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 512
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.
- Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- EACH statement ALONE is sufficient.
- Statements (1) and (2) TOGETHER are not sufficient.
“A certain truck uses \(\frac{1}{12} +kv^2 \) gallons of fuel per mile”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.
Solution and Explanation:
Approach Solution 1:
It is asked,At what speed should the truck travel so that it uses\(\frac{5}{12}\)
gallon of fuel per mile A if 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.
We can begin by entering the precise "fuel usage" that the question asks us to consider into the provided equation:
Lets solve further,
\(\frac{5}{12}=\frac{1}{12} +kv^2 \)
So, in order to calculate the speed (V), we must be aware of the constant (K).
Statement 1 alone says
The value of k is \(\frac{1}{10800}\).
Given that statement 1 provides the constant, we can calculate the value of V (and since there is no such thing as a "negative speed," \(V^2\) can only have one value, the positive one).
Statement 1 is alone Sufficient.
Statement 2 alone says
When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.
This information can be plugged into the equation to provide us with…
\(\frac{1}{6}=\frac{1}{2} +k*30^2\)
We may then determine K using this equation (which we could then plug back into the original question and solve for V).
Statement 2 alone is Sufficient.
Hence, EACH statement ALONE is sufficient.
Correct Andwer: D
Approach Solution 2:
We must determine v when.:
\(\frac{5}{12}=\frac{1}{12} +kv^2 \)
\(\frac{4}{12}=kv^2 \)
\(\frac{1}{3}=kv^2 \)
Statement 1 alone says
The value of k is \(\frac{1}{10800}\).
Thus, we have:
\(\frac{1}{3}=\frac{1}{10800}v^2\)
3600 = \(v^2\)
60 = v
Statement 1 alone is Sufficient.
Statement 2 alone says
When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.
This means
\(\frac{1}{6}=\frac{1}{2} +k*30^2\)
\(\frac{1}{12}=900k\)
\(\frac{1}{10800}\)= k
We can determine v since we know the value of k which is the same value as k in statement one.
Statement two alone is sufficient to answer the question.
Hence, EACH statement ALONE is sufficient.
Correct Andwer: D
Approach Solution 3:
What speed should the truck drive at such that it may use \(\frac{5}{12}\)
fuel gallons per mile A if \(\frac{1}{12} +kv^2 \) truck travels at v miles per hour and burns gallons of fuel per mile, where k is a constant.
We may start by putting the specific "fuel use" into the given equation that is specified in the question:
Let's continue to solve
\(\frac{5}{12}=\frac{1}{12} +kv^2 \)
Therefore, we need to be aware of the constant in order to determine the speed (V) (K).
Just Statement 1 says
K has a value of \(\frac{1}{10800}\)
Given that statement 1 includes the constant, we can determine V's value (and since there is no such thing as a "negative speed," \(V^2\) can only have one value, the positive one).
Statement 1 is sufficient on its own.
Just Statement 2 says
The truck consumes 1/6 gallon of fuel each mile when it is moving at 30 miles per hour.
This information may be added to the equation to give us…
\(\frac{1}{6}=\frac{1}{2} +k*30^2\)
Using this equation, we can then calculate K. (which we could then plug back into the original question and solve for V).
Statement 2 is sufficient by itself.
Hence, EACH statement ALONE is sufficient.
Correct Andwer: D
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