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Three grades of milk are 1 percent, 2 percent, and 3 percent

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Intern
Joined: 22 Oct 2008
Posts: 3
Three grades of milk are 1 percent, 2 percent, and 3 percent [#permalink]

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22 Oct 2008, 14:11
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Three grades of milk are 1 percent, 2 percent, and 3 percent fat by volume. If x gallons of the 1 percent, y gallons of the 2 percent, 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?
a. y+3z
b. y+z/4
c. 2y+3z
d. 3y+z
e. 3y+4.5z

another question
5^21 * 4^11 = 2 * 10^n, what is the value of n
a.11
b.21
c.22
d.23
e.32

cant figure it out
Senior Manager
Joined: 31 Jul 2008
Posts: 289
Re: help with some quant problems [#permalink]

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22 Oct 2008, 14:47
a and b respectively
Intern
Joined: 22 Oct 2008
Posts: 3
Re: help with some quant problems [#permalink]

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22 Oct 2008, 15:27
thank you
Manager
Joined: 15 Oct 2008
Posts: 104
Re: help with some quant problems [#permalink]

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22 Oct 2008, 15:33
burnsy wrote:
Three grades of milk are 1 percent, 2 percent, and 3 percent fat by volume. If x gallons of the 1 percent, y gallons of the 2 percent, 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?
a. y+3z
b. y+z/4
c. 2y+3z
d. 3y+z
e. 3y+4.5z

another question
5^21 * 4^11 = 2 * 10^n, what is the value of n
a.11
b.21
c.22
d.23
e.32

cant figure it out

For Q1:
0.01x + 0.02y + 0.03z = 0.015(x+y+z)
x + 2y + 3z = 1.5x + 1.5y + 1.5z
0.5x = 0.5y + 1.5z
x = y + 3z

For Q2:
5^21 * 4^11 = 2 * 10^n
5^21 * 2^11 * 2^11 = 2 * 2^n * 5^n (note: 4^11 = (2*2)^11 = 2^11 * 2^11, and 10^n = (2*5)^n = 2^n * 5^n
we divide both sides by 2, we will get:
5^21 * 2^10 * 2^11 = 2^n * 5^n
5^21 * 2^21 = 2^n * 5^n (note: 2^10 * 2^11 = 2^21)
Therefore n = 21

Intern
Joined: 22 Oct 2008
Posts: 3
Re: help with some quant problems [#permalink]

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22 Oct 2008, 15:42
thank you very much
haha, i overestimated the simplicity of the milk question
everything is crystal clear now
Re: help with some quant problems   [#permalink] 22 Oct 2008, 15:42
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Three grades of milk are 1 percent, 2 percent, and 3 percent

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