A company will create different ID numbers for its employees. Senior

Question

A company will create different ID numbers for its employees. Senior-level employees will receive 4-digit ID numbers, and junior level employees will receive 5-digit ID numbers. If the first digit of any ID number cannot be zero, and if no digits will be repeated in any ID number, what is the ratio of the total number of senior level ID numbers possible to the total number of junior level ID numbers possible?

A. 1/12
B. 1/6
C. 1/4
D. 1/3
E. 1/2

A. 1/12
B. 1/6
C. 1/4
D. 1/3
E. 1/2

pushpitkc · Answer

When we read this question, the important takeaway are

1. The first digit of any ID number will not be 0.
2. Every Senior-level employee will have a 4-digit ID number
3. Every Junior-level employee will have a 5-digit ID number
4. No digits can be repeated in any employee's ID number

The total number of Senior-Level employees possible is 9*9*8*7
Similarly, the total number of Junior-Level employees possible is 9*9*8*7*6

Hence, the ratio of Senior-level employee ID's to Junior-level employee ID's is  \frac{9*9*8*7}{9*9*8*7*6} = \frac{1}{6}   (Option B)

globaldesi · Answer

Ratio = total ways to form ID for seniors/ total ways to form ID for junior
= 9*9*8*7/9*9*8*7*6
=1/6
Hence B

JeffTargetTestPrep · Answer

The first digit of a senior-level ID number can be any of the 9 digits 1-9, inclusive (can’t be zero). The second digit can be any of the 10 digits (0-9, inclusive), but it can’t be a repeat of the previous digit. Thus, there are 9 possibilities. The third digit can not repeat either of the two previous digits, so there are only 8 possibilities. The fourth digit cannot repeat any of the previous digits, so there are 7 possibilities. Thus, we have a total of 9 x 9 x 8 x 7 possible senior-level IDs.

Determination of the possible number of junior-level IDs is identical to the process for senior-level IDs, except there are 5 numbers in the junior-level ID: 9 x 9 x 8 x 7 x 6 possibilities.

Thus, the ratio of the number of senior level IDs to junior level IDs is:

(9 x 9 x 8 x 7)/(9 x 9 x 8 x 7 x 6) = 1/6

Answer: B

avi94 · Answer

I'm sorry I'm a little confused, it says that no number can be repeated in any ID number so for the junior level shouldn't it be 6x5x4x3x2?

VeritasPrepErika · Answer

This is an understandable misinterpretation of the problem — what the problem means is that no digit can be repeated in any  individual  ID number. So it's fine if two different employees have a digit in common, so long as that digit appears only once in each of their ID numbers.

We can also think about the implications of this misinterpretation logically: if digits couldn't be shared among any employees, the company couldn't have more than two employees. There are 10 digits in total. So two employees would eat up 8-10 digits, depending on their level. It wouldn't make much sense for there to be employee ID numbers if there were only two employees, and the distinction between "senior" and "junior" employees would be largely meaningless. The GMAT tends to write reasonable scenarios, and this scenario doesn't seem particularly reasonable, so we should look to see if there's a different, more reasonable interpretation.

avi94 · Answer

VeritasPrepErika

Thank you!

A company will create different ID numbers for its employees. Senior

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