Bob just filled his car's gas tank with 20 gallons of gasohol, a mixtu

Question

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

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

smarinov · Accepted Answer

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%.

fluke · Answer

Originally; the fuel contained 20*5/100 = 1 gallon of ethanol

After adding x gallons of ethanol; 
the total weight of the fuel=20+x
Amount of ethanol in it will be = 1+x

(1+x) is 10% of (20+x)

(1+x/20+x)*100=10
100+100x=200+10x
90x=100
x=10/9

Ans: "C"

Bunuel · Answer

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.

Himalayan · Answer

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.

CrackTheGmatInSFO · Answer

its c. Lets say you add x gallons of ethanol more. Than 
(1+x)=(20+x)/10

x=10/9

shaselai · Answer

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

sanjaysingh82 · Answer

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..

gmatpapa · Answer

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.

MHIKER · Answer

5% ethanol = 20*5% = 1
Let x liter ethanol has to be mixed
1+x = 0.10(20+x)
1+x = 2+0.10x
0.90x = 1
x= 10/9
Ans. C

Cmplkj123 · Answer

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% 20/V2= (100-10)/(10-5) V2= 100/90= 10/9 :-D

KarishmaB · Answer

These are standard mixture problems. I have discussed a couple of such problems on my blog and videos. https://anaprep.com/arithmetic-mixtures/ https://www.youtube.com/watch?v=VdBl9Hw0HBg Also, you should get many such problems under the topic 'mixtures' in any standard GMAT prep book.

ENAFEX · Answer

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?

Bunuel · Answer

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.

Hope it's clear.

chanchalkalra · Answer

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

Emaco · Answer

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 ???

KarishmaB · Answer

.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

KarishmaB · Answer

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)

KarishmaB · Answer

In this post above: https://gmatclub.com/forum/bob-just-fill ... l#p1253824 I have already shown how to use scale method here.

JeffTargetTestPrep · Answer

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

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