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, 06:20
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 &nbs [#permalink] 14 Nov 2017, 06:20
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