A certain truck uses 1/12 + kv^2 gallons of fuel

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jjjinapinch: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Mon Jul 24, 2017 8:16 am; Followed by:1 members

A certain truck uses 1/12 + kv^2 gallons of fuel

by jjjinapinch » Tue Aug 01, 2017 10:11 am

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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

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Source: Beat The GMAT — Data Sufficiency | Tue Aug 01, 2017 10:11 am

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by [email protected] » Tue Aug 01, 2017 12:25 pm

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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

Contact Rich at [email protected]

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Wed Aug 09, 2017 11:09 am

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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

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]