Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 19 Jul 2019, 03:53

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The roll numbers of students in a college are alpha-numeric sequences

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56302
The roll numbers of students in a college are alpha-numeric sequences  [#permalink]

### Show Tags

25 Jun 2019, 03:00
00:00

Difficulty:

35% (medium)

Question Stats:

71% (02:51) correct 29% (03:26) wrong based on 62 sessions

### HideShow timer Statistics

The roll numbers of students in a college are alpha-numeric sequences of 6 characters. The first and fourth characters are letters while the other four are non-zero digits. While the first character is a vowel, the fourth is a letter from a to e (both inclusive). The second character is 2 and the third is a multiple of 2. The sixth character is 5 more than the fifth. How many roll numbers can be formed?

A. 200
B. 240
C. 300
D. 360
E. 400

_________________
Director
Joined: 20 Jul 2017
Posts: 547
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: The roll numbers of students in a college are alpha-numeric sequences  [#permalink]

### Show Tags

25 Jun 2019, 05:43
2
1
Bunuel wrote:
The roll numbers of students in a college are alpha-numeric sequences of 6 characters. The first and fourth characters are letters while the other four are non-zero digits. While the first character is a vowel, the fourth is a letter from a to e (both inclusive). The second character is 2 and the third is a multiple of 2. The sixth character is 5 more than the fifth. How many roll numbers can be formed?

A. 200
B. 240
C. 300
D. 360
E. 400

1st letter should be a vowel --> Number of ways = 5 {a, e, i, o, u}
4th is a letter from a to e --> Number of ways = 5 {a, b, c, d, e}
2nd character is 2 --> Number of ways = 1 {2}
3rd is a multiple of 2 --> Number of ways = 4 {2, 4, 6, 8} Non Zero Digits!!
6th character is 5 more than 5th --> Possible combinations are {16, 27, 38, 49} --> Number of ways of selecting 5&6 together = 4

So, total number of ways = 5*5*1*4*4 = 400

IMO Option E

Pls Hit Kudos if you like the solution
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4247
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: The roll numbers of students in a college are alpha-numeric sequences  [#permalink]

### Show Tags

26 Jun 2019, 03:06
1
given its a 6 character alpha numeric sequence
so
first = a,e,i,o,u ; 5
2nd = 2; 1
3rd=2,4,6,8 ; 4
4th = a,b,c,d,e; 5
5th & 6th has to be non zero ; 16,27,38,49 ; 4 possible

total cases possible ; 5*1*4*5*4 ; 400 IMO E

Bunuel wrote:
The roll numbers of students in a college are alpha-numeric sequences of 6 characters. The first and fourth characters are letters while the other four are non-zero digits. While the first character is a vowel, the fourth is a letter from a to e (both inclusive). The second character is 2 and the third is a multiple of 2. The sixth character is 5 more than the fifth. How many roll numbers can be formed?

A. 200
B. 240
C. 300
D. 360
E. 400

_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6925
Location: United States (CA)
Re: The roll numbers of students in a college are alpha-numeric sequences  [#permalink]

### Show Tags

01 Jul 2019, 17:41
Bunuel wrote:
The roll numbers of students in a college are alpha-numeric sequences of 6 characters. The first and fourth characters are letters while the other four are non-zero digits. While the first character is a vowel, the fourth is a letter from a to e (both inclusive). The second character is 2 and the third is a multiple of 2. The sixth character is 5 more than the fifth. How many roll numbers can be formed?

A. 200
B. 240
C. 300
D. 360
E. 400

There are 5 options (a, e, i, o , u) for the first character

There is 1 option (2) for the second

There are 4 options (2,4,6,8) for the third

There are 5 options (a, b, c, d, e) for the fourth

There are 4 options for the fifth (1, 2, 3, and 4)

There is only 1 option for the sixth (It must be exactly 5 more than the fifth character)

Thus, the total number of options is 5 x 1 x 4 x 5 x 4 x 1 = 20 x 20 = 400

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Senior Manager
Joined: 12 Sep 2017
Posts: 297
Re: The roll numbers of students in a college are alpha-numeric sequences  [#permalink]

### Show Tags

10 Jul 2019, 19:45
Archit3110 wrote:
given its a 6 character alpha numeric sequence
so
first = a,e,i,o,u ; 5
2nd = 2; 1
3rd=2,4,6,8 ; 4
4th = a,b,c,d,e; 5
5th & 6th has to be non zero ; 16,27,38,49 ; 4 possible

total cases possible ; 5*1*4*5*4 ; 400 IMO E

Bunuel wrote:
The roll numbers of students in a college are alpha-numeric sequences of 6 characters. The first and fourth characters are letters while the other four are non-zero digits. While the first character is a vowel, the fourth is a letter from a to e (both inclusive). The second character is 2 and the third is a multiple of 2. The sixth character is 5 more than the fifth. How many roll numbers can be formed?

A. 200
B. 240
C. 300
D. 360
E. 400

Hello Archit3110!

How do we find the red numbers?

Kind regards!
Re: The roll numbers of students in a college are alpha-numeric sequences   [#permalink] 10 Jul 2019, 19:45
Display posts from previous: Sort by