Solution X is 10 percent alcohol by volume, and solution Y is 30 perce

\(10% 200 + 30% Y = 25% (200 + Y )\)
Solving for Y = 600
Answer E .

another approach is to use weighted average trick.

we know that X is 10% , Y is 30% and W.Avg = 25% . what does this mean with respect to W.Avg technique ?
W.Avg is 1 portion away from Y and 3 portion away from X so for every 1 portion of X we will have to add 3 portions of Y.
If X = 200 then Y = 600 .

Hi All,

This is a 'Weighted Average' question, so it can be solved in a number of different ways. For most Test Takers, setting up the Weighted Average formula and doing the necessary algebra is a straight-forward way to get to the solution, but there ARE alternatives. Since the question asks for the number of milliliters of Solution Y that are needed, and the answer choices are NUMBERS, we can TEST THE ANSWERS.

From the prompt, we are told to mix 200 milliliters of a 10% alcohol solution with an unknown number of milliliters of a 30% alcohol solution to get a 25% total alcohol solution.

IF....we mixed 200 milliliters with another 200 milliliters, then we'd end up with a 20% mixture (since the average of 10% and 30% is 20%). That result would be TOO LOW, so we clearly need a lot MORE milliliters of the 30% solution. From this, we can eliminate Answers A and B from consideration.

Let's TEST Answer D....

IF...we have 480 milliliters of Solution Y, we have....

Does [.1(200) + .3(480)]/680 = .25?

Does 20 + 144 = .25(680)?

Does 164 = 170?

No it doesn't, so Answer D is NOT the answer. We likely need to add MORE of the 30% solution to get the two 'sides' to match, but we can confirm this by TESTing Answer E.

IF....we have 600 milliliters of Solution Y, we have...

Does [.1(200) + .3(600)]/800 = .25?

Does 20 + 180 = .25(800)?

Does 200 = 200?

Yes it does, so this MUST be the answer.

Final Answer:

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

10 % Alcohol of Solution X = 20
Let amount of Solution Y to be added be X

(20 + 0.3x)/(200+X) = 25/100

x = 600

Ans : E

MAGOOSH OFFICIAL SOLUTION:

ans 600, Using allegations method.
X : 10% : 200 Y : 30% : 'V'
Mixture: 25%
X : 5% : 200 Y : 15% : 'V'

Thus, 5/15 = 200/V => V = 200*3 = 600.

Easy one.

Alcohol in 200 ml of X = 20 ml.

Alcohol in 100y ml of Y = 30y ml

Now as per question,

20 + 30y = 25% of (200 + 100y)

or y = 6.

Therefore, required quantity of solution y = 600 ml. Hence, E

x = 10%
y= 30%
x= 200 milliliters

.1x + .3Y = .25(x+Y)

.1(200) + .3Y = .25(200 + Y)

20 + .3Y = 50 + .25Y

0.05Y = 30

Y = 600 milliliters E

Let x be the total vol.
Then .2*100+.3*(x-200)=.25x
so, x=40/.05=800 and hence 800-200=600
E is the correct choice

Using weighted average method -

Y (y ml) X (200 ml)
30 10
25 (200+y ml)
15 5
3 : 1

Therefore Y:X is in the ratio 3:1
Since X is 200 ml, Y will be 3 times 200 ml
Hence Y = 600 ml
Ans E.

Please press Kudos if this helped

Brutal...occasionally a basic arithmetic error hits me with an additional 5 minutes off the clock.

200(10) + 30y = 25(200 + y)
2000 + 30y = 5000 + 25y
5y = 3000
y = 600

Answer is E.

Let's just Plug In The Answers (PITA). I usually like trying B and D, but C looks so easy, let's start there.

C: We start with 200mL of x, so 20mL of alcohol. We add 400mL of y, so add 120mL of alcohol. We now have 140mL of alcohol out of 600 mL total. That's lower than 25%. We need more y. A, B, and C are out.

Between D and E, E is easier to work with.

E: We start with 200mL of x, so 20mL of alcohol. We add 600mL of y, so add 180mL of alcohol. We now have 200mL of alcohol out of 800 mL total. That's 25%. Yay!

Answer choice E.


ThatDudeKnowsPITA

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