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

It is currently 18 Oct 2018, 20:46

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

Tourist purchased a total of 30 travelers checks in $50 and

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

Hide Tags

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: Tourist purchased a total of 30 travelers checks in $50 and  [#permalink]

Show Tags

New post 05 Sep 2017, 18:04
GMATBaumgartner wrote:
Tourist purchased a total of 30 travelers checks in $50 and $100 denominations. The total worth of the travelers checks is $1800. How many checks of $50 denominations can he spend so that average amount (arithmetic mean) of the remaining travelers checks is $80?

A. 4
B. 12
C. 15
D. 20
E. 24


We can let x = the number of $50 traveler’s checks and y = the number of $100 traveler’s checks. Thus, we can create a “number of traveler’s checks” equation:

x + y = 30

x = 30 - y

We can also create a “monetary value” equation:

50x + 100y = 1800

We substitute (30 - y) for x:

50(30 - y) + 100y = 1800

1500 - 50y + 100y = 1800

50y = 300

y = 6

Since y = 6 and x = 30 - y, x = 24.

We can let n = the number of $50 traveler’s checks spent and create the following equation:

[50(24 - n) + 100(6)]/(30 - n) = 80

1200 - 50n + 600 = 2400 - 80n

30n = 600

n = 20

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

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

Intern
Intern
avatar
Joined: 19 Aug 2016
Posts: 1
Re: Tourist purchased a total of 30 travelers checks in $50 and  [#permalink]

Show Tags

New post 24 Sep 2017, 15:54
Solving Algebraically:

X = the number of checks in the $50 denominations
Y = the number of checks in the $100 denominations
Total number of checks = X + Y = 30

Total value of the checks = $50X + $100Y = $1800

let n = the number of $50 denomination checks the tourist spends

Calculate the average amount of the remaining checks:

=($1800 - $50n)/(X+Y-n) = $80
=($1800 - $50n)/(30- n) = $80
=$1800 - $50n = $80(30- n)
=$1800 - $50n = $2400 - $80n
=$30n = $600
n = 20
Answer: D
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12676
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Tourist purchased a total of 30 travelers checks in $50 and  [#permalink]

Show Tags

New post 29 Nov 2017, 21:25
Hi All,

There are a couple of different ways to approach this question - depending on how you 'see' the math involved. This question can be solved rather quickly by TESTing THE ANSWERS.

From the prompt, we know that there are 30 checks in total (some are 50s and some are 100s) and the the SUM of their value is $1800. That means the 'starting average value' is 1800/30 = $60. As we remove 50s from that calculation, the average will INCREASE. The question asks how many of the 50s we have to remove to get the average up to $80.

Since $80 is a nice 'round number', it's likely that we'll end up removing a number of checks that will create a 'nice' number to divide by (such as a multiple of 5 or a multiple of 10). Looking at the answers, I would start with answer D, since removing 20 checks would leave us with 10 checks (and 10 will be easy to divide into whatever the new numerator is...

Let's TEST Answer D: 20

If we remove twenty 50s from the total value, then the new total value will be 1800 - (20)(50) = $800.
After removing those twenty checks, there will be 30 - 20 = 10 checks remaining.
The average of these remaining checks is $800/10 = $80
This matches what we were told, so this MUST be the answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3886
Location: United States (CA)
Re: Tourist purchased a total of 30 travelers checks in $50 and  [#permalink]

Show Tags

New post 04 Dec 2017, 11:37
GMATBaumgartner wrote:
Tourist purchased a total of 30 travelers checks in $50 and $100 denominations. The total worth of the travelers checks is $1800. How many checks of $50 denominations can he spend so that average amount (arithmetic mean) of the remaining travelers checks is $80?

A. 4
B. 12
C. 15
D. 20
E. 24


We can let a = the number of checks in 50-dollar denomination and b = the number of checks in 100-dollar denomination and create the equation:

50a + 100b = 1800

a + 2b = 36

We also know that a + b = 30.

Subtracting our second equation from our first, we have:

b = 6, so a = 24

We can let n = the number of 50-dollar checks to be spent and create the equation:

[50(24 - n) + 100(6)]/(30 - n) = 80

50(24 - n) + 100(6) = 80(30 - n)

5(24 - n) + 10(6) = 8(30 - n)

120 - 5n + 60 = 240 - 8n

3n = 60

n = 20

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: Tourist purchased a total of 30 travelers checks in $50 and &nbs [#permalink] 04 Dec 2017, 11:37

Go to page   Previous    1   2   [ 24 posts ] 

Display posts from previous: Sort by

Tourist purchased a total of 30 travelers checks in $50 and

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


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®.