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

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

There are x people and y chairs in a room where x and

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2058
Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members
Thanked: 1 times
by M7MBA » Sat May 05, 2018 11:53 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

There are x people and y chairs in a room where x and y are positive prime numbers. How many ways can the x people be seated in the y chairs (assuming that each chair can seat exactly one person)?

(1) x + y = 12

(2) There are more chairs than people.

The OA is the option A.

How can I show that the statement (1) is sufficient? Could someone clarify this to me? Please.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members
Thanked: 6 times

by Vincen » Sun May 06, 2018 9:31 am
Hello M7MBA.

Let's take a look at this question.

(1) x + y = 12

Since "x" and "y" are prime, then we have two options:

(i) x=5 and y=7.

First, we have to select 5 chairs from 7, this can be done with a combination: $$7C5=\frac{7!}{2!5!}=\frac{7\cdot6\cdot5!}{2\cdot5!}=21.$$ Now, we have to organize the 5 people in the 5 selected chairs, this can be done in 5! different ways. Therefore, the answer to the original question is: $$7C5\cdot5!=21\cdot5!=2520.$$

(ii) x=7 and y=5.

First, we have to select 5 people from 7, this can be done with a combination: $$7C5=\frac{7!}{2!5!}=\frac{7\cdot6\cdot5!}{2\cdot5!}=21.$$ Now, we have to organize the 5 selected people in the 5 chairs, this can be done in 5! different ways. Therefore, the answer to the original question is: $$7C5\cdot5!=21\cdot5!=2520.$$

Since both answers are the same, we can conclude that this statement is SUFFICIENT.

(2) There are more chairs than people.

This doesn't give enough information. Therefore, this statement is NOT SUFFICIENT.

Finally, the correct answer is the option A .

I hope it helps.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1