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runnerxc
Posts: **399**Registered User Member

1. All the survivors who live in a certain a post-apocalyptic settlement spend their miserable days hunting mutant buffalo or growing broccoli, and some do both. If, in total, 45 survivors grow broccoli, 30 hunt, and 37 of them perform only one of those tasks, how many perform both tasks?

(A) 56

(B) 38

(C) 19

(D) 11

(E) 9

2. At the Biltmore Hotel, 86 guests are in rooms with king size beds and 57 guests are in rooms with bathtubs. If 83 of the guests are in rooms with only a bathtub OR a king size bed, how many guests are in rooms with both features?

(A) 60

(B) 56

(C) 36

(D) 30

(E) 27

3. The equation of a certain parabola is y = ax^2 + bx + c. If a>0 and c<0, which of the following could be the graph of the parabola? (I don't have pics so I'll describe them)

(A) vertex in 3rd quadrant, opens upward

(B) vertex in 4th quadrant, opens upward

(C) same as (A) but vertex is slightly moved over closer to the y-axis

(D) vertex in 1st quadrant, opens downward

(E) vertex in 2nd quadrant, opens downward

Please help me with these problems and explain your solutions. Thank you!

(A) 56

(B) 38

(C) 19

(D) 11

(E) 9

2. At the Biltmore Hotel, 86 guests are in rooms with king size beds and 57 guests are in rooms with bathtubs. If 83 of the guests are in rooms with only a bathtub OR a king size bed, how many guests are in rooms with both features?

(A) 60

(B) 56

(C) 36

(D) 30

(E) 27

3. The equation of a certain parabola is y = ax^2 + bx + c. If a>0 and c<0, which of the following could be the graph of the parabola? (I don't have pics so I'll describe them)

(A) vertex in 3rd quadrant, opens upward

(B) vertex in 4th quadrant, opens upward

(C) same as (A) but vertex is slightly moved over closer to the y-axis

(D) vertex in 1st quadrant, opens downward

(E) vertex in 2nd quadrant, opens downward

Please help me with these problems and explain your solutions. Thank you!

Post edited by runnerxc on

## Replies to: Tricky Math Problems

399Registered User MemberJust look at Question 16 on this diagnostic drill and see if you can figure it out and explain your answer:

[url]https://****/file/d/0Bwar2-EatDDSNzhjYmE3ZjItNGMwOC00YzI4LWIzZTYtNGQ3ZWQwZGMyY2Q2/edit?hl=en_US&pli=1[/url]

261Registered User Junior Member2) Make a diagram. There are 143 amenities of any kind. 83 people have only a single amenity in their rooms, leaving 60 amenities for the remainder of the guests. Again, we divide this by two to find how many have both 60/2 = 30. 30 people have both a king size bed and a bath tub. (D)

3) Because a > 0, the parabola will open downward. Because c < 0, the vertex will be below the x-axis. We have thus narrowed it down to A, B, and C. Now think about the zeroes. (A) can't be the answer because both zeroes are negative. For example, (x-1)(x-1) will yield x^2 - 2x + 2 ... meaning c > 0. (B) can't be the answer either because both zeroes are positive. The only viable parabola is the one in which one of the zeroes is negative and the other positive. (C)

2,972Registered User Senior MemberA parabola opens up means that it "holds" water -- i.e. y=f(x) is large and positive as x approaches plus or minus infinity.

Since a>0 the parabola opens up -- hence eliminating choices D and E.

The x intercept of the parobola is y=f(0)=c. c is negative and hence the answer is C. Both A and B have positive x intercepts.

76Registered User Junior Memberx+1

x

x-2

x+2

-x+1

and

If x greater than 0, which of the following are equivalent to x ^ (3 over 2)?

1. x times square root x

2. square root x^3

3. (x ^ 2) over square root x

Help is more than welcomed..

149Registered User Junior Member149Registered User Junior Member47Registered User Junior Member