Problem Solving

1.) Which of the following inequalities has a solution set that,when graphed on the number line, is a single line segment of finite length?
x^4 is bigger or equal to 1;
x^3 is small or equal to 27;
x^2 is bigger or equal to 16;
x is equal to a number with between 2 and 5 inclusive;
3x+4 is equal to a number between 2 and 6 inclusive

2.) A thin piece of wire 40 metres long is cut into two pieces.One piece is used to form a circle with radius R, and the other is used to form a square. No wire is left over.Which of the following represents the total area, in square metres,in terms of the circular and square regions in terms of R?

TTR^2 ;
TTR^2+10;
TTR^2 + 0.25TT^2r^2;
TTr^2 + (40 - 2TTr)^2 ;
TTr^2 + (10-0.5TTr)^2

3.) A furniture dealer decided to purchase a desk for 150 and then set the selling price equal to the purchase price plus a mark up that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross proft from the purchase and sale of the desk? I solved this by backsolving but can you please show me how to solve this algebraically.

40
60
80
90
100

4.) What does square root of x^2)/x equal?

-1
0
1
x
|x|/x

5.) For which of the following fuctions f is f (x)=f (1-x) for all x?
f (x)=(1-x)
f (x) = 1 - x^2
f (x) = x^2 - (1-x)^2
f (x) = x^2 (1-x)^2
f (x) = x/(1-x)

6.)At the speed of fifty miles per hour, a certain car uses 1 gallon per 30 minutes. If the car starts with a full tank of 12 gallons and travels for five hours at 50 miles per hour, the amount of gasoline used would be what fraction of a full tank? I made the answer 10/12 but it is 25/36. please explain.

Lookingfor700GMAT wrote: 2.) A thin piece of wire 40 metres long is cut into two pieces.One piece is used to form a circle with radius R, and the other is used to form a square. No wire is left over.Which of the following represents the total area, in square metres,in terms of the circular and square regions in terms of R?

TTR^2 ;
TTR^2+10;
TTR^2 + 0.25TT^2r^2;
TTr^2 + (40 - 2TTr)^2 ;
TTr^2 + (10-0.5TTr)^2

............40 meters
|----------|---------------------|
....2TTr...........40-2TTr

Area Circle: TTr^2

Area Square: ((1/4)*(40-2TTr))^2 = (10-0.5TTr)^2

ANS: [spoiler]TTr^2 + (10-0.5TTr)^2[/spoiler]

Lookingfor700GMAT wrote:3.) A furniture dealer decided to purchase a desk for 150 and then set the selling price equal to the purchase price plus a mark up that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross proft from the purchase and sale of the desk? I solved this by backsolving but can you please show me how to solve this algebraically.

40
60
80
90
100

.40 *150 = .40(100) + .40(50) = 40 + 20 = 60

5.) For which of the following fuctions f is f (x)=f (1-x) for all x?
f (x)=(1-x)
f (x) = 1 - x^2
f (x) = x^2 - (1-x)^2
f (x) = x^2 (1-x)^2
f (x) = x/(1-x)

IF
f(x) = x^2 (1-x)^2
THEN
f(1-x) = (1-x)^2 (1-1-x)^2 = (1-x)^2 (-x)^2
since (-x)^2 is always positive then it can be considered = x^2
SO
f(x) = x^2 (1-x)^2 = f(1-x) = x^2 (1-x)^2