P/S Help

[msorola]

1. One night a certain motel rented 3/4 of its rooms, including 2/3 of its air-conditioned rooms. If 3/5 of its
rooms were air-conditioned, what percent of the rooms that were not rented were air-conditioned?

(A) 20%
(B) 33 1/3%
(C) 35%
(D) 40%
(E) 80%

[Ans E]
***no idea.***

2. The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 16, how many more dollars, in terms of x, will it cost per person?
(A) x/6
(B) x/10
(C) x/16
(D) 3x/40
(E) 3x/80

[Ans E]
***Problems setting up the algebraic eq.***

3.If x is an integer and y=3x+2, which of the following CANNOT be a divisor of y ?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

[Ans C]
***I guessed at it from plugging in 0-9 for x, is there a faster way?***

Thanks in advance,
Matt

[Anurag@Gurome]

1. One night a certain motel rented 3/4 of its rooms, including 2/3 of its air-conditioned rooms. If 3/5 of its rooms were air-conditioned, what percent of the rooms that were not rented were air-conditioned?

Say, there were 60 rooms.
(I picked 60 as it is divisible by all the given denominators, i.e. 3, 4, and 5)

Number of rented rooms = (3/4)*60 = 45
Number of not rented rooms = (60 - 45) = 15

Number of AC rooms = (3/5)*60 = 36
Number of rented AC rooms = (2/3)*36 = 24
Number of not rented AC rooms = (36 - 24) = 12

Hence, required percentage = 100*(12/15) = 80

The correct answer is E.

[Anurag@Gurome]

2. The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 16, how many more dollars, in terms of x, will it cost per person?

If 10 persons take the trip, cost per person in dollars = x/10
If 16 persons take the trip, cost per person in dollars = x/16

Hence, it will cost (x/10 - x/16) = (8x - 5x)/80 = 3x/80 dollars more.

The correct answer is E.

[Anurag@Gurome]

3.If x is an integer and y=3x+2, which of the following CANNOT be a divisor of y?

As y is always 2 greater than a multiple of 3, y can never be divisible by 3 and hence by 6.

The correct answer is C.