In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
A. 6!/2!
B. 3!*3!
C. 4!/2!
D. 4!*3!/2!
E. 3!*3!/2!
The OA is D.
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
In how many ways can the letters of the word ABACUS...
This topic has expert replies
-
BTGmoderatorLU
- Moderator
- Posts: 2218
- Joined: Sun Oct 15, 2017 1:50 pm
- Followed by:6 members
-
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
Since the vowels must appear together, put them together in a BLOCK: [AAU].BTGmoderatorLU wrote:In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
A. 6!/2!
B. 3!*3!
C. 4!/2!
D. 4!*3!/2!
E. 3!*3!/2!
Now count the number of ways to arrange the 4 elements [AAU], B, C and S.
The number of ways to arrange 4 distinct elements = 4!.
Now we must account for the number of ways that the vowels themselves can be arranged WITHIN the [AAU] block.
The vowels can be arranged as follows:
AAU, AUA, UAA.
Total ways = 3.
Multiplying the results above, we get:
4! * 3.
This is the value yielded by answer choice D:
(4! * 3!)/2! = 4! * 3.
The correct answer is D.
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
-
Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
We can arrange the letters as follows:BTGmoderatorLU wrote:In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
A. 6!/2!
B. 3!*3!
C. 4!/2!
D. 4!*3!/2!
E. 3!*3!/2!
[A-A-U] - B - C - S
Thinking of [A-A-U] as a single element, [A-A-U] - B - C - S can be arranged in 4! ways.
We must also consider that [A-A-U] can be arranged in 3!/2! ways (by the formula for permutations with indistinguishable objects).
Thus, the total number of ways is 4! * 3!/2!.
Answer: D
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
