Solution Y is 40 percent sugar by volume, and solution X is 20 percent

Question

Solution Y is 40 percent sugar by volume, and solution X is 20 percent sugar by volume. How many gallons of solution X must be added to 150 gallons of solution Y to create a solution that is 25 percent sugar by volume?

(A) 37.5
(B) 75
(C) 150
(D) 240
(E) 450

(A) 37.5
(B) 75
(C) 150
(D) 240
(E) 450

LighthousePrep · Accepted Answer

In order to solve this problem you must be able to translate English into Algebra equations. Once you have written one or more algebraic equations it becomes a simple math problem to solve. You should look out for some keywords such as added, percent and so on while creating the equations. In this case, lets go step by step:

1. The problem states that there is 150 gallons of Y solution and X will be added to create a solution - this shows that the total number of gallons in the new solution will be  150+x .
2. The new solution is 25 percent sugar by volume. So, that becomes  \frac{25}{100}* (150+x) .
3. Solution Y is 40 percent sugar and we know that there are 150 gallons of Y solution. Solving for that gives  \frac{40}{100} * 150 . This gives us 60 gallons of sugar by volume in Solution Y out of the 150 total gallons
4. Solution X is 20 percent sugar and this will be added to 60 gallons of Y. So the translation here is  60 + \frac{20}{100}(x)

Now we can form the equation ->  60 + \frac{20}{100}(x) = \frac{25}{100}(150+x)

This is solving equation with one variable.

60 + 0.2x = 37.5 + .25x

.05x = 22.5

x = 450

The answer is E.

Temurkhon · Answer

Differential method:

40----------25----20

15x=5y
x/y=5/15=1/3, so 1 part of 40% sol should be added 3 part of 20%. 
So 150*3=450

E

BrentGMATPrepNow · Answer

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

Start with 150 gallons of solution that is 40% sugar:
 https://i.imgur.com/Hcd4SR1.png 
When we draw this with the ingredients separated, we see we have  60  gallons of sugar in the mixture.

Next, we'll let x = the number of gallons of solution X we need to add. 
Since 20% of the solution X is sugar, we know that  0.2x  = the volume of sugar in this solution:
 https://i.imgur.com/y2g6Zba.png

At this point, we can ADD the two solutions (PART BY PART) to get the following volumes:
 https://i.imgur.com/y5nktDo.png

Since the resulting solution is 25% sugar (i.e., 25/100 of the solution is sugar), we can write the following equation:
( 60 + 0.2x )/(150 + x) = 25/100
Simplify to get: ( 60 + 0.2x )/(150 + x) = 1/4
Cross multiply to get: 4( 60 + 0.2x ) = 1(150 + x)
Expand: 240 + 0.8x = 150 + x
Rearrange: 90 = 0.2x
Solve: x = 450

Answer: E

RELATED VIDEO
 https://www.youtube.com/watch?v=7Or9gzROsjQ

PareshGmat · Answer

Answer = E = 450

Solution Y

Sugar ................ Water .............. Total

40 ............................ 60 .................. 100

60 .......................... 90 .................... 150

Say x litres of Solution x added; New equation would be

60+\frac{20x}{100}  ..............  90+\frac{80x}{100}  ............ 150+x

New sugar concentration is 25%; setting up the equation

\frac{25}{100} (150+x) = 60 + \frac{20x}{100}

x = 450

Ashishmathew01081987 · Answer

Sol Y = 40% sugar---------------------Sol Mix = 25 % sugar-----------------Sol X = 20% sugar

Sol Y = +0.15 than Avg---------------Avg = 0.25------------------------------Sol X = -0.05 than avg

0.15 Y - 0.05 X = 0
0.15 Y = 0.05 X

X/Y = 0.15/0.05 = 3:1

X:Y:Total = 3:1:4

If Y = 150 Gallons then by ratio X:Y = 3:1

X/150= 3/1
X = 150 * 3 = 450 Gallons

Ans E

gracie · Answer

(.4)(150)+.2x=.25(150+x)
x=450 gallons

DJ1986 · Answer

I did a slightly different differential method.

40----25----20
--15------5---

So Y has to be 5/20 of the new solution. Given Y = 150 gallons

150 = 5/20(total)
Total = 600 
X = 600 - 150

Ans E) 450

EMPOWERgmatRichC · Answer

Hi All,

Mixture questions can also be answered with the Part/Whole formula:

In this case, we're dealing with Sugar/Total

Solution X = 20% sugar 
Solution Y = 40% sugar

We're told to mix a certain amount of Solution X with 150 gallons of Solution Y to get a 25% sugar solution:

X = number of gallons of Solution X

/ (X + 150) = .25

Now, it's just algebra steps:

.2X + 60 = .25X + 37.5

22.5 = .05X

450 = X

Final Answer:  E

GMAT assassins aren't born, they're made, 
Rich

adkikani · Answer

2504 sol.jpeg Bunuel niks18 chetan2u gmatbusters VeritasPrepKarishma I am trying to master concept of weighted average by scaling since I find it very time efficient and applicable in multiple scenarios. Please help if my approach is correct (with help taken from this blog.)

GMATBusters · Answer

Your method is correct, and infact I find weighted average/mixture alligation method to be the best approach to solve such questions.

Posted from my mobile device

AkshdeepS · Answer

Weighted Average Method :

Let's add G gallons of solution X

So we have,  \frac{G}{150}  =  \frac{40 - 25}{25 - 20}

G = 150 * \frac{15}{5}

G = 450

Algebraic Method:

0.20X + 0.40Y = 0.25(X +Y)

0.20X + 0.40Y = 0.25X + 0.25Y

0.5X = 0.15Y

X = \frac{0.15*150}{0.5}

X = 450

Archit3110 · Answer

solution Y is 150 gallons of which sugar is 40% ; 60 gallon
and solution X is 20% sugar by vol let that be X.
given in question that many gallons of solution X must be added to 150 gallons of solution Y to create a solution that is 25 percent sugar by volume?

60+20/100*(x) = 25/100 * ( 150+x)
solve for x we get
60+.2x= 1/4 *(150+x)
x=450 
OPTION E

Basshead · Answer

X/Y = 40-25 / 25-20 = 15/5 = 3/1

25% is closer to 20%, meaning that 20% is weighted more heavily.

Therefore 3 * 150 = 450.  Answer is E .

krishna_sunder_ · Answer

"  35 second solution  "

Take weighted avg

VALUES            20.....................25........................40
WEIGHT'S                    150                     X

25-20 unit's  =  150
5 unit's = 150
therefore 40-25 unit's = 15 unit's => 3(150) => 450.

Oppenheimer1945 · Answer

Y: 0.4sugar, 0.6 remaining
X= 0.2sugar, 0.8 remaining

60+0.2X/(150+X)=0.25
=>60+0.2X=37.5+0.25X
=>0.05X=22.5
=> x=450

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Solution Y is 40 percent sugar by volume, and solution X is 20 percent

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Solution Y is 40 percent sugar by volume, and solution X is 20 percent

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