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M18-21

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M18-21  [#permalink]

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New post 16 Sep 2014, 01:04
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  15% (low)

Question Stats:

80% (01:14) correct 20% (01:30) wrong based on 189 sessions

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If a 30%-solution of alcohol was mixed with a 50%-solution of alcohol to obtain 10 liters of a 45%-solution of alcohol, how much of the 30%-solution was used?

A. 2.0 liters
B. 2.5 liters
C. 2.7 liters
D. 3.0 liters
E. 3.2 liters

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M18-21  [#permalink]

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New post 16 Sep 2014, 01:04
Official Solution:

If a 30%-solution of alcohol was mixed with a 50%-solution of alcohol to obtain 10 liters of a 45%-solution of alcohol, how much of the 30%-solution was used?

A. 2.0 liters
B. 2.5 liters
C. 2.7 liters
D. 3.0 liters
E. 3.2 liters


Say there are \(x\) liters of a 30%-solution of alcohol then there would be \(10-x\) liters of a 50%-solution of alcohol.

Equate the amount of alcohol in 10 liters of mixture \(0.3x+0.5(10-x)=0.45*10\), which gives \(x=2.5\) liters.


Answer: B
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M18-21  [#permalink]

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New post 27 Sep 2014, 07:31
1
Bunuel wrote:
Official Solution:

If a 30%-solution of alcohol was mixed with a 50%-solution of alcohol to obtain 10 liters of a 45%-solution of alcohol, how much of the 30%-solution was used?

A. 2.0 liters
B. 2.5 liters
C. 2.7 liters
D. 3.0 liters
E. 3.2 liters


Say there are \(x\) liters of a 30%-solution of alcohol then there would be \(10-x\) liters of a 45%-solution of alcohol.

Equate the amount of alcohol in 10 liters of mixture \(0.3x+0.5(10-x)=0.45*10\), which gives \(x=2.5\) liters.


Answer: B


Bunuel,

Kindly correct me if i am wrong but isn't 50% solution of alcohol supposed to come in the above highlighted section.
ie: there would be \(10-x\) liters of a 50%-solution of alcohol.
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Joined: 02 Sep 2009
Posts: 50009
Re: M18-21  [#permalink]

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New post 27 Sep 2014, 13:09
earnit wrote:
Bunuel wrote:
Official Solution:

If a 30%-solution of alcohol was mixed with a 50%-solution of alcohol to obtain 10 liters of a 45%-solution of alcohol, how much of the 30%-solution was used?

A. 2.0 liters
B. 2.5 liters
C. 2.7 liters
D. 3.0 liters
E. 3.2 liters


Say there are \(x\) liters of a 30%-solution of alcohol then there would be \(10-x\) liters of a 45%-solution of alcohol.

Equate the amount of alcohol in 10 liters of mixture \(0.3x+0.5(10-x)=0.45*10\), which gives \(x=2.5\) liters.


Answer: B


Bunuel,

Kindly correct me if i am wrong but isn't 50% solution of alcohol supposed to come in the above highlighted section.
ie: there would be \(10-x\) liters of a 50%-solution of alcohol.


Typo edited. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Joined: 05 Feb 2017
Posts: 2
Re: M18-21  [#permalink]

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New post 16 Feb 2017, 12:23
It can be useful to think in terms of a picture to solve this

30% 35% 40% 45% 50%
0----1----2----3----4

the ratio of space between 30% - 45% and 45% to 50% is 3:1

45% is closer to 50% than to 30 %, so there is 3 times as much 50% solution mixed in as there is 30% solution

so for every 4 litres added, 1L will be 30% solution
(1/4) * 10 L = 2.5L

Hopefully this helps :?
GMAT Club Bot
Re: M18-21 &nbs [#permalink] 16 Feb 2017, 12:23
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