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# How many ounces of water must be added to a 30-ounce solution that is

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Math Expert
Joined: 02 Sep 2009
Posts: 46214
How many ounces of water must be added to a 30-ounce solution that is [#permalink]

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21 May 2017, 12:26
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Difficulty:

5% (low)

Question Stats:

90% (01:21) correct 10% (01:56) wrong based on 99 sessions

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How many ounces of water must be added to a 30-ounce solution that is 40 percent alcohol to dilute the solution to 25 percent alcohol?

(A) 9
(B) 10
(C) 15
(D) 16
(E) 18

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Senior Manager
Joined: 13 Oct 2016
Posts: 297
Concentration: Operations, Leadership
GMAT 1: 600 Q44 V28
Re: How many ounces of water must be added to a 30-ounce solution that is [#permalink]

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21 May 2017, 12:43
1
30-ounce solution that is 40 percent alcohol = 30*0.4 =12 ounce alcohol

30-12 = 18 ounce water.

Backsolving method: Take the middle option C - 15

18+15 = 33 ounce water ; 12 ounce alcohol ;

12/45 = 4/15 which is greater than 25 %

Lets go to next greater option which is D - 16

18+16 = 34 ounce water ; 12 ounce alcohol ;

12/46 = 6/23 which is greater than 25 %

Lets go to next greater option which is E - 18

18+18 = 36 ounce water ; 12 ounce alcohol ;

12/48 = 1/4 which is 25 % .

Hence option E is the answer.
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Intern
Joined: 20 May 2017
Posts: 10
Re: How many ounces of water must be added to a 30-ounce solution that is [#permalink]

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21 May 2017, 12:47
12 / ( x +30) = 0.25, x = 18.
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Joined: 22 May 2016
Posts: 1756
Re: How many ounces of water must be added to a 30-ounce solution that is [#permalink]

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21 May 2017, 13:21
2
Bunuel wrote:
How many ounces of water must be added to a 30-ounce solution that is 40 percent alcohol to dilute the solution to 25 percent alcohol?

(A) 9
(B) 10
(C) 15
(D) 16
(E) 18

Let x = number of ounces of water to be added

(concentration of A)*(Volume of A) + (concentration of B to be added)*(Volume of B to be added)= (resultant concentration of new mixture)*(total volume of new mixture = A + B)

Water has an alcohol concentration of 0

(.40)*(30) + (0)(x) = (.25) (30 + x)

12 + 0x = 7.5 + .25x

4.5 = .25x

$$\frac{4.5}{.25}$$ = 18 = x. Number of ounces of water to be added is
(E) 18
Hope it helps
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Joined: 07 Dec 2014
Posts: 1018
Re: How many ounces of water must be added to a 30-ounce solution that is [#permalink]

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21 May 2017, 14:03
1
Bunuel wrote:
How many ounces of water must be added to a 30-ounce solution that is 40 percent alcohol to dilute the solution to 25 percent alcohol?

(A) 9
(B) 10
(C) 15
(D) 16
(E) 18

let x=ounces of water to be added
.6*30+x=.75(30+x)
x=18 ounces
E
Manager
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Posts: 167
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GMAT 2: 600 Q48 V25
GMAT 3: 660 Q42 V39
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How many ounces of water must be added to a 30-ounce solution that is [#permalink]

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28 May 2017, 11:56
1
$$\frac{Total Alcohol}{total solution + added water} = \frac{1}{4}$$

$$\frac{12}{30+x} = \frac{1}{4} =>30+X = 12*4 => X = 48-30=18$$

Option: E

Hit Kudos should the solution is easy and simple.
Intern
Joined: 28 Feb 2018
Posts: 7
Re: How many ounces of water must be added to a 30-ounce solution that is [#permalink]

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11 Mar 2018, 02:57
Heseraj wrote:
$$\frac{Total Alcohol}{total solution + added water} = \frac{1}{4}$$

$$\frac{12}{30+x} = \frac{1}{4} =>30+X = 12*4 => X = 48-30=18$$

Option: E

Hit Kudos should the solution is easy and simple.

Nice Solution! Additional Approach yet simple as above

Alcohol before = Alcohol After
40% of 30 = 25% of (30+x)
40*30/25 = 30+x
48-30 = x = 18 = E
Re: How many ounces of water must be added to a 30-ounce solution that is   [#permalink] 11 Mar 2018, 02:57
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# How many ounces of water must be added to a 30-ounce solution that is

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