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

 It is currently 23 Jul 2018, 06:56

### 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

# On a certain day, orangeade was made by mixing a certain

Author Message
TAGS:

### Hide Tags

Senior Manager
Affiliations: UWC
Joined: 09 May 2012
Posts: 386
GMAT 1: 620 Q42 V33
GMAT 2: 680 Q44 V38
GPA: 3.43
WE: Engineering (Entertainment and Sports)

### Show Tags

24 May 2012, 23:32
4
24
00:00

Difficulty:

45% (medium)

Question Stats:

69% (01:23) correct 31% (01:45) wrong based on 681 sessions

### HideShow timer Statistics

On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per glass on the second day? A.$0.15
B. $0.20 C.$0.30
D. $0.40 E.$0.45
Math Expert
Joined: 02 Sep 2009
Posts: 47219

### Show Tags

25 May 2012, 01:49
17
10
macjas wrote:
On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per glass on the second day? A.$0.15
B. $0.20 C.$0.30
D. $0.40 E.$0.45

On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;

So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3.

We are told that "the revenue from selling the orangeade was the same for both days" so the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day.

Say the price of the glass of the orangeade on the second day was $x then 2*0.6=3*x --> x=$0.4.

Hope it's clear.
_________________
Intern
Joined: 21 Oct 2011
Posts: 10

### Show Tags

03 Jun 2012, 06:20
5
1
Bunuel

Is it ok to plugin for this sum.

100 ltrs of the orangeade= 50 W + 50 Concentrate
150 ltrs of the orangeade-= 100W + 50 concentrate

since total revenue is the same
100*.6 = 150* x
thus x = 0.4

Can i take the above approach?
##### General Discussion
Intern
Status: ISB 14...:)
Joined: 26 May 2012
Posts: 29
Location: India
Concentration: Strategy
Schools: ISB '14 (A)
GMAT 1: 750 Q51 V39
GPA: 3.62
WE: Engineering (Energy and Utilities)

### Show Tags

07 Jun 2012, 00:32
Let the amount of orange juice be X.

Orangeade made on first day = X + X(same amount of water) = 2X

Orangeade made on second day = X + 2X (twice the amount of water) = 3X

So the total number of glasses made will be of the ratio 2:3

As total revenue is same on both days,

(2)(0.16) = (3)(Price on second day)

Price per glass on second day = 0.32/3 = 0.107
SVP
Joined: 06 Sep 2013
Posts: 1866
Concentration: Finance

### Show Tags

05 Feb 2014, 13:07
2
1
I really like this one

So first you sold 1:1 water and orange, let's say a liter of each so total per glass is 2 liters
After you sold 2:1 water and orange, let's say a liter of each again so total per glass is 3 liters

Now since the revenue is the same and the ratio in the quantity increased to 3/2 then the price has to be the inverse 2/3

So 0.6 * 2.3 - 0.4

Hope it clarifies
Cheers
J
Senior Manager
Joined: 25 Mar 2013
Posts: 265
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5

### Show Tags

23 Aug 2014, 02:20
On fist day 0.60$per glass and assume sold 10 glasses of orange = 6$
On next Day on adding double amount of water, might sold 20 glasses of orange , so 0.30$x 20 = 6$
So C
But My answer is wrong... Even i understood Above solutions, But why analysis is wrong
Pls help
_________________

I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

Math Expert
Joined: 02 Sep 2009
Posts: 47219

### Show Tags

23 Aug 2014, 12:31
kanusha wrote:
On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per glass on the second day? A.$0.15
B. $0.20 C.$0.30
D. $0.40 E.$0.45

On fist day 0.60$per glass and assume sold 10 glasses of orange = 6$
On next Day on adding double amount of water, might sold 20 glasses of orange , so 0.30$x 20 = 6$
So C
But My answer is wrong... Even i understood Above solutions, But why analysis is wrong
Pls help

On the first day orangeade was made by mixing a certain amount of orange juice with an equal amount of water. So, if 10 glasses of orangeade was sold on the first day, then it was made by mixing 5 glasses of orange juice with 5 glasses of water.

On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water, so it was made with 5 glasses of orange juice and 10 glasses of water, which makes total of 15 glasses of orangeade.

10*0.6 = 15*x --> x = 0.4.

