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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% (02:34) correct
36% (01:31) wrong based on 840 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
1
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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
3
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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
This post received KUDOS
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
This post received KUDOS
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
This post received KUDOS
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
1
This post received KUDOS
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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