GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 21:18

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# What is the volume of milk present in a mixture of milk and water?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58385
What is the volume of milk present in a mixture of milk and water?  [#permalink]

### Show Tags

17 Oct 2018, 00:47
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:23) correct 26% (01:28) wrong based on 116 sessions

### HideShow timer Statistics

What is the volume of milk present in a mixture of milk and water?

(1) When 2 liters of milk is added to the mixture, the resultant mixture has equal quantities of milk and water.

(2) The initial mixture had 2 parts of water to 1 part milk.

_________________
examPAL Representative
Joined: 07 Dec 2017
Posts: 1140
Re: What is the volume of milk present in a mixture of milk and water?  [#permalink]

### Show Tags

17 Oct 2018, 04:12
Bunuel wrote:
What is the volume of milk present in a mixture of milk and water?

(1) When 2 liters of milk is added to the mixture, the resultant mixture has equal quantities of milk and water.

(2) The initial mixture had 2 parts of water to 1 part milk.

We'll translate our question stem into equations, so we understand what we need to do.
This is a Precise approach.

(1) This yields m+2 = w, which we cannot use to solve for m.
Insufficient.

(2) This yields m = 2w, which we also cannot use to solve for m.
Insufficient.

Combined.
2 equations with 2 variables --> one solution!
Sufficient.

_________________
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: What is the volume of milk present in a mixture of milk and water?  [#permalink]

### Show Tags

17 Oct 2018, 13:02
Bunuel wrote:
What is the volume of milk present in a mixture of milk and water?

(1) When 2 liters of milk is added to the mixture, the resultant mixture has equal quantities of milk and water.

(2) The initial mixture had 2 parts of water to 1 part milk.

$$\left\{ \matrix{ \,m\,\,:\,\,{\rm{milk}}\, \hfill \cr \,w\,\,\,:\,\,{\rm{water}}\,\,\, \hfill \cr} \right.\,\,\,\left( {\,{\rm{volumes}}\,\,{\rm{in}}\,\,{\rm{liters}}\,} \right)\,\,\,\,$$

$$? = m\,\,$$

$$\left( 1 \right)\,\,\,\,m + 2 = w\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {1,3} \right)\,\,\,\,\,\, \Rightarrow \,\,\,? = 1\,\, \hfill \cr \,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {2,4} \right)\,\,\,\,\,\, \Rightarrow \,\,\,? = 2\,\, \hfill \cr} \right.$$

$$\left( 2 \right)\,\,\,{m \over w} = {1 \over 2}\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {1,2} \right)\,\,\,\,\,\, \Rightarrow \,\,\,? = 1\,\, \hfill \cr \,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {2,4} \right)\,\,\,\,\,\, \Rightarrow \,\,\,? = 2\,\, \hfill \cr} \right.$$

$$\left( {1 + 2} \right)\,\,\,\,w\,\,\mathop = \limits^{\left( 2 \right)} \,\,2m\,\,\,\,\,\mathop \Rightarrow \limits^{\left( 1 \right)} \,\,\,\,\,m + 2 = 2m\,\,\,\,\, \Rightarrow \,\,\,\,m\,\,\,{\rm{unique}}$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Re: What is the volume of milk present in a mixture of milk and water?   [#permalink] 17 Oct 2018, 13:02
Display posts from previous: Sort by