gasoline

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j_shreyans: Legendary Member; Posts: 510; Joined: Thu Aug 07, 2014 2:24 amFollowed by: 5 members; Thanked: 3 times

by j_shreyans » Sat Aug 30, 2014 9:19 pm

Bob just filled his car's gas tank with 20 gallons of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If his car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many gallons of ethanol must he add into the gas tank for his car to achieve optimum performance?

A)9/10
B)1
C)10/9
D)20/19
E)2

OAC

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Source: Beat The GMAT — Problem Solving | Sat Aug 30, 2014 9:19 pm

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by [email protected] » Sat Aug 30, 2014 10:22 pm

Hi j_shreyans,

This type of weighted-average question can be solved in a number of ways. Here's an algebra approach that uses the part/whole formula:

We know that we have 20 gallons of gasohol (5% ethanol and 95% gasoline). This means....

20 gallons gasohol =
1 gallon ethanol + 19 gallons gasoline

We're asked to add ethanol until the total becomes 10% ethanol. Let's call "X" the amount of additional ethanol added. Remember that when we add ethanol, we're increasing the total amount of liquid too....

Part/Whole = ethanol/All = .1

(1 + X)/(20 + X) = .1

1 + X = 2 + .1X

.9X = 1

X = 1/.9 = 10/9

Final Answer: C

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sun Aug 31, 2014 1:48 am

Bob just filled his car's tank with 20 gallons of gasohol, a mixture containing of 5% ethanol and 95% gasoline. If his car runs best on a mixture containing of 10% ethanol and 90% gasoline, how many gallons of ethanol must he add into the gas tank for his car to achieve optimal performance?
A) 9/10
B) 1
C) 10/9
D) 20/19
E) 2

Bob just filled his car's tank with 20 gallons of gasohol, a mixture containing of 5% ethanol and 95% gasoline.
5% of 20 gallons is 1 gallon.
So, PRESENTLY, there is 1 gallon of ethanol in the car's tank.

We want to add some PURE ethanol to the tank in order to get a 10% mixture of ethanol.
Let x = number of gallons of pure ethanol we ADD to the tank.

FACT #1: Once we add x more gallons of pure ethanol, the car's tank contains 1+x gallons of ethanol.

FACT #2: Once we add x gallons of ethanol, the car's tank contains a TOTAL of 20+x gallons of mixture.

We want the tank to have a 10% mixture of ethanol. In other words, we want the mixture in the tank to contain 1/10 ethanol.
So, we can write the equation: (1+x)/(20+x) = 1/10
Cross multiply to get: 10(1 + x) = 1(20 + x)
Expand: 10 + 10x = 20 + x
Rearrange: 9x = 10
Divide both sides by 9 to get: x = [spoiler]10/9[/spoiler]

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Aug 31, 2014 2:51 am

j_shreyans wrote:Bob just filled his car's gas tank with 20 gallons of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If his car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many gallons of ethanol must he add into the gas tank for his car to achieve optimum performance?

A)9/10
B)1
C)10/9
D)20/19
E)2

Amount of ethanol in the original volume = 5% of 20 gallons of gasohol = 1 gallon.
Thus, the amount of gasoline in the original volume = 20-1 = 19 gallons.
After pure ethanol is added, these 19 gallons of gasoline must constitute 90% of the resulting volume:
19 = (9/10)x
x = 190/9.
Thus, the amount of ethanol added = new volume - original volume = 190/9 - 20 = 190/9 - 180/9 = 10/9.

The correct answer is C.

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Tue Sep 02, 2014 10:00 pm

j_shreyans wrote:Bob just filled his car's gas tank with 20 gallons of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If his car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many gallons of ethanol must he add into the gas tank for his car to achieve optimum performance?

A)9/10
B)1
C)10/9
D)20/19
E)2

OAC

Answer: Option C

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by Jeff@TargetTestPrep » Thu Dec 14, 2017 5:02 pm

j_shreyans wrote:Bob just filled his car's gas tank with 20 gallons of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If his car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many gallons of ethanol must he add into the gas tank for his car to achieve optimum performance?

A)9/10
B)1
C)10/9
D)20/19
E)2

We can let x = the number of gallons of ethanol to be added to the gas tank.

Note that since the 20-gallon mixture of gasohol is 5% ethanol, there is 20 x 0.05 = 1 gallon of ethanol already in the tank. Since we want the gasohol to be 10% ethanol, we have the following equation:

(1 + x)/(20 + x) = 10/100

(1 + x)/(20 + x) = 1/10

10(1 + x) = 20 + x

10 + 10x = 20 + x

9x = 10

x = 10/9

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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