GMAT Prep
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?
A. 3,024
B. 4,536
C. 5,040
D. 9,000
E. 10,000
OA B.
A company plans to assign identification numbers to its
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Take the task of creating the identification numbers and break it into stages.AAPL wrote:GMAT Prep
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?
A. 3,024
B. 4,536
C. 5,040
D. 9,000
E. 10,000
OA B.
Stage 1: Select the first digit of the identification number
The first digit can be 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 1 in 9 ways
Stage 2: Select the second digit of the identification number
The second digit can be any digit from 0 to 9 OTHER THAN the digit chosen in stage 1
So, we can complete stage 2 in 9 ways .
Stage 3: Select the third digit of the identification number
The third digit can be any digit from 0 to 9 OTHER THAN the 2 digits digit chosen in stages 1 and 2
So we can complete this stage in 8 ways.
Stage 4: Select the fourth digit of the identification number
The third digit can be any digit from 0 to 9 OTHER THAN the 3 digits digit chosen earlier
So we can complete this stage in 7 ways.
By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create all of the identification numbers) in (9)(9)(8)(7) ways (= 4,536 ways)
Answer: B
--------------------------
Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat ... /video/775
You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776
Then you can try solving the following questions:
EASY
- https://www.beatthegmat.com/what-should ... 67256.html
- https://www.beatthegmat.com/counting-pr ... 44302.html
- https://www.beatthegmat.com/picking-a-5 ... 73110.html
- https://www.beatthegmat.com/permutation ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html
MEDIUM
- https://www.beatthegmat.com/combinatori ... 73194.html
- https://www.beatthegmat.com/arabian-hor ... 50703.html
- https://www.beatthegmat.com/sub-sets-pr ... 73337.html
- https://www.beatthegmat.com/combinatori ... 73180.html
- https://www.beatthegmat.com/digits-numbers-t270127.html
- https://www.beatthegmat.com/doubt-on-se ... 71047.html
- https://www.beatthegmat.com/combinatori ... 67079.html
DIFFICULT
- https://www.beatthegmat.com/wonderful-p ... 71001.html
- https://www.beatthegmat.com/permutation ... 73915.html
- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladi ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html
Cheers,
Brent
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Immediate application of the Multiplicative Principle:AAPL wrote:GMAT Prep
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?
A. 3,024
B. 4,536
C. 5,040
D. 9,000
E. 10,000
\[\begin{array}{*{20}{c}}
{\underline {{\text{not}}\,\,0} } \\
9
\end{array}\begin{array}{*{20}{c}}
{\underline {{\text{nr}}} } \\
9
\end{array}\begin{array}{*{20}{c}}
{\underline {{\text{nr}}} } \\
8
\end{array}\begin{array}{*{20}{c}}
{\underline {{\text{nr}}} } \\
7
\end{array}\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{Multipl}}{\text{.}}\,{\text{Principle}}} \,\,\,\,? = {9^2} \cdot 8 \cdot 7\,\,\,\,\,\,\,\,\,\,\left[ {nr = {\text{no}}\,\,{\text{repetition}}} \right]\]
\[\left\langle ? \right\rangle = \left\langle {{9^2}} \right\rangle \cdot \left\langle {8 \cdot 7} \right\rangle = 1 \cdot 6 = 6\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ {\left\langle N \right\rangle = {\text{units}}\,\,{\text{digit}}\,\,{\text{of}}\,\,N} \right]\]
Just one alternative choice with unit´s digit equal to the correct one... we are done!
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7247
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
There are 9 choices for the first digit (1 through 9, inclusive). The second digit can be any of the 10 digits (0 through 9, inclusive) EXCEPT it can't repeat the first digit; thus, there are 9 options for the second digit. The third digit can't repeat either of the first two digits, so there are 8 options. Similarly, the fourth digit can't repeat any of the first 3 digits, so there are 7 options. Thus, the total number of options is 9 x 9 x 8 x 7 = 4,536.AAPL wrote:GMAT Prep
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?
A. 3,024
B. 4,536
C. 5,040
D. 9,000
E. 10,000
Answer: B
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews