Solution X is 15% salt and solution Y is 50% salt.

Question

Solution X is 15% salt and solution Y is 50% salt. If the two solutions are combined to form 7 gallons of a 30% solution, how many gallons of solution X must be used?

(A) 2

(B) 2.5

(C) 3

(D) 4

(E) 4.2

JeffTargetTestPrep · Accepted Answer

We can let the number of gallons of solution in solution X = x and the number of gallons of solution in solution Y = y. Thus:

0.15x + 0.5y = 0.3(x + y)

15x + 50y = 30x + 30y

20y = 15x

4y = 3x

We also know that x + y = 7, or y = 7 - x, and thus:

4(7 - x) = 3x

28 - 4x = 3x

28 = 7x

x = 4

Answer: D

chetan2u · Answer

By Weighted Average method, we can find the ratio of X and Y..
 \frac{X}{Y}=\frac{50-30}{30-15}=4/3 ..
So in 7 litres x is 4 and y is 3..

D

gracie · Answer

let x=gallons of solution X to be used
.15x+.5(7-x)=.3*7
x=4
E

KarishmaB · Answer

The weighted average formula w1/w2 = (A2 - Aavg)/(Aavg - A1) Check out this blog post: https://anaprep.com/arithmetic-weighted-averages/ and this video: https://www.youtube.com/watch?v=_GOAU7moZ2Q

KrishnakumarKA1 · Answer

Solution X is 15% salt and solution Y is 50% salt. If the two solutions are combined to form 7 gallons of a 30% solution, how many gallons of solution X must be used?

(A) 2

(B) 2.5

(C) 3

(D) 4

let x amount be from soln X and y amount be from soln Y

x +y = 7
0.15x + 0.5y = 0.3(x+y)

solving 2 equation
x = 4, y = 3

Option D

EMPOWERgmatRichC · Answer

Hi vikasp99,

This question can be solved rather easily by TESTing THE ANSWERS.

We're told to mix a certain amount of 15% salt solution with a certain amount of 50% salt solution to get a total solution that is 7 GALLONS and 30% salt. We're asked for the number of gallons of the 15% solution in that mixture.

To start, if we had the SAME amount of each solution, then the mixture would be (15 + 50)/2 = 65/2 = 32.5% salt. This is clearly TOO MUCH salt, so we need MORE of the 15% solution - meaning more than 3.5 of the 7 total gallons. Thus, the correct answer must be either D or E.

Let's TEST Answer D: 4 gallons

IF we have....
4 gallons of 15%
3 gallons of 50%
then the average would be....
 /7 = (.6 + 1.5)/7 = 2.1/7 = 21/70 = 3/10 = 30%
This is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer:  D

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

CareerGeek · Answer

Given, x + y = 7

Also, 30 = (15x + 50y)/7
—> 210 = 15x + 50*(7 - x)
—> 210 = 350 - 35x
—> 35x = 350 - 210 = 140
—> x = 140/35 = 4 gallons

Alternate Method:

x ————— y
15—————50
———30– ——
(50-30)—(30-15)
20—————15

—> x : y = 20 : 15 = 4 : 3

Value of x = 4/(3 + 4)*7 = 4

IMO Option D

Pls Hit kudos if you like the solution

Posted from my mobile device

Shrey9 · Answer

using allegation
X.............Y
15.........50
.....30......
20........15
4...........3

X = 4 only option D is a multiple of 4, hence it should be the answer..

bumpbot · Answer

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Solution X is 15% salt and solution Y is 50% salt.

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Solution X is 15% salt and solution Y is 50% salt.

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