A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee

Question

A certain truck uses  \frac{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  \frac{5}{12}  gallon of fuel per mile?

(1) The value of k is  \frac{1}{10800} .
(2) When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.

Konstantin1983 · Accepted Answer

The correct answer is D.
The question is (1/12)+k(v^2)=5/12 (1). V-?
From st.1 we know k hence we can find v. Sufficient
From st.2 v=30 and (1/12)+k(30^2)=1 Hence we can find k and solve equation (1). Sufficient

LakerFan24 · Answer

You can solve this problem without doing any math.
 
Understand you're given  1 equation  w/  2 variables  (k & v). To rephrase the Q,  you need to find one variable to get the answer here .

(I) Gives you 1 variable (K). With this, you can find V. sufficient. 
- Elim BCE

(II) Gives you equation: (1/6) = 1/12 + (30)^2(k). 30=V, so since they (indirectly) gave you (V), you can find (K). sufficient.
- Elim A

Ans: D

paisaj87 · Answer

Consumption of fuel= 1/12+ kv^2

1. It gives you the actual value for the constant k, therefore you are able to find v from the original question. SUFFICIENT 
2. It gives you: 1/6 = 1/12+ k30^2 , therefore you could find k and the use this to find v. SUFFICIENT

ANSWER D

paisaj87 · Answer

Consumption of fuel= 1/12+ kv^2

1. It gives you the actual value for the constant k, therefore you are able to find v from the original question. SUFFICIENT 
2. It gives you: 1/6 = 1/12+ k30^2 , therefore you could find k and the use this to find v. SUFFICIENT

ANSWER D

ThisandThat · Answer

Statement 1 asks us to solve an equation with a squared variable, so why are there not two solutions? I thought equations to the second power always had two solutions. I answered B for this one.

Bunuel · Answer

v is the speed of the truck. Can it be negative?

EMPOWERgmatRichC · Answer

Hi All,

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

ScottTargetTestPrep · Answer

We need to determine v when:

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

TheUltimateWinner · Answer

Hello experts,
 EMPOWERgmatRichC ,  VeritasKarishma ,  IanStewart ,  Bunuel ,  chetan2u ,  ArvindCrackVerbal ,  GMATGuruNY ,  GMATinsight 
What if the  highlighted  part is removed from the question prompt or it says 'k' is not 'constant'? Should the correct choice be A?

Also, if the highlighted part is not removed from the question prompt, can we say the rephrased version is something like ''what is k''? If yes, can you explain 'how'?

Thanks__

GMATinsight · Answer

Asad Highlighted part can NOT be removed from the question. A valid question is one which clearly defines the scope of used variables in any given mathematical expression. So there is no acceptable "if" here in my opinion.

IanStewart · Answer

The highlighted part can't be removed from the prompt. If a question gives you a formula, it needs to tell you what each letter is. If you didn't know if k was constant or variable, there'd be no way to decide if Statement 2 was sufficient. In a formula, each letter is either a variable that stands for some quantity that can change (temperature, number of people, speed, etc), or is a constant, so stands for some (unknown) number. You would never see the phrase "not constant" in a question; that's not a thing in math. A letter is a constant or a variable.

In this question, yes, if you leave the highlighted part as is, the question asks "what is v equal to when 5/12 = 1/12 + kv^2?" Since we know v is positive, that boils down to "what is k?", since with the value of k we get an equation we can solve for v. But in other similar-looking questions, the situation might not be as straightforward. For example, you might have two variables, or might have two or more solutions for a given value of k, so the nature of the formula matters.

CrackverbalGMAT · Answer

Hello Asad,

I understand your effort to experiment by trying to look at a problem from different angles by trying cases similar, albeit with minor changes, to the ones defined in the problem. This is a great way of learning a lot from a given problem. However, there’s always a thin line between doing something and overdoing it. As such, you need to be extremely aware of this line. Otherwise, you will end up overthinking about the question, which is not a good thing to do.

In this case, making k as a variable will just invalidate the question.

Fuel consumption = ½ + k v^2  for a certain truck. Apart from the velocity v, let’s assume that the variable ‘k’ accounts for all other influencers like load carried, number of people, tyre pressure, road conditions etc., If we kept ‘k’ as a variable, then it would be humanely impossible to answer this question knowing that there may be hundreds of variables that influence the fuel consumption.

That’s probably why the equation defines the fuel consumption as a function of velocity and nothing else. Higher the velocity, greater the consumption and vice versa.

Also, the question is not about finding ‘k’. It’s about finding ‘v’ at which the consumption is 5/12 gallons per mile.
Hope that helps!

Shubhi09 · Answer

Does it mean with statement one, there can be many possible answers to it

Posted from my mobile device

EMPOWERgmatRichC · Answer

Hi Shubhi09,

The prompt gives us an equation for the number of gallons of gas used per mile at a particular speed:

(1/12) + (K)(V^2) gallons of gas are used per mile when the truck travels at a speed "V" (in miles per hour). We're also told that K is a constant - meaning that it is NOT a variable that changes (it's a value, but we don't know exactly what the value is yet). We are asked how fast the truck must travel to us 5/12 of a gallon of gas per mile.

Fact 1 gives us the additional information that K = 1/10800. Plugging in this value into the given equation, we have....

(1/12) + (1/10800)(V^2) = 5/12

(1/10800)(V^2) = 4/12

(V^2) = (4/12)(10800)

In the situation described, since "V" refers to speed, then it must be a POSITIVE number. Thus, the above equation would have just ONE solution. If you really wanted to do the math, then you could find that solution, but that work is ultimately unnecessary. With the information in Fact 1, there will be just one answer, so Fact 1 is SUFFICIENT. 
 
GMAT assassins aren't born, they're made,
Rich

ModiHarsh1993 · Answer

Can someone please explain how we are equating '1/12 + kv^2' with '5/12'? Somehow I am not able to grasp it.

EMPOWERgmatRichC · Answer

Hi ModiHarsh1993,

The prompt starts off by telling us that a truck uses (1/12) + (K)(V^2) GALLONS of gas are USED PER MILE when the truck travels at a certain speed (where K is a constant and V is the speed of the truck in miles/hour). The specific question asked is "at what speed is the truck using 5/12 GALLONS per MILE?"

We have two references to the same thing: the equation for gallons used per mile (at a particular speed) and a question asking about gallons used per mile (what is the particular speed?). Thus, we can create the initial equation:

(1/12) + (K)(V^2) = 5/12

To solve for V (the speed), we'll need the value of the constant (re: K). 
 
GMAT assassins aren't born, they're made,
Rich

GMATinsight · Answer

Answer: Option D

Video solution by  GMATinsight

https://www.youtube.com/watch?v=ckj1hwkeNu8

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=SnDLdOPUhoA

rochan7 · Answer

Hello,

I am still not able to figure out how we are equating the two equations. Could you please provide a detailed explanation, it would be very helpful. Thanks in advance.

A certain truck uses 1/12 +kv^2 gallons of fuel per mile when its spee

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