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

It is currently 20 Oct 2019, 17:55

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

Find Similar Topics 
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
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
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

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: 15294
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
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8117
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

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13317
Re: Tourist purchased a total of 30 travelers checks in $50 and  [#permalink]

Show Tags

New post 06 Feb 2019, 07:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: Tourist purchased a total of 30 travelers checks in $50 and   [#permalink] 06 Feb 2019, 07:28

Go to page   Previous    1   2   [ 25 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  





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