Hope it's clear.
_________________
Manager
Joined: 02 Sep 2014
Posts: 74
Location: United States
GMAT 1: 700 Q49 V37
GMAT 2: 700 Q47 V40
GMAT 3: 720 Q48 V41
GPA: 3.26
WE: Consulting (Consulting)

### Show Tags

13 Dec 2014, 16:11
I also like this question. I just wanted to post another way to think about this question.

The first day was a ratio of 1:1, which gives a total of 2 parts: 1L + 1W = 2X
The second day was a ratio of 1:2, which gives a total of 3 parts: 1L + 2W = 3X

Since the revenue was the same for both says, and since there was a quantity increase of 50% (3 is an increase of 50% from 2), you can think of the answer this way:

What number when increased by 50% equals .6? That number is .4

Also, as previously mentioned, since the increase was 3/2, you can also multiply .6 by 2/3, which is the inverse of 3/2. Admittedly, this method is probably better. I just wanted to point out a different method / different way to think about the problem.
Manager
Joined: 10 Jun 2015
Posts: 120

### Show Tags

14 Aug 2015, 06:15
1
macjas wrote:
On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per glass on the second day? A.$0.15
B. $0.20 C.$0.30
D. $0.40 E.$0.45

1o +1w = 2j*0.60=1.20
1o + 2w= 3j*0.40=1.20
the correct option is D
Intern
Joined: 04 Feb 2014
Posts: 14

### Show Tags

11 Sep 2015, 07:32
when people are saying of multiplying by the inverse, do we do this because the price was the same?
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2993
Location: United States (CA)

### Show Tags

02 May 2016, 08:27
macjas wrote:
On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per glass on the second day? A.$0.15
B. $0.20 C.$0.30
D. $0.40 E.$0.45

We are given that orangeade is made on Day 1 with an EQUAL AMOUNT of water and orange juice. We can set this information up into a ratio using a variable multiplier:

W : OJ = x : x

Thus, orangeade quantity = amount of water + amount of OJ = x + x = 2x

We are next given that orangeade on Day 2 was made by mixing the SAME AMOUNT of orange juice with TWICE THE AMOUNT of water. We can set this information up into a ratio using a variable multiplier:

W : OJ = 2x : x

Thus, orangeade quantity = amount of water + amount of OJ = 2x + x = 3x

We also know that all orangeade made was sold and that the revenue on both days was the same. We can therefore set up the following equation:

Day 1 Revenue = Day 2 Revenue

That is,

(quantity sold Day 1)(price per glass Day 1) = (quantity sold Day 2)(price per glass Day 2)

Let a be the amount of orangeade a glass can hold, then

quantity sold Day 1 = the number of glasses of orangeade sold on Day 1 = 2x/a

Similarly,

quantity sold Day 2 = the number of glasses of orangeade sold on Day 2 = 3x/a

We also know that the price per glass on day 1 = $0.6 But we don’t know the price per glass on day 2, so let’s label it as variable p. We now have: (2x/a)(0.6) = (3x/a)(p) Multiplying both sides by a, we have: (2x)(0.6) = (3x)(p) 1.2x = 3xp 1.2 = 3p p = 0.4 Thus, each glass of orangeade was sold for$0.40 on Day 2.

_________________

Scott Woodbury-Stewart
Founder and CEO

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

Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 657
Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GRE 1: Q168 V169
WE: Education (Education)

### Show Tags

Updated on: 07 Dec 2016, 20:08
Attached is a visual that should help. Part of the key here is realizing that a "glass" is a constant, and that you can insert numbers to "make it true".
Attachments

Screen Shot 2016-12-07 at 7.06.07 PM.png [ 144.29 KiB | Viewed 6377 times ]

_________________

Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both in-person (San Diego, CA, USA) and online worldwide, since 2002.

One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).

You can download my official test-taker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y94hlarr Date of Birth: 09 December 1979.

GMAT Action Plan and Free E-Book - McElroy Tutoring

Contact: mcelroy@post.harvard.edu

Originally posted by mcelroytutoring on 17 May 2016, 19:25.
Last edited by mcelroytutoring on 07 Dec 2016, 20:08, edited 5 times in total.
GMAT Club Legend
Joined: 16 Oct 2010
Posts: 8135
Location: Pune, India

### Show Tags

18 May 2016, 02:23
macjas wrote:
On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per glass on the second day? A.$0.15
B. $0.20 C.$0.30
D. $0.40 E.$0.45

Revenue = Number of glasses * Price per glass

On second day, twice the amount of water was added so number of glasses was 3/2 the number of glasses on first day. Revenue on both days was the same so

N * 0.6 = (3N/2) * Cost on day 2

Cost on day 2 = 0.4

_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

VP
Joined: 07 Dec 2014
Posts: 1042

### Show Tags

09 Jun 2017, 20:01
macjas wrote:
On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $0.60 per glass on the first day, what was the price per glass on the second day? A.$0.15
B. $0.20 C.$0.30
D. $0.40 E.$0.45

g=number of glasses sold day 1
x=price per glass day 2
r=revenue both days
g*.6=r
3/2*g*x=r
3/2*g*x=g*.6
x=$.40 D Director Joined: 09 Mar 2016 Posts: 664 On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 08 Apr 2018, 05:50 macjas wrote: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at$0.60 per glass on the first day, what was the price per glass on the second day?

