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Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4806**

WE:**Business Development (Energy and Utilities)**

At the beginning of a trip, the tank of Diana’s car
[#permalink]
25 May 2016, 15:37

Expert Reply

4

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Question Stats:

At the beginning of a trip, the tank of Diana’s car was filled with gasoline to half of its capacity. During the trip, Diana used 30 percent of the gasoline in the tank. At the end of the trip, Diana added 8 gallons of gasoline to the tank. The capacity of the tank of Diana’s car was x gallons. Which of the following expressions represent the number of gallons of gasoline in the tank after Diana added gasoline to the tank at the end of the trip?

Indicate all such expressions.

A. \(\frac{x}{2} - \frac{3x}{20} +8\)

B. \(\frac{7x}{20} +8\)

C. \(\frac{3x}{20} +8\)

D. \(\frac{x}{2} + \frac{3x}{20} -8\)

E. \(\frac{7x}{20} -8\)

_________________

Indicate all such expressions.

A. \(\frac{x}{2} - \frac{3x}{20} +8\)

B. \(\frac{7x}{20} +8\)

C. \(\frac{3x}{20} +8\)

D. \(\frac{x}{2} + \frac{3x}{20} -8\)

E. \(\frac{7x}{20} -8\)

Practice Questions

Question: 15

Page: 84

Question: 15

Page: 84

_________________

Sandy

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Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4806**

WE:**Business Development (Energy and Utilities)**

Re: At the beginning of a trip, the tank of Diana’s car
[#permalink]
25 May 2016, 15:51

3

Expert Reply

Explanation

The capacity of the car’s tank was x gallons of gasoline. Before the trip, the tank was half full and therefore contained \(\frac{x}{2}\), gallons of gasoline. During the trip, 30 percent of the gasoline in the tank was used, so the number of gallons left was 70 percent of \(\frac{x}{2}\), or \(\frac{7}{10}*\frac{x}{2} = \frac{7x}{20}\). After Diana added 8 gallons of gasoline to the tank, the total number of gallons in the tank was \(\frac{7x}{20}+8\). Thus one correct choice is Choice B, \(\frac{7x}{20}+8\).

However, the question asks you to find all of the answer choices that represent the number of gallons of gasoline in the tank at the end of the trip. So you need to determine whether any of the other choices are equivalent to \(\frac{7x}{20}+8\). Of the answer choices, only Choices A and C have the same constant term as Choice B: 8. So these are the only choices that need to be checked. Choice A, \(\frac{x}{2} - \frac{3x}{20} +8\), can be simplified as follows.

\(\frac{x}{2} - \frac{3x}{20} +8\)

\(\frac{10x}{20} - \frac{3x}{20} +8\)

\(\frac{7x}{20} +8\)

So Choice A is equivalent to \(\frac{7x}{20} +8\). Choice C, \(\frac{3x}{20} +8\), is clearly not equivalent to \(\frac{7x}{20} +8\).

Thus the correct answer consists of Choices A and B.

_________________

Sandy

If you found this post useful, please let me know by pressing the Kudos Button

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The capacity of the car’s tank was x gallons of gasoline. Before the trip, the tank was half full and therefore contained \(\frac{x}{2}\), gallons of gasoline. During the trip, 30 percent of the gasoline in the tank was used, so the number of gallons left was 70 percent of \(\frac{x}{2}\), or \(\frac{7}{10}*\frac{x}{2} = \frac{7x}{20}\). After Diana added 8 gallons of gasoline to the tank, the total number of gallons in the tank was \(\frac{7x}{20}+8\). Thus one correct choice is Choice B, \(\frac{7x}{20}+8\).

However, the question asks you to find all of the answer choices that represent the number of gallons of gasoline in the tank at the end of the trip. So you need to determine whether any of the other choices are equivalent to \(\frac{7x}{20}+8\). Of the answer choices, only Choices A and C have the same constant term as Choice B: 8. So these are the only choices that need to be checked. Choice A, \(\frac{x}{2} - \frac{3x}{20} +8\), can be simplified as follows.

\(\frac{x}{2} - \frac{3x}{20} +8\)

\(\frac{10x}{20} - \frac{3x}{20} +8\)

\(\frac{7x}{20} +8\)

So Choice A is equivalent to \(\frac{7x}{20} +8\). Choice C, \(\frac{3x}{20} +8\), is clearly not equivalent to \(\frac{7x}{20} +8\).

Thus the correct answer consists of Choices A and B.

_________________

If you found this post useful, please let me know by pressing the Kudos Button

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Re: At the beginning of a trip, the tank of Diana’s car
[#permalink]
26 May 2016, 04:04

1

The amount of gas initially is x/2. Now after using 30% of the gas, the remaining gas is 70% of x/2. Now adding 8 gallons, the gas is 70% of x/2 +8 or 7x/20 + 8. Hence B.

