A warehouse is labeling computer inventory with 4-digit code

Question

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

Bunuel · Accepted Answer

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Bunuel · Answer

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.

tchang · Answer

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

shameekv · Answer

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

Thoughtosphere · Answer

This can even be solved, if we consider the number of possibilities which would have first digit as 0.
= 1*10*10*10
= 1000

sach24x7 · Answer

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?

vietnammba · Answer

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:

How do you know its just 1 zero?

desaichinmay22 · Answer

I have same doubt. Can any expert clarify? Ans should be 999.

hwgmat2015 · Answer

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.

Archit3110 · Answer

leading with 0 ; 10^4
not leading with 0 ; 9*10^3 
so difference ; 10^4-9*10^3 ; 10^3 ; 1000
IMO B

CEdward · Answer

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.

GMATmona07 · Answer

Bunuel , why shouldn't we consider leading 2 or 3 zeros before any non zero number including one leading zero??
Please clarify.

Bunuel · Answer

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:  0 0..

Hope it's clear.

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A warehouse is labeling computer inventory with 4-digit code

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A warehouse is labeling computer inventory with 4-digit code

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