Problem Solving

1. Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
(A) 81
(B) 159
(C) 166
(D) 285
(E) 324

2. A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment?
(A) 24
(B) 25
(C) 26
(D) 28
(E) 30

3. If a 3-digit integer is selected at random from the integers 100 through 199, inclusive, what is the probability that the first digit and the last digit of the integer are each equal to one more than the middle digit?
(A) 2/225
(B) 1/111
(C) 1/110
(D) 1/100
(E) 1/150


I need to know the steps in details. Can anyone help :

I would say
Q1 : answer E
Q2 : answer E
Q3 : answer D


Q1

removing 80 books coming from the same science implies that it concerns exclusively either physics or chemistry.
you can remove 50 + 50 +65 + 79 + 79 = 323 books without having 80 books of physics or chemistry
you then need one more book to be sure, i.e 324 books in total

Q2

cost = 300
mean cost price = 300 / x
mean sale price = mean cost price + 5
number of calculators sold = x - 2

total revenue = mean sale price x number of calculators sold = 300 + 120
total revenue = (mean cost price + 5) * (x - 2) = 420
replacing the mean cost price by 300 / x in he equation above gives you the quadratic equation 5x^2 - 130x - 600 = 0
you resolve it and you get x = 30


Q3

the first digit if the integer choosen randomly is automatically 1, as that integer is choosen between 100 and 199
the second digit must be 0, as the wording states that the first digit is equal to one more than the second digit
the third digit must be 1, as it is also equal to one more that the second digit

there is therefore only one possibility for that integer and it is 101

given that you have 100 possible integers to choose from, the probability to choose 101 is 1/100

removing 80 books coming from the same science implies that it concerns exclusively either physics or chemistry.
you can remove 50 + 50 +65 + 79 + 79 = 323 books without having 80 books of physics or chemistry
you then need one more book to be sure, i.e 324 books in total

I did not get this clearly. Why did you take 79?