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

 It is currently 19 Oct 2019, 07:02 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

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.  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 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

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

_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com

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

Show Tags

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
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15281
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

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.

GMAT assassins aren't born, they're made,
Rich
_________________
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8109
Location: United States (CA)
Re: Tourist purchased a total of 30 travelers checks in \$50 and  [#permalink]

Show Tags

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

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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 Joined: 09 Sep 2013
Posts: 13275
Re: Tourist purchased a total of 30 travelers checks in \$50 and  [#permalink]

Show Tags

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.
_________________ 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  