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Bob just filled his car's gas tank with 20 gallons of [#permalink]
18 May 2007, 15:38

5

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00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

64% (02:36) correct
36% (01:33) wrong based on 642 sessions

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?

Re: Word Problem - chemical mixture [#permalink]
18 May 2007, 20:35

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

E = 5% of 20 gl = 1 gl
G = 95% of 20 gl = 19

we need to add E. if so, added E = 10% of (19/.9) - 1 = 10/9 gl
C.

Re: Word Problem - chemical mixture [#permalink]
22 Jun 2009, 09:27

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I also agree it is C. you need to go from 1/20 to (1+x)/(20+x) = 1/10 The trap answer is 1 since 1+1=2/20 =1/10 when it really is 2/21 _________________

Re: Word Problem - chemical mixture [#permalink]
23 Jun 2009, 07:09

Arvindgmat wrote:

What do you think is the difficulty level of the question. I did solve it but took a lot of time to find the answer. Took a couple of wrong approaches to solve the problem.

i am guessing medium difficulty. Pretty straightforward if someone done the type of question before. _________________

Re: Word Problem - chemical mixture [#permalink]
23 Jun 2009, 08:47

the solution is simple..

if your try using simple maths its an easy question 500-600 level question , but if you start using logic it becomes relatively a difficult question 600-700 level..

mathematical way: let x litres be added,, so x+1/ 20+x = 1/10 and find x easy as every one else has done here........ but if you start to use logic.. you will end up eating too much time..

Re: Word Problem - chemical mixture [#permalink]
24 Jun 2009, 11:14

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My vote is for C.

First find the current ratio:

E (ethanol) = 5% x 20 = 1 G (gasoline) = 20 - 1 = 19

Now, set up the new ratio that we are trying to obtain using the current one:

1/9 = (1 + x)/19 19 = 9 + 9x 10 = 9x x = 10/9

1/9 represents the new ratio we are trying to get of 10% ethanol and 90% gasoline. x is for the amount of gallons we need to add to the current 1 gal. of ethanol to achieve the new 10%.

Re: Word Problem - chemical mixture [#permalink]
11 Feb 2011, 15:11

Is it that we dont't need to have 20 litres of gasohol? Because if we do, I think the answer will be B.

Currently there is 5% of ethanol out of 20 litres of fuel that means the mixture contains 1 litre of ethanol. To have 10% ethanol, Bob needs to have 2 litres of ethanol, therefore he needs to add 1 more litre of ethanol. _________________

Re: Word Problem - chemical mixture [#permalink]
11 Feb 2011, 15:25

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Expert's post

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gmatpapa 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

Is it that we dont't need to have 20 litres of gasohol? Because if we do, I think the answer will be B.

Currently there is 5% of ethanol out of 20 litres of fuel that means the mixture contains 1 litre of ethanol. To have 10% ethanol, Bob needs to have 2 litres of ethanol, therefore he needs to add 1 more litre of ethanol.

Please read the question carefully: "how many gallons of ethanol must he add ..." add not replace.

19 gallons of gasoline which is now in the tank must comprise 90% of the whole fuel after adding some amount of ethanol --> thus whole amount of fuel after adding must be 19/(9/10)=190/9 gallons --> amount of the ethanol which Bob must add is 190/9-20=10/9 gallons.

Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]
05 Apr 2012, 05:30

2

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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

It is better to apply formula of weighted average:

V1/V2= (C2-C3)/ (C3-C1)

V1 and V2=> initial and final volumes of mixture respectively C1= Initial concentation of fluid= 5% C2= Concentration of additive fluid= 100% ethanol in our case C3= Desired concentration of fluid= 10%

Re: Word Problem - chemical mixture [#permalink]
30 Sep 2012, 23:01

Bunuel wrote:

gmatpapa 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

Is it that we dont't need to have 20 litres of gasohol? Because if we do, I think the answer will be B.

Currently there is 5% of ethanol out of 20 litres of fuel that means the mixture contains 1 litre of ethanol. To have 10% ethanol, Bob needs to have 2 litres of ethanol, therefore he needs to add 1 more litre of ethanol.

Please read the question carefully: "how many gallons of ethanol must he add ..." add not replace.

19 gallons of gasoline which is now in the tank must comprise 90% of the whole fuel after adding some amount of ethanol --> thus whole amount of fuel after adding must be 19/(9/10)=190/9 gallons --> amount of the ethanol which Bob must add is 190/9-20=10/9 gallons.

Answer: C.

Bunuel, Help me with this.

I am clear with this - 19 gallons of gasoline which is now in the tank must comprise 90% of the whole fuel after adding some amount of ethanol --> thus whole amount of fuel after adding must be 19/(9/10)=190/9 gallons

Now the total fuel is 190/9 gallons(Gasoline+ethanol). As given in the question ethanol will be 10% of this new solution which is 19/9. What is the mistake here? _________________

Re: Word Problem - chemical mixture [#permalink]
01 Oct 2012, 07:04

1

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Expert's post

ENAFEX wrote:

Bunuel wrote:

gmatpapa 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

Is it that we dont't need to have 20 litres of gasohol? Because if we do, I think the answer will be B.

Currently there is 5% of ethanol out of 20 litres of fuel that means the mixture contains 1 litre of ethanol. To have 10% ethanol, Bob needs to have 2 litres of ethanol, therefore he needs to add 1 more litre of ethanol.

Please read the question carefully: "how many gallons of ethanol must he add ..." add not replace.

19 gallons of gasoline which is now in the tank must comprise 90% of the whole fuel after adding some amount of ethanol --> thus whole amount of fuel after adding must be 19/(9/10)=190/9 gallons --> amount of the ethanol which Bob must add is 190/9-20=10/9 gallons.

Answer: C.

Bunuel, Help me with this.

I am clear with this - 19 gallons of gasoline which is now in the tank must comprise 90% of the whole fuel after adding some amount of ethanol --> thus whole amount of fuel after adding must be 19/(9/10)=190/9 gallons

Now the total fuel is 190/9 gallons(Gasoline+ethanol). As given in the question ethanol will be 10% of this new solution which is 19/9. What is the mistake here?

Yes, there will be 19/9 gallons of ethanol in the tank. But we are asked "how many gallons of ethanol must he add ..." and since there were 20*5%=1 gallon of ethanol initially, then we should add 19/9-1=10/9 gallons of ethanol.

Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]
22 Nov 2012, 19:56

3

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Total -20 gallon gasohol. 95% ethanol and 5%gasoline which is 19:1 Optimal mixture should be 18:2 as per details given. Now, 19 gallon of ethanol should be equal to 90%.So for that you should add more than 1 gallon of gasoline. i.e 19/9/10-20=10/9

Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]
01 Jan 2013, 13:34

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 ???

Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]
01 Jan 2013, 20:51

Expert's post

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 _________________

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