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!
1) There are 75 total jobs. 37 people perform only one job. Meaning there are 38 jobs remaining that are performed by people who do two jobs. 38/2 = 19. 19 people perform two jobs. (C)
2) 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)
Plug in a random value for X, anything over 0.. really.. ANYTHING. and plug in the original formula and you get an answer, remember it, now plug in the same value you used for x in the answer choices and 1 plus 3 should be your correct answers so I and III only
wait so for the first and second question asking about the people who do both, i got up to getting 38 for the first question and 60 for the second... but why are you dividing by 2?
Replies to: Tricky Math Problems
Just look at Question 16 on this diagnostic drill and see if you can figure it out and explain your answer:
https://docs.google.com/file/d/0Bwar2-EatDDSNzhjYmE3ZjItNGMwOC00YzI4LWIzZTYtNGQ3ZWQwZGMyY2Q2/edit?hl=en_US&pli=1
2) 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)
A 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.
x+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..