GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 23 Sep 2018, 20:53

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

A certain car dealership sells only Full-size and Mid-size c

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Director
Director
avatar
Joined: 29 Nov 2012
Posts: 802
A certain car dealership sells only Full-size and Mid-size c  [#permalink]

Show Tags

New post 12 Sep 2013, 03:26
3
1
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

77% (01:35) correct 23% (01:15) wrong based on 132 sessions

HideShow timer Statistics

A certain car dealership sells only Full-size and Mid-size cars. One of its sales representatives receives an annual salary of $15,000. He also receives a commission of $800 for each full size car he sells and $500 for each midsize car he sells. What is the least number of cars he must sell in a year to receive total annual earnings of exactly $25,000?

A) 7
B) 12
C) 13
D) 14
E) 17

I'm getting E can someone explain?

_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49323
Re: A certain car dealership sells only Full-size and Mid-size c  [#permalink]

Show Tags

New post 12 Sep 2013, 03:36
1
fozzzy wrote:
A certain car dealership sells only Full-size and Mid-size cars. One of its sales representatives receives an annual salary of $15,000. He also receives a commission of $800 for each full size car he sells and $500 for each midsize car he sells. What is the least number of cars he must sell in a year to receive total annual earnings of exactly $25,000?

A) 7
B) 12
C) 13
D) 14
E) 17

I'm getting E can someone explain?


\(15,000+800F+500M=25,000\) --> \(8F+5M=100\).

We need to minimize F+M. To do that we need to minimize M (or which is the same we need to maximize F) --> \(M=4\) and \(F=10\) --> \(F+M=14\).

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
User avatar
B
Joined: 07 Feb 2017
Posts: 179
Re: A certain car dealership sells only Full-size and Mid-size c  [#permalink]

Show Tags

New post 30 Jun 2018, 19:47
10,000=800*12+400
10,000=800*11+1200
10,000=800*10+2000

Answer C) 14
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 1979
Premium Member CAT Tests
A certain car dealership sells only Full-size and Mid-size c  [#permalink]

Show Tags

New post 30 Jun 2018, 21:34
fozzzy wrote:
A certain car dealership sells only Full-size and Mid-size cars. One of its sales representatives receives an annual salary of $15,000. He also receives a commission of $800 for each full size car he sells and $500 for each midsize car he sells. What is the least number of cars he must sell in a year to receive total annual earnings of exactly $25,000?

A) 7
B) 12
C) 13
D) 14
E) 17


He gets $15,000 in salary, so to earn $25,000, he needs $10,000 in sales.

Focus on the $800 cars. In order to minimize the total number of cars, we should maximize the number of more expensive full size cars, F -- we need fewer of them to get a high total dollar amount.

Another reason to focus in the $800 cars: divisibility. $800 and $500 are awkward together. We need the $800 car number to make a round total that is divisible by $500 for medium cars, M.

He needs exactly $10,000 from commissions.

To be a "round" number divisible by $500, $800 must be multiplied by 5, 10, or 15

$800 * 5F = $4,000
$6,000 left
$6,000/$500 per M = 12M
Total cars: 17

$800 * 10F = $8,000
$2,000 left
$2,000/$500 per M = 4M
Total cars: 14

The next number of $800F that is round is 15, which is a greater number of cars than the 14 we just calculated. Reject.

Least number of cars: 14
10 are F
4 are M

Answer D
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3528
Location: United States (CA)
Re: A certain car dealership sells only Full-size and Mid-size c  [#permalink]

Show Tags

New post 04 Jul 2018, 19:24
fozzzy wrote:
A certain car dealership sells only Full-size and Mid-size cars. One of its sales representatives receives an annual salary of $15,000. He also receives a commission of $800 for each full size car he sells and $500 for each midsize car he sells. What is the least number of cars he must sell in a year to receive total annual earnings of exactly $25,000?

A) 7
B) 12
C) 13
D) 14
E) 17


Since the sales rep makes $15,000 per year, he needs to make exactly $10,000 in commision.

Let f = the number of full-size cars and m = the number of mid-size cars he sells. We have:

800f + 500m = 10,000

8f + 5m = 100

m = (100 - 8f)/5

Since we want the least number of cars he must sell to make the exact $10,000 commision, he must sell as many full-size cars as possible. We see that the maximum value of f can be 10 where (100 - 8f) is still a multiple of 5. Therefore, he sells 10 full-size cars and (100 - 8(10))/5 = 20/5 = 4 mid-size cars, for a total of 14 cars.


Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

GMAT Club Bot
Re: A certain car dealership sells only Full-size and Mid-size c &nbs [#permalink] 04 Jul 2018, 19:24
Display posts from previous: Sort by

A certain car dealership sells only Full-size and Mid-size c

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.