Questions from the GMAC Practice test

[AWR83]

Dear All,

the following questions appeared on the practice tests. Unfortunately, they dont have explanations on those tests. Appreciate if someone would help me out in determinig the answer:

1) for which of the following functions is f(x)=f(x-1) for all x?
a) f(x)=x^2(1-x)^2
b) f(x)=1-x
c) f(x)=1-x^2

2)if n is a positive integer and the product of all the integers from 1 to n inclusive is a multiple of 990, what is the least possible value of n?

3) Three grades of milk are 1, 2, and 3 percent by volume. if x gallons of the 1% grade, y gallons of the 2% grade and z gallons of the 3% grade are mixed to give x+y+z gallons of 1.5% grade, what is x in terms of y and z?

Thanks,

[aroon7]

For the first question - none of the 3 answer choices will satisfy f(x) = f(x-1)...
ok. i will tell how i solved this...

a) f(x-1) = (x-1)^2(1-(x-1))^2
=> (x-1)^2(2-x)^2
this is not equal to f(x), which is x^2(1-x)^2

b) f(x-1) = 1-(x-1) = 2-X
this is not equal to f(x), which in this case is 1-x

c) f(x-1) = 1 - (x-1)^2
this is not equal to f(x), which is 1-x^2

so none of the answers suits the condition... Can you tell me the other two options??

2) product of 1 to n is n!
we need that value to be divisible by 990
990 = 9*11*10
so, 11! should be a multiple of 990 since 11! contains product of all the 3 numbers 9,10 and 11

3) we have,
(0.01)x + (0.02)y + (0.03)z = (0.015)(x+y+z)
solving this we get,
0.005x = 0.005y + 0.015z

what is the OA?

[AWR83]

Thanks for your reply..
for the 1st question, here are all the answer choices:
a) f(x)=1-x
b) f(x)=1-x^2
c) f(x)=x^2-(1-x)^2
d) f(x)=x^2(1-x)^2
e) f(x)=x/1-x

however, the answer shown is d.

for the last question, answers are
a) y+3z
b) y+z/4
c) 2y + 3z
d) 3y + z
e) 3y + 4.5z

Thanks again

[aroon7]

Thanks for your reply..
for the 1st question, here are all the answer choices:
a) f(x)=1-x
b) f(x)=1-x^2
c) f(x)=x^2-(1-x)^2
d) f(x)=x^2(1-x)^2
e) f(x)=x/1-x

however, the answer shown is d.

for the last question, answers are
a) y+3z
b) y+z/4
c) 2y + 3z
d) 3y + z
e) 3y + 4.5z

Thanks again

For first, I too couldnot make out how it is D. Sorry!
For the last question ans is A
dividing both sides by 0.005, you get
x = y + 3z

[AWR83]

Thanks for your help!!

Would any one be able to give his insights to the 1st Q?

Thanks,

[dmateer25]

You typed the question wrong for the first one.

It is f(1-x) not f(x-1).


Here is a link to a discussion on this question:

https://www.beatthegmat.com/gmat-prep-fu ... html#25298