Practice Problem Solving Test 3

Q1. An auction house charges a commission of 15 percent on the first $50,000 of the
sale price of an item, plus 10 percent on the amount of the sale price in excess of
$50,000. What was the sale price of a painting for which the auction house charged
a total commisson of $24,000?
a. 115,000
b. 160,000
c. 215,000
d. 240,000
e. 365,000
15 % of 50, 000 = 7,5000
24 ,000 – 7,500 = 16,500
10 % of x = 16,500
X = 165,000
TOTAL AMOUNT = 165000+ 50,000 = 215,000
Answer = C
Q2. A hiker walking at a constant rate of 4 miles/hour is passed by a cyclist traveling
in the same direction at a constant rate of 20 miles/hour. The cyclist stops to wait for
the hiker 5 minutes after passing her, while the hiker continues to walk her constant
rate. How many minutes must the cyclist wait until the runner catches up?
A) 6 and 2/3
B) 15
C) 20
D) 25
E) 26 and 2/3
after the cyclist passes the pedestrian, their relative rate is 16 miles/hr (20 - 4, since
they're traveling in the same direction): in other words, the cyclist is going to get 16
miles farther ahead of the pedestrian each hour. so, in five minutes, which is 1/12
hour, the cyclist will go (16 mi/hr)(1/12 hr) = 4/3 miles ahead of the pedestrian.
then, the cyclist must wait for the pedestrian to walk 4/3 mile. this takes t = d / r =
(4/3 mi) / (4 mi/hr) = 1/3 hr = 20 minutes.
Answer = C
Q3. Joshua and Jose work at an auto repair center with four other workers. For a
survey on a healthcare insurance, 2 of the 6 workers will be randomly chosen to be
interviewed. What is the probability that Joshua and Jose will be both chosen?
A. 1/15
B. 1/12
C. 1/9
D. 1/6
E. 1/3
Chance that 1st person is one of the two is 2/6.
Once we've chosen one of them, chance that second person is the other J is 1/5.
2/6 * 1/5 = 2/30 = 1/15.
Answer = A
Q4. . A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its desert
platter. If each dessert platter contains an equal number of kinds of cheese and
kinds of fruit, how many different dessert platters could the restaurant offer?
(A)8
(B)12
(C)15
(D)21
(E)27
Equal chees kinds and fruit kinds
2C-2F = 6C2*2C2=15*1=15
1C-1F=6C1*2C1=12
Total 27
Answer = E
Q5. A certain city with a population of 132,000 is to be divided into 11 voting districts,
and no district is to have a population that is more than 10 percent greater than the
population of any other district. What is the minimum possible population that the
least populated district could be?
A) 10,700
(B) 10,800
(C) 10,900
(D) 11,000
(E) 11,100
The important insight for this problem is to realize that the way to minimize the
population in the least populous voting district is to have the maximum permitted
population in each of the other districts. So you have the least populous district with
population, p, and then each of the remaining 10 districts would have a population
10% greater than the least populous district or 1.1p. We know the total city
population is 132,000 so
10 % greater than p = 110 /100 p
= 1.1p
According to the question ,
P +10x( 1.1p ) =132,000
P= 11,000
Answer = D