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GMATprep problems, please explain!

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GMATprep problems, please explain!

by Veronica » Mon Oct 11, 2010 11:57 pm
For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?
a. f(x) = x^2
b. f(x) = x +1
c. f(x) = square root of x
d. f(x) = 2/x
e. f(x) = -3x

A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: blue, green, yellow, or pink. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
a. 6, b.8, c.16, d.24, e. 32
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by Geva@EconomistGMAT » Tue Oct 12, 2010 12:03 am
Veronica wrote:For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?
a. f(x) = x^2
b. f(x) = x +1
c. f(x) = square root of x
d. f(x) = 2/x
e. f(x) = -3x
Plug in numbers for a and b into the answer choices and eliminate answer choices. For example, if a=2 and b=1, then the question is asking for which of the following functions is f(3) equal to f(2) + f(1)?
A f(3) = 3^2 = 9
But
f(2) + f(1) = 2^2+1^2 = 4+1=5. Not equal, so A is eliminated.
Do the same for all five answer choices - you will eliminate all answer choices except for E, which correct because one answer choice in five has to be correct.
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by Geva@EconomistGMAT » Tue Oct 12, 2010 12:11 am
Veronica wrote:
A certain office supply store stocks 2 sizes of self-stick notepads, each in 4 colors: blue, green, yellow, or pink. The store packs the notepads in packages that contain either 3 notepads of the same size and the same color or 3 notepads of the same size of 3 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
a. 6, b.8, c.16, d.24, e. 32
Break it down into two separate scenarios:

1) 3 notepads of same size and same color:
there are 2 sizes, for each we have 4 colors, so there are 2*4=8 ways of choosing size and color for the entire package. Here all three notepads are the same, so no need to think about individual step by step.

2) 3 notepads same size, different color.
let's go with one size first: the number of ways of choosing 3 small notepads of different colors is 4*3*2, divide by 3! because the order does not matter. Total of 4*3*2 / 3*2*1 = 4 ways of choosing colors for each size. Note that this is basically 4C3, for those into formulas.
Since they come in two sizes, double that to get 2*4=8 again.

Add the two scenarios to get 8+8=16 different ways of choosing. Answer should be C.
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