Mixture of fatty milks
This topic has expert replies
Three grades of milk are 1 percent, 2 percent, and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+ y + z gallons of a 1.5 percent grade, what is x in terms of y and z?
GMAT/MBA Expert
- Anju@Gurome
- GMAT Instructor
- Posts: 511
- Joined: Wed Aug 11, 2010 9:47 am
- Location: Delhi, India
- Thanked: 344 times
- Followed by:86 members
The concentration of milk in the mixture = 1% of x + 2% of y + 3% of z = (x + 2y + 3z)/100actofman wrote:Three grades of milk are 1 percent, 2 percent, and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x + y + z gallons of a 1.5 percent grade, what is x in terms of y and z?
Also, the concentration of milk in the mixture = 1.5% of (x + y + z) = (1.5)*(x + y + z)/100
So, x + 2y + 3z = 1.5x + 1.5y + 1.5z
--> 0.5y + 1.5z = 0.5x
--> y + 3z = x
Anju Agarwal
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Quant Expert, Gurome
Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.
§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Thanks! I did get the x +2y + 3z part but somehow it eluded me to do 1.5(x + y + z). I was thinking there was something more complex to it.Anju@Gurome wrote:The concentration of milk in the mixture = 1% of x + 2% of y + 3% of z = (x + 2y + 3z)/100actofman wrote:Three grades of milk are 1 percent, 2 percent, and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x + y + z gallons of a 1.5 percent grade, what is x in terms of y and z?
Also, the concentration of milk in the mixture = 1.5% of (x + y + z) = (1.5)*(x + y + z)/100
So, x + 2y + 3z = 1.5x + 1.5y + 1.5z
--> 0.5y + 1.5z = 0.5x
--> y + 3z = x
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
The desired grade -- 1.5% -- is equal to the AVERAGE of x=1% and y=2%3 grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of 1% grade, y gallons of 2% grade and z gallons of 3 % grade are mixed to give x+y+z gallons of 1.5% grade, what is x in terms of y & z?
1) y+3z
2) (y+z)/4
3) 2y+3z
4) 3y+2
5) 3y+4.5z
(1% + 2%)/2 = 1.5%.
Thus, a mixture composed of equal amounts of x and y will be 1.5% grade.
Let x=2, y=2, and z=0, implying that the mixture will composed of equal amounts of x and y (2 units each).
The question stem asks for the value of x=2. This is our target.
Now plug y=2 and z=0 into the answers to see which yields our target of 2.
Only A works:
y + 3z = 2 + 3(0) = 2.
The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Thanks Mitch!GMATGuruNY wrote:The desired grade -- 1.5% -- is equal to the AVERAGE of x=1% and y=2%3 grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of 1% grade, y gallons of 2% grade and z gallons of 3 % grade are mixed to give x+y+z gallons of 1.5% grade, what is x in terms of y & z?
1) y+3z
2) (y+z)/4
3) 2y+3z
4) 3y+2
5) 3y+4.5z
(1% + 2%)/2 = 1.5%.
Thus, a mixture composed of equal amounts of x and y will be 1.5% grade.
Let x=2, y=2, and z=0, implying that the mixture will composed of equal amounts of x and y (2 units each).
The question stem asks for the value of x=2. This is our target.
Now plug y=2 and z=0 into the answers to see which yields our target of 2.
Only A works:
y + 3z = 2 + 3(0) = 2.
The correct answer is A.
In your first paragraph, why was Z ignored? Only bec 1.5 is average of x and y values? So if 1% was y and 2% was Z, we'll ignore x bec y and z average to 1.5%?
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
=
Here, the desired grade -- 1.5% -- is equal to the AVERAGE of y=1% and z=2%
(1% + 2%)/2 = 1.5%.
Thus, a mixture composed of equal amounts of y and z will be 1.5% grade.
In this case, we could plug in the following combination of values:
x=0, y=2, and z=2, with the result that the mixture will composed of equal amounts of y and z (2 units each).
Correct!actofman wrote:Thanks Mitch!GMATGuruNY wrote:The desired grade -- 1.5% -- is equal to the AVERAGE of x=1% and y=2%3 grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of 1% grade, y gallons of 2% grade and z gallons of 3 % grade are mixed to give x+y+z gallons of 1.5% grade, what is x in terms of y & z?
1) y+3z
2) (y+z)/4
3) 2y+3z
4) 3y+2
5) 3y+4.5z
(1% + 2%)/2 = 1.5%.
Thus, a mixture composed of equal amounts of x and y will be 1.5% grade.
Let x=2, y=2, and z=0, implying that the mixture will composed of equal amounts of x and y (2 units each).
The question stem asks for the value of x=2. This is our target.
Now plug y=2 and z=0 into the answers to see which yields our target of 2.
Only A works:
y + 3z = 2 + 3(0) = 2.
The correct answer is A.
In your first paragraph, why was Z ignored? Only bec 1.5 is average of x and y values? So if 1% was y and 2% was Z, we'll ignore x bec y and z average to 1.5%?
Note the changes in red.3 grades of milk are 1 percent, 2 percent and 3 percent fat by volume. If x gallons of 3% grade, y gallons of 1% grade and z gallons of 2% grade are mixed to give x+y+z gallons of 1.5% grade, what is z in terms of x and y?
Here, the desired grade -- 1.5% -- is equal to the AVERAGE of y=1% and z=2%
(1% + 2%)/2 = 1.5%.
Thus, a mixture composed of equal amounts of y and z will be 1.5% grade.
In this case, we could plug in the following combination of values:
x=0, y=2, and z=2, with the result that the mixture will composed of equal amounts of y and z (2 units each).
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3