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Bob just filled his car's gas tank with 20 gallons of

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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]  02 Jan 2013, 11:01
In the original mixture we have 95% G= 19 gallons and 5% E= 1 gallon
We have to add X amount of Ethanol to make it 90:10 mixture,
hence:
(1+x/20+x)*100=10
(1+x)*10=20+x
9x=10; x=10/9

Last edited by nk9285 on 02 Jan 2013, 11:18, edited 1 time in total.
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]  20 May 2013, 14:17
I got 1 cause i got 5% to be 1 and the reason i forgot that is because i forgot to 95% gasoline
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]  05 Aug 2013, 21:54
Expert's post
above720 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

Responding to a pm:

Using Weighted average formula:

w1/w2 = (A2 - Avg)/(Avg - A1)

You need to mix 5% ethanol mixture with 100% ethanol to give a 10% ethanol mixture.

w1/w2 = (100 - 10)/(10 - 5) = 18/1

For every 18 parts of gasohol, you need to put 1 part of pure ethanol.
So if you have 20 gallons of gasohol, you need to put 20/18 (= 10/9) gallons of pure ethanol.
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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Manager Joined: 30 May 2013 Posts: 193 Location: India Concentration: Entrepreneurship, General Management GPA: 3.82 Followers: 0 Kudos [?]: 29 [0], given: 72 Re: Bob just filled his car's gas tank with 20 gallons of [#permalink] 14 Aug 2013, 04:49 VeritasPrepKarishma wrote: above720 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 Responding to a pm: Using Weighted average formula: w1/w2 = (A2 - Avg)/(Avg - A1) You need to mix 5% ethanol mixture with 100% ethanol to give a 10% ethanol mixture. w1/w2 = (100 - 10)/(10 - 5) = 18/1 For every 18 parts of gasohol, you need to put 1 part of pure ethanol. So if you have 20 gallons of gasohol, you need to put 20/18 (= 10/9) gallons of pure ethanol. Answer (C) Hi, Is this alligation rule method? Regrds, Rrsnathan. Senior Manager Joined: 10 Jul 2013 Posts: 343 Followers: 3 Kudos [?]: 152 [0], given: 102 Re: Bob just filled his car's gas tank with 20 gallons of [#permalink] 15 Aug 2013, 03:38 above720 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 Ethanol now = 5% of 20 = 1 gallon Let, we need x gallons of ethanol . so, (20+x)/(1+x) = 100/10 or, x = 10/9 (Answer) _________________ Asif vai..... Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5137 Location: Pune, India Followers: 1244 Kudos [?]: 6037 [0], given: 171 Re: Bob just filled his car's gas tank with 20 gallons of [#permalink] 15 Aug 2013, 21:42 Expert's post rrsnathan wrote: VeritasPrepKarishma wrote: above720 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 Responding to a pm: Using Weighted average formula: w1/w2 = (A2 - Avg)/(Avg - A1) You need to mix 5% ethanol mixture with 100% ethanol to give a 10% ethanol mixture. w1/w2 = (100 - 10)/(10 - 5) = 18/1 For every 18 parts of gasohol, you need to put 1 part of pure ethanol. So if you have 20 gallons of gasohol, you need to put 20/18 (= 10/9) gallons of pure ethanol. Answer (C) Hi, Is this alligation rule method? Regrds, Rrsnathan. Yes, alligation uses a diagram (with a cross with average in the middle) which leads to this formula. This formula is very effective in solving most weighted average/mixture problems. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]  19 Sep 2013, 03:50
above720 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

Let the total gallons = 100.
therefore, it has 5 gallon ethanol and 95 gallon gasoline and we need to make the mixture of 10:90 instead.
Let the volume of ethanol added be 'x' in order to make the ratio 10:90.
therefore, (5+x)/95 = 10/90.
x = 50/9.

Now, if in 100 gallons of fuel we need to add, 50/9 gallons of ethanol to make the ratio 10:90
In 20 gallons we would add = (50/9)/100 X 20 (simple unitary method)
= 10/9 (Ans)
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]  19 Sep 2014, 07:56
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]  19 Nov 2014, 04:17
Let x is the gallons of ethanol to be added in the mixture => x has 100% ethanol.
Totally ignore the information about gasoline because we're dealing with ethanol now.

The new mixture should be 20 + x (gallons) and have 10% ethanol => (20+x)*10%
Add x gallons of 100% ethanol to 20 gallons of 5% ethanol => x*100% + 20*5% = x+1

We have the equation: (20 + x)*0,1 = x + 1 => x = 10/9
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Bob just filled his car's gas tank with 20 gallons of [#permalink]  01 Dec 2014, 17:08
initial 20 = 1E + 19G

new 20+E = (20+E)/10 +19 (as amount of G same only E added)

=> 18 +9E/10 = 19

HENCE E = 10/9
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]  02 Dec 2014, 01:46
Ethanol ............... Gasoline .............. Total

1 ............................. 19 ..................... 20 (Current fill)

1+x ........................... 19 ................... 20+x (Say "x" litres of ethanol is added to make it 10%)

Equation can be setup in two ways

\frac{10}{100} (20+x) = 1+x

OR

\frac{90}{100} (20+x) = 19

For both, computation of x would be the same

x = \frac{10}{9}

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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]  11 Dec 2014, 06:40
VeritasPrepKarishma wrote:
Emaco wrote:
Guys, I made the following formula, could anyone of you please tell me what's wrong with it ?
0.95 (20) + X = 90/100 (20+x)
1+X = 18+0.9x
0.1x = 17 ???

.95 of 20 is the amount of gasoline already in his car. He adds more ethanol and not gasoline so you cannot add x (amount of ethanol added) to .95 of 20.

Instead, you need to find the current amount of ethanol and add x to it.

.05(20) + x = .10 (20 + x)
.9x = 1
x = 10/9

I solved it using algebra, for concepts sake, is it possible to use alligation or the scale method here?
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]  14 Dec 2014, 03:15
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I solved it using algebra, for concepts sake, is it possible to use alligation or the scale method here?

In this post above: bob-just-filled-his-car-s-gas-tank-with-20-gallons-of-45790-20.html#p1253824
I have already shown how to use scale method here.
For more on the formula, check: http://www.veritasprep.com/blog/2011/03 ... -averages/
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Re: Bob just filled his car's gas tank with 20 gallons of   [#permalink] 14 Dec 2014, 03:15

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