An empty fuel tank is filled with brand Z gasoline. When the

Question

An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent of the gasoline in the tank is brand Z?

A. 50%
B. 40%
C. 37.5%
D. 331⁄3%
E. 25%

A. 50%
B. 40%
C. 37.5%
D. 331⁄3%
E. 25%

Bunuel · Answer

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.

KarishmaB · Answer

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)

EMPOWERgmatRichC · Answer

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:  C

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

PareshGmat · Answer

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

JeffTargetTestPrep · Answer

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

bumpbot · Answer

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An empty fuel tank is filled with brand Z gasoline. When the

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