Three grades of Milk are 1%,2% and 3% fat by Vol. If x gallons of 1% grade, ygallons 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 and z ?
a. y+3z
b. 2y+3z
c. 3y+4.5z
d. y+z/4
e. 3y+z
OA - a. y +3z
Plz explain...[/quote]
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Anurag@Gurome
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Solution:shrey2287 wrote:Three grades of Milk are 1%,2% and 3% fat by Vol. If x gallons of 1% grade, ygallons 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 and z ?
a. y+3z
b. 2y+3z
c. 3y+4.5z
d. y+z/4
e. 3y+z
OA - a. y +3z
Plz explain...
This means that x/100 + y * 2/100 + z * 3/100 =(x+y+z) * 1.5/100
Or 2x + 4y + 6z = 3x + 3y + 3z
Or x = y + 3z
The correct answer is a.
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sl750
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You are mixing 1% of x grade milk along with 2% of y grade milk along with 3% of z grade milk.
The final mixture's concentration is 1.5% of those 3 grades of milk. Just add up the quantities
x+2y+3z=1.5(x+y+x)
0.5x=0.5y+1.5z or x=y+3z
The final mixture's concentration is 1.5% of those 3 grades of milk. Just add up the quantities
x+2y+3z=1.5(x+y+x)
0.5x=0.5y+1.5z or x=y+3z
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GMATGuruNY
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Since 1.5% is halfway between 1% and 2%, combining equal amounts of X (1% milkfat) and of Y (2% milkfat) will yield a mixture that is 1.5% milkfat.shrey2287 wrote:Three grades of Milk are 1%,2% and 3% fat by Vol. 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 and z ?
a. y+3z
b. 2y+3z
c. 3y+4.5z
d. (y+z)/4
e. 3y+z
OA - a. y +3z
Plz explain...
Let x=2, y=2 and z=0 (implying that no Z will be in the mixture).
The question asks for the value of x=2. This is our target.
Now we plug y=2 and z=0 into the answers to see which yields our target of 2.
Only answer choice A works:
y+3z = 2 + 3*0 = 2.
The correct answer is A.
Last edited by GMATGuruNY on Thu Oct 20, 2011 7:53 pm, edited 1 time in total.
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Why did you pick these particular numbers?GMATGuruNY wrote:Combining equal amounts of X (which is 1% milkfat) and of Y (which is 2% milkfat) will yield a mixture that is 1.5% milkfat.shrey2287 wrote:Three grades of Milk are 1%,2% and 3% fat by Vol. 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 and z ?
a. y+3z
b. 2y+3z
c. 3y+4.5z
d. (y+z)/4
e. 3y+z
OA - a. y +3z
Plz explain...
Let x=2, y=2 and z=0 (implying that no Z will be in the mixture).
The question asks for the value of x=2. This is our target.
Now we plug y=2 and z=0 into the answers to see which yields our target of 2.
Only answer choice A works:
y+3z = 2 + 3*0 = 2.
The correct answer is A.
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GMATGuruNY
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I chose z=0 so that there would be no z in the mixture.rooster wrote:Why did you pick these particular numbers?GMATGuruNY wrote:Combining equal amounts of X (which is 1% milkfat) and of Y (which is 2% milkfat) will yield a mixture that is 1.5% milkfat.shrey2287 wrote:Three grades of Milk are 1%,2% and 3% fat by Vol. 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 and z ?
a. y+3z
b. 2y+3z
c. 3y+4.5z
d. (y+z)/4
e. 3y+z
OA - a. y +3z
Plz explain...
Let x=2, y=2 and z=0 (implying that no Z will be in the mixture).
The question asks for the value of x=2. This is our target.
Now we plug y=2 and z=0 into the answers to see which yields our target of 2.
Only answer choice A works:
y+3z = 2 + 3*0 = 2.
The correct answer is A.
Without z, the needed grade (1.5%) is HALFWAY between x (1%) and y (2%).
Since the needed grade is HALFWAY between x and y, EQUAL amounts of x and y are needed.
I chose x=2 and y=2 because small numbers typically make it easier to spot the correct answer, often just by eyeballing the 5 answer choices.
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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].
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