Rudy414 wrote:The afternoon after a party, Traci prepares a cleaning solution of x liters of water and y liters of bleach. The bleach comes in half-liter containers. How many such containers will Traci require for her cleaning solution?

1) Traci will need a total of 25 liters of solution altogether.
2) To halve the concentration of bleach in her solution, Traci would need to add 2.4y liters of water, and reduce the number of liters of bleach by 1.

We need to determine the value of 2y, i.e. the value of y.

Statement 1: (x + y) = 25
As we don't know x, we cannot determine y.

Not sufficient

Statement 2: Original concentration of bleach = y/(x + y)
New concentration of bleach = (y - 1)/[(x + 2.4y) + (y - 1)]

So, (y - 1)/[(x + 2.4y) + (y - 1)] = [y/(x + y)]/2
--> 2(y - 1)/(x + 3.4y - 1) = y/(x + y)
--> 2(y - 1)(x + y) = y(x + 3.4y - 1)

This will give us a quadratic equation in y with x as the coefficient. As we don't know x, we cannot determine y.

Not sufficient

1 & 2 Together: From statement 1 --> (x + y) = 25
And from statement 2,
--> 2(y - 1)(x + y) = y(x + 3.4y - 1)
--> 2(y - 1)(x + y) = y(2.4y + x + y - 1)
--> 50(y - 1) = y(2.4y + 24)
--> 2.4y² - 26y + 50 = 0
--> 12y² - 130y + 250 = 0
--> 6y² - 65y + 125 = 0
--> 6y² - 15y - 50y + 125 = 0
--> 3y(2y - 5) - 25(2y - 5) = 0
--> (2y - 5)(3y - 25) = 0

Hence, y can be 5/2 or 25/3

Not sufficient

The correct answer is E.

AragornII wrote:@Anju,

Here we know that bleach comes in half-liter containers and we need the number of containers (which means a proper integer number). Now combining both statement, we get 2 values of Y. But only the first value (5/2) gives us the integer number we are looking for in terms of number of containers. While the other value doesn't. Keeping this in mind, shouldn't the answer be C?

The same reasoning crossed my mind too.
But then, what do we do for the following type of problems?

Frodo have to paint the floor of his house which covers an area of 350 sq feet. If one bucket of paint can be used to paint 90 sq. feet, how many buckets of paint Frodo should buy?

He should buy 350/90 = 3.88.. buckets of paint
As number of buckets should be integer, he should buy 4 buckets of paint.

Similarly here if y = 5/2, then Traci require 5 containers.
And if y = 25/3, then Traci require (25/3)*2 = 50/3 = 16.66... ≈ 17 containers.

The problem never said Traci cannot waste any of the bleach. It only said the bleach comes in half-liter containers.

If you are not convinced, then ask yourself what you'd have done if the problem said 'the bleach comes in one liter containers'? Then none of the values of y gives us integer numbers of containers.

rintoo22 wrote:

To halve the concentration of bleach in her solution, Traci would need to add 2.4y liters of water, and reduce the number of liters of bleach by 1.

...
My question is how did you arrive to this equation ?

Initially the solution has x liters of water and y liters of bleach.

Now, Traci would need to add 2.4y liters of water ---> volume of water = (x + 2.4y)
And, reduce the number of liters of bleach by 1 ---> volume of bleach = (y - 1)

Hence, new concentration of bleach = (Volume of bleach)/[volume of water + volume of bleach] = (y - 1)/[(x + 2.4y) + (y - 1)]

Hope that helps.