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During the last four years, a large truck company purchased [#permalink]

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07 Aug 2012, 12:40

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During the last four years, a large truck company purchased diesel at rates of $1.2, $1.4, $1.8 and $2.1 per gallon. What was the mean cost of diesel over the four-year period if the company spends the same amount of dollars on diesel each year?

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During the last four years, a large truck company purchased diesel at rates of $1.2, $1.4, $1.8 and $2.1 per gallon. What was the mean cost of diesel over the four-year period if the company spends the same amount of dollars on diesel each year?

A) $2.5 B) $2.55 C) $1.55 D) $3.25 E) $3.0

Source: 4gmat

Think of the numbers as 12, 14, 18, 21 LCM = 12*7*3

Assume the company spent $12*21 each year on diesel. Amount of diesel bought in 1st year = 21 gallons, 2nd year = 18 gallons, 3rd year = 14 gallons, 4th year = 12 gallons

Avg cost of diesel = 12*21*4/(21 + 18 + 14 + 12) = 12*21*4/65 = 15.5 (painful calculation here! I don't expect this in GMAT)

Since we ignored the decimal, the actual mean cost is 1.55. Answer (C)

Actually, what what you are doing is finding the Harmonic mean here.

HM = 4/(1/12 + 1/14 + 1/18 + 1/21) = 15.5 The calculation is the same either way.
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During the last four years, a large truck company purchased diesel at rates of $1.2, $1.4, $1.8 and $2.1 per gallon. What was the mean cost of diesel over the four-year period if the company spends the same amount of dollars on diesel each year?

A. $2.5 B. $2.55 C. $1.55 D. $3.25 E. $3.0

Source: 4gmat

5 second approach:

On the PS section one should always look at the answer choices before starts to solve a problem.

The average cost cannot possibly be more than $2.1 per gallon (the largest amount payed per gallon in four-year period). Hence only answer choice C can be the correct answer.

Re: During the last four years, a large truck company purchased [#permalink]

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09 Aug 2012, 17:33

VeritasPrepKarishma wrote:

SOURH7WK wrote:

During the last four years, a large truck company purchased diesel at rates of $1.2, $1.4, $1.8 and $2.1 per gallon. What was the mean cost of diesel over the four-year period if the company spends the same amount of dollars on diesel each year?

A) $2.5 HM = 4/(1/12 + 1/14 + 1/18 + 1/21) = 15.5 The calculation is the same either way.

Karishma sorry for such a basic question, but how do you calculate the LCM between different numbers, im forgetting my basics here..
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Karishma sorry for such a basic question, but how do you calculate the LCM between different numbers, im forgetting my basics here..

LCM is the lowest common multiple. To get the LCM of some numbers, you split the number into its prime factors.

\(12 = 2^2 * 3\) \(18 = 2*3^2\) \(24 = 2^3*3\)

Now LCM is the number that includes all the factors of each of these numbers.

\(LCM = 2^3 * 3^2 = 72\)

We take 2^3 because the highest power of 2 in any number is 2^3 so we need at least three 2s in the LCM. We take 3^2 because the highest power of 3 in any number is 3^2 so we need at least two 3s in the LCM.

Instead, if the numbers are:

\(12 = 2^2 * 3\) \(14 = 2*7\) \(LCM = 2^2*3*7\)

When looking for LCM of 12, 14, 18, 21, we know that the LCM must have each of these numbers as the factor. So I took 12 since the first number is 12. 14 has 2 which is already included in 12 and it has 7 which is not included in 12 so we need to take a 7 too. We get 12*7 18 has a 2 which is already included in 12 and it has two 3s but 12 has only one 3. So we need another 3. We get 12*7*3 21 has 3 and 7 and they both are already included.

Re: During the last four years, a large truck company purchased [#permalink]

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04 Dec 2015, 10:28

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