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Below are four questions I encountered on a PowerPrep exam that threw me off my time schedule. Could someone please explain efficent ways to solve these problems? I know this test is all about tricks and minimizing the amount of actual calculation you have to do...these just stumped me!

1. On July 1 of last year, the total # of employees at Company E was decreased by 10%. Without any change in salaries of the remaining employees, the average salary was 10% more after the decrease in the # of employees than before the decrease. The total (sum) of combined salaries after July last year was what percent of that before July 1 last year?

a) 90%
b) 99%
c) 100%
d) 101%
e) 110%

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

a) y + 3z
b) (y+4)/4
c) 2y + 3z
d) 3y + z
e) 3y + 4.5z

3. For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a+b?

a) f(x) = x^2
b) f(x) = x + 1
c) f(x) = radical x
d) f(x) = 2/x
e) f(x) = -3x

4. For every integer k from 1-10 inclusive, the Kth term of a certain sequence is given by (-1)^k+1 x (1/(2^k)). If T is the sum of the first 10 terms in the sequence, then T is:

a) greater than 2
b) between 1 and 2
c) between 1/2 and 1
d) between 1/4 and 1/2
e) less than 1/4

1. On July 1 of last year, the total # of employees at Company E was decreased by 10%. Without any change in salaries of the remaining employees, the average salary was 10% more after the decrease in the # of employees than before the decrease. The total (sum) of combined salaries after July last year was what percent of that before July 1 last year?

a) 90% b) 99% c) 100% d) 101% e) 110%

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

a) y + 3z b) (y+4)/4 c) 2y + 3z d) 3y + z e) 3y + 4.5z

1) Let Number of employees be E.
Let average Salary be A
After July 1st
Number of employees = 9E/10
Average Salary = 11A/10

Total salary before July 1st = EA
Total salary after July 1st = 99/100 * EA

Hence B

2) Amount of milk(by volume) in x gallons = 1/100 * X
Amount of milk(by volume) in y gallons = 2/100 * y
Amount of milk(by volume) in z gallons = 3/100 * z

Hence
1/100 * X + 2/100 * y + 3/100 * z = 1.5/100 * (x+y+z)

As a newbie I am shocked, surprised and dismayed by the expertise of the responders and the ease of the elegant solutions! Perhaps one day in the long distant future

I had the same confusion as Rajiv... freetheking seems to have understood something neither of us have:

(-1)^k+1 x (1/(2^k))

If we use the BODMAS rule:

This seems to me to follow the pattern (-1)^1 + 1 x (1/2^1)
= -1 + 1/2

The 2nd term would be therefore 1+1/4 etc.

As Rajiv pointed out, in this case all the -1s and 1s would cancel out and we would be left with a value between 1/2 and 1.

Now if we interpret it this way:
((-1)^1+1) * 1/(2^1)_ then it would be 0, 1/4, 0, 1/16 etc.. leading to a value between 1/4 and 1/2.

Is that what is going on? Is the question wrong or am I missing something?

I agree , it is redundant.. but hey maybe they want to confuse us

No it's not, as far as I know there's no trick like this one..

K+1 is just a superscript in a word file, if you copy it.. it just truned into a normal word font. That's why I assumed ^(k+1).
Moreover, OA is D.. thus ^(k+1) makes perfect sense. _________________