A certain truck uses 1/12 + kv^2 gallons of fuel per mile when its speed is v miles per hour, where k is a constant. At what speed should the truck travel so that it uses 5/12 gallon of fuel per mile?
(1) The value of k is 1/10,800
(2) When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.
Official Guide question
Answer: D
A certain truck uses 1/12 + kv^2 gallons of fuel
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Hi jjjinapinch,
We're told that a truck uses 1/12 + (K)(V^2) gallons of fuel per mile when its speed is V miles per hour and that K is a constant.
We're asked for the speed at which the truck travels so that it uses 5/12 gallon of fuel per mile.
To start, we can input the specific 'fuel usage' that the question asks us to deal with into the given equation:
5/12 = 1/12 + (K)(V^2)
Thus, to figure out the speed (V), we need to know the constant (K).
1) The value of K is 1/10,800
Fact 1 gives us the constant, we can figure out the value of V (and since we can't have a "negative speed", there's only one value for V^2 - the positive one).
Fact 1 is SUFFICIENT
2) When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.
We can plug this information into the equation, which gives us...
1/6 = 1/2 + (K)(30^2)
With this equation, we can then solve for K (which we could then plug back into the original question and solve for V).
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
We're told that a truck uses 1/12 + (K)(V^2) gallons of fuel per mile when its speed is V miles per hour and that K is a constant.
We're asked for the speed at which the truck travels so that it uses 5/12 gallon of fuel per mile.
To start, we can input the specific 'fuel usage' that the question asks us to deal with into the given equation:
5/12 = 1/12 + (K)(V^2)
Thus, to figure out the speed (V), we need to know the constant (K).
1) The value of K is 1/10,800
Fact 1 gives us the constant, we can figure out the value of V (and since we can't have a "negative speed", there's only one value for V^2 - the positive one).
Fact 1 is SUFFICIENT
2) When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.
We can plug this information into the equation, which gives us...
1/6 = 1/2 + (K)(30^2)
With this equation, we can then solve for K (which we could then plug back into the original question and solve for V).
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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We need to determine v when:jjjinapinch wrote:A certain truck uses 1/12 + kv^2 gallons of fuel per mile when its speed is v miles per hour, where k is a constant. At what speed should the truck travel so that it uses 5/12 gallon of fuel per mile?
(1) The value of k is 1/10,800
(2) When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.
Official Guide question
Answer: D
5/12 = 1/12 + kv^2
4/12 = kv^2
1/3 = kv^2
Statement One Alone:
The value of k is 1/10,800.
Thus, we have:
1/3 = (1/10,800)v^2
3600 = v^2
60 = v
Statement one alone is sufficient to answer the question.
Statement Two Alone:
When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.
Thus:
1/6 = 1/12 + k(30)^2
1/12 = 900k
1/10,800 = k
Since we have determined the value of k (the very same value of k in statement one), we can determine v. Statement two alone is sufficient to answer the question.
Answer: D
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