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

 It is currently 18 Nov 2018, 19:49

### 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

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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
• ### The winning strategy for 700+ on the GMAT

November 20, 2018

November 20, 2018

06:00 PM EST

07:00 PM EST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

# Two mixtures A and B contain milk and water in the ratios

Author Message
TAGS:

### Hide Tags

Intern
Joined: 13 Jan 2015
Posts: 11
Re: Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

02 Aug 2016, 02:37
bmwhype2 wrote:
Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk?

A. 144
B. 122.5
C. 105.10
D. 72
E. 134

I tried two approaches.one in which i convereted 40% to fraction form and the second in which i converted 2/7 to % form.The later method yielded the correct OA.why???
Intern
Joined: 17 Apr 2012
Posts: 15
Location: United States
WE: Information Technology (Computer Software)
Re: Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

02 Aug 2016, 05:34
How abt this approach.

of all the options provided only 122.5 is divisible by 7 ie. ratio of A is 2:5, so the mixture need to be in multiple of 7.
CEO
Joined: 11 Sep 2015
Posts: 3122
Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

Updated on: 16 Apr 2018, 11:57
1
Top Contributor
bmwhype2 wrote:
Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk?

A. 144
B. 122.5
C. 105.10
D. 72
E. 134

When solving some mixture questions, I find it useful to sketch the solutions with the ingredients SEPARATED.

First recognize that if mixture A has a milk to water ratio of 2:5, then the mixture is 2/7 milk.
Also recognize that if mixture B has a milk to water ratio of 5:4, then the mixture is 5/9 milk.

When we draw this with the ingredients separated, we see we have 50 gallons of milk in the mixture.

Next, we'll let x = the number of gallons of mixture A we need to add.
Since 2/7 of mixture A is milk, we know that (2/7)x = the volume of MILK in this mixture:

At this point, we can ADD the two solutions (PART BY PART) to get the following volumes:

Since the RESULTING mixture is 40% milk (i.e., 40/100 of the mixture is milk), we can write the following equation:
[50 + (2/7)x]/(90 + x) = 40/100
Simplify to get: [50 + (2/7)x]/(90 + x) = 2/5
Cross multiply to get: 5[50 + (2/7)x] = 2(90 + x)
Expand: 250 + (10/7)x = 180 + 2x
Subtract 180 from both sides to get: 70 + (10/7)x = 2x
Multiply both sides by 7 to get: 490 + 10x = 14x
Rearrange: 490 = 4x
Solve: x = 490/4 = 245/2 = 122.5

RELATED VIDEO

_________________

Test confidently with gmatprepnow.com

Originally posted by GMATPrepNow on 06 Sep 2016, 14:10.
Last edited by GMATPrepNow on 16 Apr 2018, 11:57, edited 1 time in total.
Intern
Joined: 27 Nov 2016
Posts: 1
Re: Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

23 Dec 2016, 08:03
2x+50/5x+40=4/6, find x, then don't get into decimals, approx 17.something then 2(17)+5(17)= approx 122
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8550
Location: Pune, India
Re: Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

09 Nov 2017, 01:28
3
bmwhype2 wrote:
Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk?

A. 144
B. 122.5
C. 105.10
D. 72
E. 134

Responding to a pm:

Here is the weighted average method of solving it:
Concentration of milk in the first mixture = 2/7 = 18/63 = 90/315
Concentration of milk in the second mixture = 5/9 = 35/63 = 175/315
Concentration of milk in the resultant mixture = 2/5 = 126/315

w1/w2 = (A2 - Aavg)/(Aavg - A1)

w1/w2 = (175/315 - 126/315) / (126/315 - 90/315) = 49 / 36

So 36 gallons of mixture B needs 49 gallons of A
90 gallons of B will need (49/36)*90 = 122.5 gallons

The numbers in the question are hard to work with. In most GMAT questions, the numbers fall easily in place. It is the concept that you have to focus on.
_________________

Karishma
Veritas Prep GMAT Instructor

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Senior SC Moderator
Joined: 22 May 2016
Posts: 2111
Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

09 Nov 2017, 10:23
1
bmwhype2 wrote:
Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk?

A. 144
B. 122.5
C. 105.10
D. 72
E. 134

Another weighted average approach, expressed a bit differently.

Track on milk. We know the desired concentration of milk in the resultant mixture.

Milk is a fraction (or percentage or concentration) of all three mixtures of milk and water. The weighted average formula accounts for water by way of volume. Formula:

$$(Concentration_{A})(Vol_{A}) + (Concentration_{B})(Vol_{B})$$
$$=(Concentration_{A+B})(Vol_{A+B})$$

Let A = # of gallons of A (volume)

1) Use ratios and desired percentage to find the concentration of milk in A, B, and end mixture (with ratios, remember to find $$\frac{part}{whole}$$):

In A, $$\frac{M}{W}=\frac{2}{5}$$
2 parts milk, 5 parts water, total parts = 7
So milk is $$\frac{2parts}{7parts}=\frac{2}{7}$$

B: $$\frac{M}{W}=\frac{5}{4}.$$ Milk $$=\frac{5}{4+5}=\frac{5}{9}$$

Resultant mixture: 40% milk $$=\frac{2}{5}$$

We have 90 gallons for the volume of B. How much A?

