BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

In how many ways can 4 white and 3 black chess pieces be

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2589
Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members
by BTGmoderatorLU » Mon Apr 16, 2018 3:02 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

In how many ways can 4 white and 3 black chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.

A. 288
B. 144
C. 12
D. 48
E. 96

The OA is B.

Please, can somebody explain how to solve this PS question? Thanks in advance!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Tue Apr 17, 2018 7:03 pm
Hi All,

We're asked for the number of ways that 4 distinct white chess pieces and 3 distinct black chess pieces can be arranged in a row such that they occupy alternate places. This question is essentially one big Permutation question and can be solved with that type of calculation.

Since the pieces have to be in ALTERNATING colors, the arrangement must be WBWBWBW

For the 1st spot, we have 4 white pieces to choose from. Once we place one...
For the 2nd spot, we have 3 black pieces to choose from. Once we place one...
For the 3rd spot, we have 3 white pieces to choose from. Once we place one...
For the 4th spot, we have 2 black pieces to choose from. Once we place one...
For the 5th spot, we have 2 white pieces to choose from. Once we place one...
For the 6th spot, we have just 1 black piece to choose from.
For the 7th spot, we have just 1 white piece to choose from.

(4)(3)(3)(2)(2)(1)(1) = 144 possible arrangements.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members
Location: New York, NY
Thanked: 39 times

by Jeff@TargetTestPrep » Thu Apr 19, 2018 4:39 pm
BTGmoderatorLU wrote:In how many ways can 4 white and 3 black chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.

A. 288
B. 144
C. 12
D. 48
E. 96
Since the chess pieces must occupy alternate places, the first piece must be white. In that case, the number of ways they can be arranged is :

4 x 3 x 3 x 2 x 2 x 1 x 1 = 144

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Sun Apr 22, 2018 10:03 am
Since the pieces have to be in alternating colors of the class piece, the arrangement = W B W B W B W ( where W= White piece and B= black piece)
4 white + 3 black piece= 7 (it will be on 7 spot)
(W) 1st spot= we can choose from 4 white pieces
(B) 2nd spot= we can choose from 3 black pieces
(W) 3rd spot= we can choose from 3 white pieces
(B) 4th spot = we can choose from 2 black pieces
(W) 5th spot= we can choose from 2 black pieces
(B)6th spot= we can choose from 1 black pieces
(W)7th spot=we can choose from 1 black pieces

Arrangement= (4 (3 (3)(2)(2)(1)(1)
= 4*3*3*2*2*1*1
=144 possible arrangements
Hence the answer is B
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1