Choice A can also be reduced to 7x/20 + 8. Hence answer A and B

Choice A can also be reduced to 7x/20 + 8. Hence answer A and B

Re: At the beginning of a trip, the tank of Diana’s car
[#permalink]
12 Feb 2019, 04:43

sandy wrote:

Explanation

The capacity of the car’s tank was x gallons of gasoline. Before the trip, the tank was half full and therefore contained \(\frac{x}{2}\), gallons of gasoline. During the trip, 30 percent of the gasoline in the tank was used, so the number of gallons left was 70 percent of \(\frac{x}{2}\), or \(\frac{7}{10}*\frac{x}{2} = \frac{7x}{20}\). After Diana added 8 gallons of gasoline to the tank, the total number of gallons in the tank was \(\frac{7x}{20}+8\). Thus one correct choice is Choice B, \(\frac{7x}{20}+8\).

However, the question asks you to find all of the answer choices that represent the number of gallons of gasoline in the tank at the end of the trip. So you need to determine whether any of the other choices are equivalent to \(\frac{7x}{20}+8\). Of the answer choices, only Choices A and C have the same constant term as Choice B: 8. So these are the only choices that need to be checked. Choice A, \(\frac{x}{2} - \frac{3x}{20} +8\), can be simplified as follows.

\(\frac{x}{2} - \frac{3x}{20} +8\)

\(\frac{10x}{20} - \frac{3x}{20} +8\)

\(\frac{7x}{20} +8\)

So Choice A is equivalent to \(\frac{7x}{20} +8\). Choice C, \(\frac{3x}{20} +8\), is clearly not equivalent to \(\frac{7x}{20} +8\).

Thus the correct answer consists of Choices A and B.

The capacity of the car’s tank was x gallons of gasoline. Before the trip, the tank was half full and therefore contained \(\frac{x}{2}\), gallons of gasoline. During the trip, 30 percent of the gasoline in the tank was used, so the number of gallons left was 70 percent of \(\frac{x}{2}\), or \(\frac{7}{10}*\frac{x}{2} = \frac{7x}{20}\). After Diana added 8 gallons of gasoline to the tank, the total number of gallons in the tank was \(\frac{7x}{20}+8\). Thus one correct choice is Choice B, \(\frac{7x}{20}+8\).

However, the question asks you to find all of the answer choices that represent the number of gallons of gasoline in the tank at the end of the trip. So you need to determine whether any of the other choices are equivalent to \(\frac{7x}{20}+8\). Of the answer choices, only Choices A and C have the same constant term as Choice B: 8. So these are the only choices that need to be checked. Choice A, \(\frac{x}{2} - \frac{3x}{20} +8\), can be simplified as follows.

\(\frac{x}{2} - \frac{3x}{20} +8\)

\(\frac{10x}{20} - \frac{3x}{20} +8\)

\(\frac{7x}{20} +8\)

So Choice A is equivalent to \(\frac{7x}{20} +8\). Choice C, \(\frac{3x}{20} +8\), is clearly not equivalent to \(\frac{7x}{20} +8\).

Thus the correct answer consists of Choices A and B.

Hello,

If i wanted to solve this question by Plug-In method, can anyone show me an example please. As i want to know how we will consider the phrase "was filled with gasoline to half of its capacity" in my solution.

Thanks

Re: At the beginning of a trip, the tank of Diana’s car
[#permalink]
14 Feb 2019, 11:03

Expert Reply

Hi,

it is difficult to solve this question, it will become cumbersome plugging numbers because the question itself by the test makers is conceived to test your understanding theoretically of the underlined concepts.

However, you could give a try.

suppose x is 10 then the tank is down of 30% which means the tank is 7 full now. Then you add 8. But at the beginning, the tank was half of its capacity was 5.

Nonetheless, at this point even looking at the answer choices is difficult to pinpoint the right answer/s.

Instead, think this way

at the end 8 is added. So, D and E are impossible.

At the beginning, the tank was half so \(\frac{x}{2}\). From this, C is impossible.

Now, the cunning part is that A and B are equal, only in a different format.

A and B must be the answers.

Regards

it is difficult to solve this question, it will become cumbersome plugging numbers because the question itself by the test makers is conceived to test your understanding theoretically of the underlined concepts.

However, you could give a try.

suppose x is 10 then the tank is down of 30% which means the tank is 7 full now. Then you add 8. But at the beginning, the tank was half of its capacity was 5.

Nonetheless, at this point even looking at the answer choices is difficult to pinpoint the right answer/s.

Instead, think this way

at the end 8 is added. So, D and E are impossible.

At the beginning, the tank was half so \(\frac{x}{2}\). From this, C is impossible.

Now, the cunning part is that A and B are equal, only in a different format.

A and B must be the answers.

Regards

Re: At the beginning of a trip, the tank of Diana’s car
[#permalink]
21 Feb 2019, 07:15

1

Expert Reply

SKH121 wrote:

Hello,

If i wanted to solve this question by Plug-In method, can anyone show me an example please. As i want to know how we will consider the phrase "was filled with gasoline to half of its capacity" in my solution.

Thanks

If i wanted to solve this question by Plug-In method, can anyone show me an example please. As i want to know how we will consider the phrase "was filled with gasoline to half of its capacity" in my solution.

Thanks

Hi..

Take x as 40, then half the capacity is half of 40 = 20.

Now, 30% of 20 is used, so 70% is remaining = 70% of 20=14, add 8 liters to it, so 14+8=22.

Now check the choices after plugging x as 20 in the examples. You will get A and B as answer.

Hope it helps

_________________

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Re: At the beginning of a trip, the tank of Diana’s car
[#permalink]
17 Aug 2021, 18:22

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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