Each student at a certain business school is assigned a 4-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?
A. 9,000
B. 3,600
C. 2,700
D. 2,592
E. 1,944
The OA is the option B.
I got confused here. Experts, should I use combinations? I need some help. <i class="em em-confused"></i>
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Each student at a certain business school is assigned a
This topic has expert replies
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Number of options for the 1st digit = 9. (Any digit 1 through 9)M7MBA wrote:Each student at a certain business school is assigned a 4-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?
A. 9,000
B. 3,600
C. 2,700
D. 2,592
E. 1,944
Number of options for the 2nd digit = 10. (Any digit 0 through 9)
Number of options for the 3rd digit = 10. (Any digit 0 through 9)
Number of options for the 4th digit = 4. (Must be 2, 3, 5 or 7)
To combine the options above, we multiply:
9*10*10*4 = 3600.
The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
-
Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7243
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
There are 9 possible options for the first digit, 10 for the second digit, 10 for the third digit, and 4 for the last digit, since the prime digits are 2, 3, 5, and 7.M7MBA wrote:Each student at a certain business school is assigned a 4-digit student identification number. The first digit of the identification number cannot be zero, and the last digit of the identification number must be prime. How many different student identification numbers can the school create?
A. 9,000
B. 3,600
C. 2,700
D. 2,592
E. 1,944
Thus, the number of codes that can be created is 9 x 10 x 10 x 4 = 3600.
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
-
deloitte247
- Legendary Member
- Posts: 2214
- Joined: Fri Mar 02, 2018 2:22 pm
- Followed by:5 members
From the question, there are 4 digit number
*First digit cannot be 0 , which means it can be any of the digit between 1 to 9= ways of selecting first digit
*Second digit can be any of 0-9 which means 10 ways of selecting second digit
*Third digit can be any of 0-9 also which means 10 ways of selecting third digit and there is no information that indicates whether the numbers cannot be repeated
*Fourth digit can only be prime numbers which means fourth digit can only be 2,3,5,7=4ways of selecting fourth digit.
Total student identification number that can be created = $$9ways\cdot10ways\cdot10ways\cdot4ways=9\cdot10\cdot10\cdot4=3600\ student\ I.D\ \ number$$
Option B is very correct
*First digit cannot be 0 , which means it can be any of the digit between 1 to 9= ways of selecting first digit
*Second digit can be any of 0-9 which means 10 ways of selecting second digit
*Third digit can be any of 0-9 also which means 10 ways of selecting third digit and there is no information that indicates whether the numbers cannot be repeated
*Fourth digit can only be prime numbers which means fourth digit can only be 2,3,5,7=4ways of selecting fourth digit.
Total student identification number that can be created = $$9ways\cdot10ways\cdot10ways\cdot4ways=9\cdot10\cdot10\cdot4=3600\ student\ I.D\ \ number$$
Option B is very correct
