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

 It is currently 18 Sep 2019, 23:35

### 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

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

Author Message
TAGS:

### Hide Tags

SVP
Joined: 29 Aug 2007
Posts: 2143
Re: rates - milk and water  [#permalink]

### Show Tags

18 Aug 2009, 10:38
I found Ian7777's all posts very clear, detail and useful. More than that his attitude is humble and highly positive. I always enjoy reading his posts and learned a lot from him.

Thanks Ian.

GT
ian7777 wrote:
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?

How can I do this without using the ratio approach?

As you may have seen in a previous post, I like to shy away from algebra if there is some other framework I can use instead. For mixtures and solutions, I simply draw this box, fill in what is given, and then make everything work out to the bottom right corner.

The rows represent the solutions being mixed. The first solution first, the added solution second, and the resulting solution third. The columns represent the parts of the solution. The first (left) column is the total solution, the middle represents the percentage of the "stuff" (in this case, milk, but could be acid, salt, alcohol, etc), and the third column is the total "stuff" in the solution.

We multiply the first column by the second column to get the third column. When we mix them together, the total amounts mix, as do the amounts of the "stuff", so we add down. Note that the middle column doesn't add - it's just there to get us from the left to the right.

So here is how I applied it to this problem. We know how much of B there is, and we are asked how much of A is mixed with it to get 40% milk all together. Follow the chart, and you see that the bottom row multiplies to the right box, and the right column adds to the right box, so we have the right box from two directions. That's how we solve.

50 + 2/7x = .4(90 + x)
x = 122.5

Check out some earlier posts I made on this topic.

http://www.gmatclub.com/forum/7-t8140
http://www.gmatclub.com/forum/7-t10946
http://www.gmatclub.com/forum/7-t40699
http://www.gmatclub.com/forum/7-t48296

Ian

_________________
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT
Manager
Joined: 15 Jun 2009
Posts: 97
Re: rates - milk and water  [#permalink]

### Show Tags

25 Aug 2009, 02:57
Milk Water Total

A 2 5 x

B 5 4 90

----------------------------------------------
Total 2 3 90+x
-----------------------------------------------

Equation 2/5(90+x) = 50 + 2/7x...sove for x....
x = 122.5

sorry...tried but unable to edit....tab is not working..
VP
Joined: 07 Dec 2014
Posts: 1233
Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

Updated on: 12 Jun 2018, 20:33
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

let x=gallons of A to be mixed
(2x/7)+(5*90)/9=.4(x+90)
x=122.5 gallons
B

Originally posted by gracie on 15 Jun 2016, 12:44.
Last edited by gracie on 12 Jun 2018, 20:33, edited 2 times in total.
Intern
Joined: 13 Jan 2015
Posts: 10
Re: Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

02 Aug 2016, 03:37
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: 14
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, 06:34
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.
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, 09:03
2x+50/5x+40=4/6, find x, then don't get into decimals, approx 17.something then 2(17)+5(17)= approx 122
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2819
Re: Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

12 Nov 2017, 08:45
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.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
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
Joined: 12 Jan 2018
Posts: 5
Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

12 Jun 2018, 02:44
1
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: 462
Schools: Dartmouth College
Re: Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

12 Jun 2018, 05:57
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: 517
Location: India
Re: Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

12 Jun 2018, 13:05
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
_________________
Intern
Joined: 16 Apr 2018
Posts: 16
Re: Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

23 Jun 2019, 00:37
GMATPrepNow
I'm not able to figure this question out. I'm not sure how to use a ratio of solution A to find an answer. Could you help me solve this one?

Aman
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9637
Location: Pune, India
Re: Two mixtures A and B contain milk and water in the ratios  [#permalink]

### Show Tags

24 Jun 2019, 03:25
pkloeti wrote:
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!

I understand what you are saying and that is a valid point. Though these numbers are not very GMAT-like. If they have given 122.5 as the answer (presumably the calculations would involve decimals), I would worry about some other option being the answer with the intermediate steps having decimals.
Hence, with 15 secs on hand to make a quick guess and move on, your logic is great - but given 2 mins, I would actually solve the question.
_________________
Karishma
Veritas Prep GMAT Instructor

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

### Show Tags

04 Aug 2019, 10:54
i tried like this:

Out of all the given options for amount of A, only one option is completely divisible by 7 i.e., B) 122.5
verified the answer by considering A=122.5 gallons.
So total mixture =90+122.5=212.5
(2/7)*(122.5)+(5/9)*(90)=(4/10)*(212.5)
35+50=4*21.25
85=85

so option B) is the answer
Re: Two mixtures A and B contain milk and water in the ratios   [#permalink] 04 Aug 2019, 10:54

Go to page   Previous    1   2   [ 33 posts ]

Display posts from previous: Sort by