Graph practice phần 6 doc

The best answer is A.
The range of prices for the sum of both cars is between the two minimum prices to the
two maximum prices. In other words, the minimum price is (50,000 + 35,000 =
85,000) and the maximum possible price is (95,000 + 100,000 = 195,000).
Among the answers given, A is the only one that is out of range.




6. Two cars were stolen from a car dealership in Boise, Idaho. Which of the following
cannot represent the loss of the car dealership’s owner?
A. $18,000.
B. $198,000.
C. $10,000.
D. $200,000.
E. There isn’t enough data to determine the answer.

The best answer is C.
Find the possible range of any two cars since we don’t know what kind of cars were
there in the dealership.
The minimum price of any car is the low end of the range of the compact cars, which
is approximately $7,500. And therefore the minimum price for two cars is $15,000.
The maximum price is determined by the highest price in the chart, the highest price
for a sports car, which is $100,000 and therefore the maximum price for two cars is
$200,000.
The only answer which is not in the range is C, $10,000.

7. If Michael has $20,000, which of the following cars are in his budget?
A. Compact car.
B. Japanese car.
C. American car.

D. European car.
E. answers A-C are correct.

The best answer is E.
Go to the 200 line in the graph and find out which of the categories have a possible
range under that line. Answers A, B and C are possible and therefore E is the answer.

8. Robert bought a sports car in 1988 and sold it after a few weeks in a price that
ranges from $35,000 to $43,000. What would be his financial loss on the car?
A. $7,000 to $15,000.
B. $15,000 to $35,000.
C. $12,000 to $42,000.
D. $7,000 to $65,000.
E. $15,000 to $68,000.

The best answer is D.
The financial loss also has a range, let’s find it.
The minimum loss would occur if he bought the car at the lowest price (50,000) and
sold it in the highest price (43,000), the loss is $7,000.
The maximum loss is exactly the opposite. He bought the car at the highest price and
sold it at the lowest price, thus (100,000 – 35,000 = 65,000).
We can see that D is the correct range.


9. Antonio bought a compact car and sold it after a year at 75% of its original price.
What was the price of the car that Antonio sold?
A. $15,000 to $25,000.
B. $7,545 to $35,000.
C. $15,000 to $70,000.
D. $5,000 to $25,000.

E. $5,625 to $30,000.

The best answer is E.
Antonio bought a car between $7,500 and $40,000. Take 75% of both edges and
you’ll receive the price that he sold the car. 75% of 40,000 is $30,000 and since
answer E is the only one with that number, that is the answer.

The following graph represents the prices of apartments in Chicago in different parts
of the city. Each shape represents the ranges of prices and sizes of apartments in each
of the areas mentioned in the key. For example, point A represents an apartment in the
Chicago suburbs that is 140 meters squared and costs 210 thousand dollars.

Key:
 The rectangle represents apartments in the West side of Chicago.
 The ellipse represents apartments in the down-town area of Chicago.
 The triangle represents apartments in the East side of Chicago.
 The parallelogram represents apartments in the suburbs of Chicago.

150
160
170
180
190
200
210
220
230
95 100 105 110 115 120 125 130 135 140 145 150 155 160

Size [meters squared]
Price



1. What size of apartment can be bought only in one area of Chicago?
A. 110 meters squared.
B. 115 meters squared.
C. 125 meters squared.
D. 130 meters squared.
E. 155 meters squared.

The best answer is A.
To each of the possible answers, draw an imaginary vertical line and see where it
intersects.
110 meters intersects the rectangle only while all the others intersect at least two
geometric shapes and therefore A is the answer.

2. Which of the following sizes of apartments (in meters squared) can be found in the
greatest number of place across Chicago?
A. 115.
B. 123.
C. 135.
D. 142.
E. 158.

The best answer is D.
Again, draw a vertical line and count how many different geometric shapes the line
intersects. All the lines except for one intersect 2 geometric places. The size 142
meters squared can be found in three different places in Chicago and therefore this is

the answer.

3. Ruth and Bill are interested in buying an apartment building that is at least 130
meters squared, in the lowest price possible. In which of the areas of Chicago should
they buy an apartment?
A. West side.
B. East side.
C. Downtown area.
D. Suburbs.
E. Answers C and D are both possible.

The best answer is C.
Go to the 130 line (in the horizontal axis) and look to the right of it.
There are three possibilities: downtown, suburbs and East side.
The apartments with the lowest price are the ones in the ellipse and therefore they
should buy an apartment in the downtown area of Chicago.

4. In which of the following areas in Chicago, when the size of the apartment
increases the price decreases?

A. West side.
B. East side.
C. Downtown area.
D. Suburbs.
E. Answers A and B are both possible.

The best answer is B.
The geometric shape that has a negative slope is the triangle and so when the sizes
increase the prices decrease. This is not a logical regularity but this is what the
graph gives us.

5. Which of the following schematic charts represents the difference (in absolute
value) between the high and the low price of an apartment building in the suburbs of
Chicago?

A. B. C.







D. E.






The best answer is D.
Look at the geometric shape that represents the suburbs of Chicago, thus the
parallelogram. In the beginning the high and the low price are both the same so the
difference graph should start from zero. Then the high price increases and the low
price stays the same, thus answers B, C and D are possible. After that the high price
and the low price remain equal and so the difference graph should also be horizontal,
answers C and D are left. The last part is the same as the first one, only in different
direction and therefore answer D is the only one left.

