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

Redeem

A and B are two salt solutions with different concentrations

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

A and B are two salt solutions with different concentrations

by Max@Math Revolution » Wed Dec 04, 2019 12:53 am
[GMAT math practice question]

A and B are two salt solutions with different concentrations. Mixing 200g of A and 100g of B makes a 4% salt solution, and mixing 100g of A and 200g of B makes a 3% salt solution. What are the concentrations of A and B?

A. 5%, 2%
B. 6%, 4%
C. 5%, 1%
D. 6%, 2%
E. 7%, 3%
Top
Source: — Problem Solving |
Junior | Next Rank: 30 Posts
Posts: 18
Joined: Mon Sep 30, 2019 5:04 pm

by henilshaht » Wed Dec 04, 2019 6:54 am
This is the approach I used:

x - represents solution A quantity
y - represents solution B quantity

the first statement can be written 2x + y = 4% and the second one can be written as x + 2y = 3%
Then I found the lcm of 4% and 3% => 12%

3 ( 2x + y ) = 4 (x + 2y)
6x + 3y = 4x + 8y
2x = 5y
x:y = 5:2
Top
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

edit

by Max@Math Revolution » Fri Dec 06, 2019 12:10 am
=>

Assume the percentages of the two salt solutions A and B are a% and b%, respectively. We need to figure out the amount of salt for salt solution questions.

The amount of salt in 200g of solution A is 200*(a/100) = 2a. The amount of salt in 100g of solution B is 100*(b/100) = b.

After mixing the 2 solutions, the new solution is (2a + b) / 300 = 4/100, 100(2a + b) = 4(300), and 200a + 100b = 1200. Dividing everything by 100 gives us 2a + b = 12.

Then, the amount of salt in 100g of solution A is 100*(a/100) = a and 200*(b/100) = 2b.

After mixing the 2 solution, the new solution is (a + 2b) / 300 = 3/100, 100(a + 2b) = 3(300), and 100a + 200b = 900. Dividing everything by 100 gives us a + 2b = 9.

When we add two equations, we have (2a + b) + (a + 2b) = 12 + 9, 3a + 3b = 21 or a + b = 7.

Then we have a = (2a + b) - (a + b) = 12 - 7 = 5 and b = (a + 2b) - (a + b) = 9 - 7 = 2.

Therefore, A is the answer
Answer: A
Top
Post new topic Post Reply
• Page 1 of 1