BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Solution \(X,\) which is \(10\%\) alcohol is combined with solution \(Y,\) which is \(18\%\) alcohol to form a new solut

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

Solution \(X,\) which is \(10\%\) alcohol is combined with solution \(Y,\) which is \(18\%\) alcohol to form a new solut

by Vincen » Thu Jul 30, 2020 8:20 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Solution \(X,\) which is \(10\%\) alcohol is combined with solution \(Y,\) which is \(18\%\) alcohol to form a new solution that is \(12\%\) alcohol. How many liters of solution \(Y\) are in the new combined solution?

1. Solution \(X\) comprises \(\dfrac34\) of the combined solution
2. The combined solution is \(16\) liters.

[spoiler]OA=B[/spoiler]

Source: Veritas Prep
Top
Source: — Data Sufficiency |
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pm
Followed by:5 members

Re: Solution \(X,\) which is \(10\%\) alcohol is combined with solution \(Y,\) which is \(18\%\) alcohol to form a new s

by deloitte247 » Sun Aug 02, 2020 8:03 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Concentration of X = 10%
Concentration of Y = 18%
Concentration of X + Y= 12%
Target question: How many liters of solution Y are in the new combined solution?
Using allegation rule to find the ratio of mixing the solutions.
$$\frac{Value\ of\ X}{Value\ of\ Y}=\frac{\left(Conc.\ of\ Y\right)-\left(Conc.\ of\ mixture\right)}{\left(Conc,\ of\ X\right)\ -\ \left(Conc.\ of\ mixture\right)}$$
$$\frac{Value\ of\ X}{Value\ of\ Y}=\frac{18-12}{10-12}=\frac{6}{2}=3$$
Their ratio is 3:1. i.e to every 3 liters of solution X, 1 liter of solution Y is added and % concentration of the combined solution =
$$\frac{3}{3+1}=\frac{3}{4}$$
Statement 1: Solution X comprises 3/4 of the combined solution.
This tells us about the concentration of solution X in the combined X+Y solution. It does not provide Y with the volume, hence, the target question cannot be evaluated. So, therefore, statement 1 is NOT SUFFICIENT.

Statement 2: The combined solution is 16 liters.
From the ratio gotten from the question stem,
The conc. of X in the combined X+Y solution = 3 / (3+1) = 3/4
The conc. ofY in the combined X+Y solution = 1 / (3+1) = 1/4
$$Therefore,\ volume\ of\ X=\frac{3}{4}\cdot16=12\ liters$$
$$Volume\ of\ Y=\frac{1}{4}\cdot16=4\ liters$$
There are 4 liters of solution Y in the combined X+Y solution. Therefore, statement 2 alone is SUFFICIENT.

Answer = Option B
Top
Post new topic Post Reply
• Page 1 of 1