2) Weighted average to find volume of A (steps can be combined)

$$\frac{2}{7}A + \frac{5}{9}(90)=\frac{2}{5}(A+90)$$

$$\frac{2}{7}A + 50=\frac{2}{5}A + \frac{2}{5}(90)$$

$$\frac{2}{7}A + 50=\frac{2}{5}A + 36$$

$$14=\frac{2}{5}A-\frac{2}{7}A$$

$$14 = \frac{4}{35}A$$

$$A = (14*\frac{35}{4})=122.5$$ gallons of A

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

12 Nov 2017, 07:45
bmwhype2 wrote:
Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk?

A. 144
B. 122.5
C. 105.10
D. 72
E. 134

Mixture A has a ratio of milk : water = 2x : 5x.

Mixture B has a ratio of milk : water = 5y : 4y.

Since there are 90 gallons of mixture B, we have:

milk : water = 50 : 40

We can now create the following equation to determine how many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk:

(2x + 50)/(7x + 90) = 40/100

(2x + 50)/(7x + 90) = 2/5

5(2x + 50) = 2(7x + 90)

10x + 250 = 14x + 180

70 = 4x

x = 17.5

So, we need 7(17.5) = 122.5 gallons of A.

_________________

Jeffery Miller

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

Intern
Joined: 12 Jan 2018
Posts: 5
Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

12 Jun 2018, 01:44
Hi,
I solved this in 15 seconds by just seeing that 122,5 is the only number that yields a "comfortable" terminating decimal (17,5) when divided by 7 (taking the ratio of 2:5). The other answers are also terminating decimals but in these type of GMAT questions they usually do not make you calculate with numbers that have more then 3 decimals.

Does that approach hold up in general? Bunuel VeritasPrepKarishma

Thanks a lot for the feedback!
Senior Manager
Joined: 04 Aug 2010
Posts: 307
Schools: Dartmouth College
Re: Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

12 Jun 2018, 04:57
bmwhype2 wrote:
Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk?

A. 144
B. 122.5
C. 105.10
D. 72
E. 134

An alternate approach is to use ALLIGATION.
Alligation can be performed only with percentages or fractions.

Step 1: Convert the ratios to FRACTIONS.
A:
Since M:W = 2:5, and 2+5=7, $$\frac{Milk}{Total}$$ = $$\frac{2}{7}$$.
B:
Since M:W = 5:4, and 5+4=9, $$\frac{Milk}{Total}$$ = $$\frac{5}{9}$$.
Mixture:
$$\frac{Milk}{Total}$$= $$\frac{2}{5}$$.

Step 2: Put the fractions over a COMMON DENOMINATOR.

A = $$\frac{2}{7}$$ = $$\frac{(2*9*5)}{(7*9*5)}$$ = $$\frac{90}{315}$$.
B = $$\frac{5}{9}$$ = $$\frac{(5*7*5)}{(9*7*5)}$$ = $$\frac{175}{315}$$.
Mixture = $$\frac{2}{5}$$ = $$\frac{(2*7*9)}{(5*7*9)}$$ = $$\frac{126}{315}$$.

Step 3: Plot the 3 numerators on a number line, with the numerators for A and B on the ends and the numerator for the mixture in the middle.
A 90-------------126-------------175 B

Step 4: Calculate the distances between the numerators.
A 90-----36-----126-----49-----175 B

Step 5: Determine the ratio in the mixture.
The ratio of A to B is equal to the RECIPROCAL of the distances in red.
A:B = 49:36.

Since $$\frac{A}{B}$$ = $$\frac{49}{36}$$, and the actual volume of B=90, we get:
$$\frac{A}{90}$$ = $$\frac{49}{36}$$
36A = 49*90
2A = 49*5
2A = 245
A = 122.5.

_________________

GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.

Director
Joined: 14 Dec 2017
Posts: 510
Re: Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

12 Jun 2018, 12:05
1
bmwhype2 wrote:
Two mixtures A and B contain milk and water in the ratios 2:5 and 5:4 respectively. How many gallons of A must be mixed with 90 gallons of B so that the resultant mixture contains 40% milk?

A. 144
B. 122.5
C. 105.10
D. 72
E. 134

Given, Mixture A with Milk: water = 2 : 5 & Mixture B with Milk : water = 5 : 4

Let X be the Quantity of Mixture A , we have

Quantity of Milk in Mixture A = 2X/7

Given Quantity of Mixture B = 90 gallons

Quantity of Milk in Mixture B = 5*90/9 = 50 gallons

When Mixture A & B are mixed we get 40% milk.

hence we have, 2X/7 + 50 = 4/10* (X + 90)

Solving we get X = 122.5 gallons

Thanks,
GyM
_________________
Re: Two mixtures A and B contain milk and water in the ratios &nbs [#permalink] 12 Jun 2018, 12:05

Go to page   Previous    1   2   [ 30 posts ]

Display posts from previous: Sort by

# Two mixtures A and B contain milk and water in the ratios

 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®.