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by shrey2287 » Tue Sep 20, 2011 6:50 pm
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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by Anurag@Gurome » Tue Sep 20, 2011 7:16 pm
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...
Solution:
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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by sl750 » Wed Sep 21, 2011 2:16 am
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
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by GMATGuruNY » Wed Sep 21, 2011 4:09 am
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...
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.

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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by shrey2287 » Wed Sep 21, 2011 4:34 am
Thank you Experts :)
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by jaguar123 » Wed Sep 21, 2011 5:30 am
1.Any tips in choosing plug in numbers for such problems.

2. What if there is one more choice y + 4z ? any clues?
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by rooster » Wed Oct 12, 2011 10:38 pm
GMATGuruNY wrote:
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...
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.

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.
Why did you pick these particular numbers?
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by GMATGuruNY » Thu Oct 13, 2011 3:19 am
rooster wrote:
GMATGuruNY wrote:
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...
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.

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.
Why did you pick these particular numbers?
I chose z=0 so that there would be no z in the mixture.

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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