Say the capacity of the tank is 100 liters.

1. An empty fuel tank is filled with brand Z gasoline --> z=100;

2. When the tank is half empty, it is filled with brand Y gasoline --> z=50 and y=50;

3. When the tank is half empty again, it is filled with brand Z gasoline --> z=25+50=75 and y=25 (when the tank is half full it has 25 liters of z and 25 liters of y);

4. When the tank is half empty again, it is filled with brand Y gasoline. --> z=37.5 and y=12.5+50=62.5.

37.5 liters is 37.5% of 100 liters.

Answer: C.
_________________

Work with fraction of brand Z in the tank.
1st step: brand Z is 1
2nd step: brand Z is 1/2
3rd step: brand Z is (1/2)*(1/2) + 1/2 = 3/4
4th step: brand Z is (1/2)*(3/4) = 3/8 = 37.5%

Answer (C)
_________________

Hi All,

I'm a big fan of TESTing VALUES in these types of questions (the approach that Bunuel used). You can also solve this problem by making a table, taking some basic notes and doing a bit of arithmetic. Let's break this prompt into 'pieces':

1) An empty fuel tank is filled with brand Z gasoline.

Tank is FULL of Z

2) When the tank is half empty, it is filled with brand Y gasoline (thus, HALF the Z is gone and the other half of the tank is filled with Y).

(1/2)Z + (1/2)Y

When the tank is half empty again, it is filled with brand Z gasoline (thus, HALF of what was there is gone and the other half is filled with Z).

(1/4)Z + (1/4)Y + (1/2)Z

When the tank is half empty again, it is filled with brand Y gasoline (thus, HALF of what was there is gone and the other half is filled with Y.

(1/8)Z + (1/8)Y + (1/4)Z + (1/2)Y

At this time, what percent of the gasoline in the tank is brand Z?

We now have (1/8 + 1/4)Z and (1/8 + 1/2)Y

1/8 + 1/4 = 3/8 so we have 3/8 = 37.5% Z

Final Answer:

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

Y ............................. Z .............................. Total

............................ 100 ................................ 100 (Say total capacity of tank initially filled with Z)

.............................. 50 .................................. 50 (Half capacity)

50 .......................... 50 .................................... 100 (Filled with Y; fuel ratio 1:1)

25 .............................. 25 ................................. 50 (Tank is half)

25 ............................... 25+50 .......................... 100 (Tank filled with Z)

12.5 .............................. 37.5 ........................ 50 (Tank is half)

12.5+50 ........................ 37.5 .......................... 100 (Filled with Y)

Required percentage = 37.5

Let’s say the tank starts with 32 gallons of gas (we use the number 32 because we can take half of this number many times over and it still will be a whole number).

To start, there are 32 gallons of Z.

When the tank is half empty and filled with brand Y, that gives us:

16 gallons of brand Z and 16 gallons of brand Y.

When the tank is half empty again and filled with brand Z, that gives us:

8 gallons of Brand Y and 8 + 16 = 24 gallons of brand Z.

When the tank is half empty again and filled with brand Y, that gives us:

4 + 16 = 20 gallons of brand Y and 12 gallons of brand Z.

Thus, 12/32 = 3/8 = 37.5% of the tank is filled with brand Z.

Answer: C
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________