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A warehouse is labeling computer inventory with 4-digit code

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Dhairya275
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A warehouse is labeling computer inventory with 4-digit code [#permalink] New post   Updated on: 07 Feb 2023, 02:27
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A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used.

The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?

A. 981
B. 1000
C. 1011
D. 1101
E. 1110
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B

Originally posted by Dhairya275 on 12 Sep 2013, 10:09.
Last edited by Bunuel on 07 Feb 2023, 02:27, edited 2 times in total.
Edited the question.
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Bunuel
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Re: A warehouse is labeling computer inventory with 4-digit code [#permalink] New post   12 Sep 2013, 10:54
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Bunuel wrote:
Dhairya275 wrote:
A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used.

The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?

A. 981
B. 1000
C. 1011
D. 1101
E. 1110

Help Please !!


The number of codes possible if leading zero is allowed = 10*10*10*10=10^4
The number of codes possible if leading zero is NOT allowed = 9*10*10*10=9*10^3

The difference = 10^4 - 9*10^3 = 10^3(10-9) = 10^3.

Answer: B.


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Hope it helps.
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Re: A warehouse is labeling computer inventory with 4-digit code [#permalink] New post   12 Sep 2013, 22:41
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Bunuel wrote:
Dhairya275 wrote:
A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used.

The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?

A. 981
B. 1000
C. 1011
D. 1101
E. 1110

Help Please !!


The number of codes possible if leading zero is allowed = 10*10*10*10=10^4
The number of codes possible if leading zero is NOT allowed = 9*10*10*10=9*10^3

The difference = 10^4 - 9*10^3 = 10^3(10-9) = 10^3.

Answer: B.


The most efficient way!! Thanks,
Though we can also solve by following :-
4 digit code for which the leading zero's are not allowed
0XXX - 1*9*10*10 = 900 (9 in the second place since 0 is not allowed there. We take care of that separately)
00XX - 1*1*9*10 = 90
000X - 9
0000 - 1

Total - 1000
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Re: A warehouse is labeling computer inventory with 4-digit code [#permalink] New post   12 Sep 2013, 10:53
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Dhairya275 wrote:
A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used.

The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?

A. 981
B. 1000
C. 1011
D. 1101
E. 1110

Help Please !!


The number of codes possible if leading zero is allowed = 10*10*10*10=10^4
The number of codes possible if leading zero is NOT allowed = 9*10*10*10=9*10^3

The difference = 10^4 - 9*10^3 = 10^3(10-9) = 10^3.

Answer: B.
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Re: A warehouse is labeling computer inventory with 4-digit code [#permalink] New post   12 Sep 2013, 22:19
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This question is just asking for the number of 4-digit codes that start with 0

They would be 0000 to 0999

That's 1000 codes

Choice B

t1000
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Re: A warehouse is labeling computer inventory with 4-digit code [#permalink] New post   05 Oct 2014, 01:24
This can even be solved, if we consider the number of possibilities which would have first digit as 0.
= 1*10*10*10
= 1000
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Re: A warehouse is labeling computer inventory with 4-digit code [#permalink] New post   28 Oct 2014, 22:39
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Bunuel wrote:
Dhairya275 wrote:
A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used.

The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?

A. 981
B. 1000
C. 1011
D. 1101
E. 1110

Help Please !!




The number of codes possible if leading zero is allowed = 10*10*10*10=10^4
The number of codes possible if leading zero is NOT allowed = 9*10*10*10=9*10^3

The difference = 10^4 - 9*10^3 = 10^3(10-9) = 10^3.

Answer: B.


Dear Bunuel,

The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used.

I think this calculation should not take 0000 into account because there is no non zero digit here. so it would be 1000-1=999.

Am i correct?
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Re: A warehouse is labeling computer inventory with 4-digit code [#permalink] New post   22 Nov 2014, 01:00
Bunuel wrote:
Dhairya275 wrote:
A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used.

The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?

A. 981
B. 1000
C. 1011
D. 1101
E. 1110

Help Please !!


The number of codes possible if leading zero is allowed = 10*10*10*10=10^4
The number of codes possible if leading zero is NOT allowed = 9*10*10*10=9*10^3

The difference = 10^4 - 9*10^3 = 10^3(10-9) = 10^3.

Answer: B.


Hi Bunuel, the question said leading zeros, so i assumed I had to calculate the nos like with two zeros or 3 zeros before a non-zero no is used. :cry: :cry: :cry: How do you know its just 1 zero?
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Re: A warehouse is labeling computer inventory with 4-digit code [#permalink] New post   22 Nov 2014, 08:37
sach24x7 wrote:
Bunuel wrote:
Dhairya275 wrote:
A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used.

The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?

A. 981
B. 1000
C. 1011
D. 1101
E. 1110

Help Please !!




The number of codes possible if leading zero is allowed = 10*10*10*10=10^4
The number of codes possible if leading zero is NOT allowed = 9*10*10*10=9*10^3

The difference = 10^4 - 9*10^3 = 10^3(10-9) = 10^3.

Answer: B.


Dear Bunuel,

The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used.

I think this calculation should not take 0000 into account because there is no non zero digit here. so it would be 1000-1=999.

Am i correct?


I have same doubt. Can any expert clarify? Ans should be 999.
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Re: A warehouse is labeling computer inventory with 4-digit code [#permalink] New post   02 Feb 2016, 08:23
Dhairya275 wrote:
A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used.

The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?

A. 981
B. 1000
C. 1011
D. 1101
E. 1110

Help Please !!


When the question says BETWEEN 0 and 9, should we actually include 0 and 9?
Shouldn't the question say between 0 and 9 inclusive. I have seen question as a trap answer in DS. So the query.
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Re: A warehouse is labeling computer inventory with 4-digit code [#permalink] New post   16 May 2019, 09:10
Dhairya275 wrote:
A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used.

The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?

A. 981
B. 1000
C. 1011
D. 1101
E. 1110

Help Please !!


leading with 0 ; 10^4
not leading with 0 ; 9*10^3
so difference ; 10^4-9*10^3 ; 10^3 ; 1000
IMO B
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Re: A warehouse is labeling computer inventory with 4-digit code [#permalink] New post   31 Jan 2021, 20:37
0 to 9 is 10 digits. This is a permutation with repeats allowed.

Total (where leading zeros are possible) = 10 x 10 x 10 x 10 = 10^4
Total (where leading zeros are not possible) = 9 x 10 x 10 x 10 = 9000

10000 - 9000 = 1000

We only care about whether the first digit is a zero for the second permutation. Any zeros after the first one are fair game.

Answer is B.
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Re: A warehouse is labeling computer inventory with 4-digit code [#permalink] New post   07 Feb 2023, 01:25
Bunuel, why shouldn't we consider leading 2 or 3 zeros before any non zero number including one leading zero??
Please clarify.
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Re: A warehouse is labeling computer inventory with 4-digit code [#permalink] New post   07 Feb 2023, 02:48
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GMATmona07 wrote:
Bunuel, why shouldn't we consider leading 2 or 3 zeros before any non zero number including one leading zero??
Please clarify.


Those codes are already included in 9*10^3. The point is, a code with 2 or more leading zeroes has the first 0, so it's already accounted in 9*10^3. So, all codes with 00.. are already in 9*10^3 because all codes with 00.. still start with 0: 00..

Hope it's clear.
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Re: A warehouse is labeling computer inventory with 4-digit code [#permalink]
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