BTGmoderatorDC wrote:A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any mixture of X and Y. Fuel X costs $3 per gallon; the vehicle can go 20 miles on a gallon of Fuel X. In contrast, Fuel Y costs $5 per gallon, but the vehicle can go 40 miles on a gallon of Fuel Y. What is the cost per gallon of the fuel mixture currently in the vehicle's tank?
(1) Using fuel currently in its tank, the vehicle burned 8 gallons to cover 200 miles.
(2) The vehicle can cover 7 and 1/7 miles for every dollar of fuel currently in its tank
Statement 1:
X = 20 miles per gallon.
Y = 40 miles per gallon.
Since the mixture of X and Y in the tank allows 200 miles to be covered using 8 gallons, we get:
X+Y = 200/8 = 25 miles per gallon.
To determine how X and Y must be combined to yield a rate of 25 miles per gallon, use ALLIGATION.
Step 1: Plot the 3 rates on a number line, with the rates for X and Y on the ends and the rate for the mixture in the middle
X 20------------25-------------40 Y
Step 2: Calculate the distances between the percentages.
X 20-----
5-----25-----
15-----40 Y
Step 3: Determine the ratio in the mixture.
The ratio of X to Y is equal to the RECIPROCAL of the distances in red.
X:Y = 15:5 = 3:1.
Of every 4 gallons in the tank, X= 3 gallons and Y = 1 gallon.
Since X = $3 per gallon and Y = $5 per gallon, the cost for 3 gallons of X and 1 gallon of Y = (3*3) + (1*5) = $14.
Since 4 gallons costs $14, the cost per gallon = 14/4 = 7/2 = $3.50.
SUFFICIENT.
Statement 2:
The cost of the 8 gallons used in Statement 1 to travel 200 miles = (8)(7/2) = $28, implying that the miles per dollar = 200/28 = 100/14 = 50/7 = 7 1/7 miles.
Implication:
Statement 2 -- which requires that 7 1/7 miles be covered for every dollar -- conveys the SAME INFORMATION as Statement 1.
Since Statement 1 is SUFFICIENT, so must be Statement 2.
SUFFICIENT.
The correct answer is
D.
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