A. $0.15 B.$0.20
C. $0.30 D.$0.40
E. $0.45 why is my reasoning wrong UPDATE I noticed one mistake, so I corrected it but still dont get how to reach final solution first day: 1 litre of juice +1 litre of water hence ratio---> 1:1 (total 2 litres) Second day: 1 litres of juice +2 litres of water hence ratio---> 1:2 ( total 3 litres ) If ratio of mixture on day one to mixture on day two is 2 to 3 and price per glace on day one is 0.60 so i assume from this ratio $$2:3$$ that $$2$$ is 0.60 and what to do next if $$2$$ is 0.60 then what is $$3$$ how to calculate or where am i wrong Director Joined: 09 Mar 2016 Posts: 664 Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 08 Apr 2018, 06:11 Bunuel wrote: macjas wrote: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at$0.60 per glass on the first day, what was the price per glass on the second day?

A. $0.15 B.$0.20
C. $0.30 D.$0.40
E. $0.45 On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade; On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade; So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3. Naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3. We are told that "the revenue from selling the orangeade was the same for both days" so the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day. Say the price of the glass of the orangeade on the second day was$x then 2*0.6=3*x --> x=$0.4. Answer: D. Hope it's clear. Bunuel can you explain the logic when we receive the ratio, know the price of glass 0.60 Say the price of the glass of the orangeade on the second day was$x then 2*0.6=3*x --> x=$0.4. I dont get why are you multiplying 0.60 by 2 ( 0.60 costs one glass and not two litres ) right ? if 2 were number of glasses than it would be ok.... GMAT Club Legend Joined: 16 Oct 2010 Posts: 8135 Location: Pune, India Re: On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 09 Apr 2018, 01:15 1 dave13 wrote: macjas wrote: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at$0.60 per glass on the first day, what was the price per glass on the second day?

A. $0.15 B.$0.20
C. $0.30 D.$0.40
E. $0.45 why is my reasoning wrong UPDATE I noticed one mistake, so I corrected it but still dont get how to reach final solution first day: 1 litre of juice +1 litre of water hence ratio---> 1:1 (total 2 litres) Second day: 1 litres of juice +2 litres of water hence ratio---> 1:2 ( total 3 litres ) If ratio of mixture on day one to mixture on day two is 2 to 3 and price per glace on day one is 0.60 so i assume from this ratio $$2:3$$ that $$2$$ is 0.60 and what to do next if $$2$$ is 0.60 then what is $$3$$ how to calculate or where am i wrong Note that Revenue is the same on both the days. That is the information that will give you the relation between 2:3 and 0.60. Revenue = Unit Price * Volume sold UnitPrice1 * VolumeSold1 = UnitPrice2 * VolumeSold2 VolumeSold1 / VolumeSold2 = UnitPrice2 / UnitPrice1 2/3 = UnitPrice2 / 0.60 UnitPrice2 = 0.40 _________________ Karishma Private Tutor for GMAT Contact: bansal.karishma@gmail.com Intern Joined: 16 Sep 2017 Posts: 6 Location: United States GPA: 4 On a certain day, orangeade was made by mixing a certain [#permalink] ### Show Tags 29 Apr 2018, 19:27 macjas wrote: On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade was the same for both days and if the orangeade was sold at$0.60 per glass on the first day, what was the price per glass on the second day?

A. $0.15 B.$0.20
C. $0.30 D.$0.40
E. \$0.45

LET THE TOTAL QUANTITY OF THE MIXTURE BE 'X'
FIRST DAY: AMOUNT OF ORANGEADE = 1/2X
SECOND DAY: AMOUNT OF ORANGEADE = 1/3X [ SINCE 2 PARTS ARE WATER AND ONE PART IS ORANGEADE ]

SINCE THE AMOUNT QUANTIFIES ONLY TO THE ORANGEADE WHILE WATER IS CONSIDERED TO HAVE NO COST -

FIRST DAY : (1/2) X = 0.60
THEREFORE, SECOND DAY : (1/3) X = (0.60 * 2)/3 = 0.40 [ CHOICE D ]
On a certain day, orangeade was made by mixing a certain &nbs [#permalink] 29 Apr 2018, 19:27
Display posts from previous: Sort by

# Events & Promotions

 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®.