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

 It is currently 22 Feb 2019, 18:49

### 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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# M16-24

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53066
M16-24  [#permalink]

### Show Tags

15 Sep 2014, 23:59
00:00

Difficulty:

25% (medium)

Question Stats:

83% (02:35) correct 17% (02:53) wrong based on 42 sessions

### HideShow timer Statistics

Ten cups and twenty glasses cost $8. If ten glasses and twenty cups cost$7, how much do fifteen cups and five glasses cost?

A. $3.5 B.$4.5
C. $5.0 D.$5.5
E. $6.5 _________________ Math Expert Joined: 02 Sep 2009 Posts: 53066 Re M16-24 [#permalink] ### Show Tags 15 Sep 2014, 23:59 Official Solution: Ten cups and twenty glasses cost$8. If ten glasses and twenty cups cost $7, how much do fifteen cups and five glasses cost? A.$3.5
B. $4.5 C.$5.0
D. $5.5 E.$6.5

Let's denote the price of one cup as $$C$$ and the price of one glass as $$G$$. Compose the following system of equations:
$$10C + 20G = 8$$
$$10G + 20C = 7$$

Solving this system, we get $$G = 0.3$$, $$C = 0.2$$. Hence, fifteen cups and five glasses cost $$15*0.2 + 5*0.3 = 4.5$$.

Answer: B
_________________
Intern
Joined: 25 Jan 2016
Posts: 9
Location: United States (NJ)
GPA: 2.34
WE: Analyst (Commercial Banking)
Re: M16-24  [#permalink]

### Show Tags

03 Jun 2017, 08:50
Hi,

Can you please post the steps to solve this system of equations?

Thanks for your help in advance
DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1431
Location: India
Re: M16-24  [#permalink]

### Show Tags

03 Jun 2017, 10:05
Prostar wrote:
Hi,

Can you please post the steps to solve this system of equations?

Thanks for your help in advance

Hi. Let me try. Let G be the cost of one glass and let C be the cost of one cup. So we have:

20G + 10C = 8
10G + 20C = 7.. we have to find 5G + 15C

We can add the two given equations, so we get:
30G + 30C = 15.. Now divide both sides by 30, we get: G + C = 1/2 Or G = 1/2 - C

We can now substitute this value of G = 1/2-C in the first equation so we get:
20(1/2 - C) + 10C = 8 or 10 - 20C + 10C = 8 or 2 = 10C or C=1/5

WE have C, we can calculate G = 1/2 - C = 1/2 - 1/5 = 3/10

We now have G and C, we can calculate 5G + 15C = 5*3/10 + 15*1/5 = 1.5 + 3 = 4.5
Intern
Joined: 04 Sep 2018
Posts: 39
GPA: 3.33
Re: M16-24  [#permalink]

### Show Tags

23 Jan 2019, 10:55
Bunnel, Can you please help explain how you were able to get G=0.3, C=0.2 from the above equations??
Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: M16-24  [#permalink]

### Show Tags

23 Jan 2019, 22:58
1
nust2017 wrote:
Bunnel, Can you please help explain how you were able to get G=0.3, C=0.2 from the above equations??

We have two distinct linear equations with two unknowns:
$$10C + 20G = 8$$
$$20C + 10G = 7$$

Multiply the first equation by 2 to get $$20C + 40G = 16$$

Now, subtract the second equation from the above: $$30G=9$$ --> $$G=0.3$$. Finally, plug this into either of the equations to get $$C=0.2$$.

Does this make sense?
_________________
Intern
Joined: 04 Sep 2018
Posts: 39
GPA: 3.33
Re: M16-24  [#permalink]

### Show Tags

05 Feb 2019, 03:12
Brilliant. Thanks a ton!
Re: M16-24   [#permalink] 05 Feb 2019, 03:12
Display posts from previous: Sort by

# M16-24

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

Moderators: chetan2u, Bunuel

 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®.