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SOURH7WK
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During the last four years, a large truck company purchased 07 Aug 2012, 13:40
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Question Stats:

92% (01:56) correct 8% (01:58) wrong based on 50 sessions

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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
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C
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During the last four years, a large truck company purchased 07 Aug 2012, 22:12
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SOURH7WK
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
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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 08 Aug 2012, 01:13
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SOURH7WK
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
Show more

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.

Answer: C.

Hope it's clear.
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During the last four years, a large truck company purchased 09 Aug 2012, 18:33
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SOURH7WK
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.
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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..
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During the last four years, a large truck company purchased 09 Aug 2012, 22:18
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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..
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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.

LCM = 12*7*3
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During the last four years, a large truck company purchased 21 Jun 2023, 21:00
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