Movie A and movie B are two new successful movies that started to play at the same
time. The following graph represents the differences in ticket sales in the first 10
weeks of sampling. The “best movie” is the one that sold more tickets after 10 weeks.

0
1
2
3
4
5
6
7
8
0 1 2 3 4 5 6 7 8 9 10
Week of play
Difference in ticket sales
Difference in ticket sales in favor of Movie A
Difference in ticket sales in favor of Movie B


1. In which week was the same number of tickets sold in both movies?
A. 4.
B. 6.
C. 8.

D. 9.
E. 10.

The best answer is C.
The points on the graph represent differences in ticket sales. The week that doesn’t
have any point is the week where the same number of tickets was sold; that would be
the eighth week and so answer C is the best.

2. If in the first week, 9,560,000 movies A tickets were sold, how many movie B
tickets were sold that week?
A. 4,650,000.
B. 9,060,000.
C. 5,650,000.
D. 9,645,000.
E. 4,560,000.

The best answer is E.
The point in the first week represents the number of tickets that movie A sold more
than movie B and therefore movie B sold 5 million tickets less than 9,560,000, which
is 4,560,000 and therefore answer E is the correct.


3. If movie A sold the same number of tickets each week then in which of the
following weeks was the least amount of tickets sold to movie B?
A. 5.
B. 6.
C. 7.
D. 8.
E. 9.

The best answer is E.
If movie A sold the same number of tickets each time all we have to do is look for the
week in which movie A sold as many more tickets than movie B, that would be on the
ninth week- there movie A sold 9 million tickets more than movie B.


4. In the fourth week, movie B sold 5 million less tickets than in the third week. What
would be the difference in the number of tickets sold to movie A between the third
and the fourth week?
A. 2.
B. 4.
C. 5.
D. 9.
E. 15.

The best answer is C.
In this question the easiest way is to plug in some numbers.
Let’s say that 20 million tickets were sold on the fourth week for movie B and
therefore 25 million were sold in the third week according to the question. Now go to
the graph; in the third week movie B sold 4 million more than A, thus A sold 21
million tickets.
As for the fourth week, A sold 6 million more than B, thus A sold 26.
The difference in ticket sales are (26 – 21 = 5 million) and therefore answer C is
correct.

5. Which movie won the title “best movie” ?
A. Movie A.
B. Movie B.
C. They both sold the same amount of tickets.
D. There isn’t enough data to answer the question.

The best answer is B.
Each week, we know which movie sold more tickets. If we sum up the differences in
each of the weeks we’ll find that movie B sold 4 million tickets more than movie A
and therefore it is the “best movie”.











The following graphs represent the total sales of the “Bulletin Newspaper” in the city
of Wisconsin, Illinois across a period of 15 years. The lower graph represents the
breakdown of production to each of the photographic engraving machines.

Total newspapers sales
0
200
400
600
800
1000
1200
1400
1600

1800
2000
2200
2400
2600
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
copies sold


Percent of breakdown of total newspapers production
by photographic engraving machines
0
10
20
30
40

50
60
70
80
90
100
Percent
Machine A
Machine B
Machine C
Machine D



1. For how many years did machine D produce more newspapers than any other
photographic engraving machine?
A. 4.
B. 5.
C. 6.
D. 7.
E. 8.

The best answer is C.
The question refers solely to the bottom graph. We are looking for years in which the
line that represents the machine D is the highest. We can see that in the years 1983
and from 1986 to 1990 machine D had the highest percentage of production and
therefore C is the answer.

2. In which of the following years was the number of copies sold closest to 2 million?
A. 1976.

B. 1978.
C. 1980.
D. 1987.
E. 1989.

The best answer is E.
2 million will be represented as 2000 in the upper graph since the units are in
thousands.
Go over all the given years (only) and see which one is the closest to 2000.
You can easily see that in the year 1989, the sales stood on approximately 1900,
which is the closest.

3. In which of the following years, was the greatest number of active photographic
engraving machines?
A. 1977.
B. 1980.
C. 1982.
D. 1987.
E. 1990.

The best answer is C.
This question requires the use of the upper graph only.
Go over all the given years and draw an imaginary vertical line to each one, see how
many “machine” line it intersects. You can easily see that in 1982 there were four
intersections.


4. In which of the following years was the least amount of active machines?
A. 1976.
B. 1978.

C. 1980.
D. 1984.
E. 1986.

The best answer is A.
This question is exactly the opposite of the previous one. Again draw a vertical line
and count the intersections, this time look for the minimum.
You can see that in 1976 only one machine did all the work and therefore A is the
answer.

5. In the year in which machine A did four times more work than machine B, how
many copies approximately of the “Bulletin Newspaper” were sold in Wisconsin
(In thousands)?
A. 550.
B. 620.
C. 740.
D. 810.
E. 900.

The best answer is C.
Go over the first years (where machine A was active) and find the year in which
machine A did 4 times the work machine B did in percent terms. You can see the in
the year 1979, 20% of the work was done by B and the rest (80%) was done by A and
therefore this is the spoken year. Go to the upper graph and find the amount of copies
sold, the answer is approximately 750 and so C is the closest answer.

6. Approximately how many copies of newspapers did machine C make in the year
1988?
A. 675,000.
B. 710,000.

C. 820,000.
D. 875,000.
E. 900,000.

The best answer is C.
Go to the bottom graph; machine C did 35% of the total work.
According to the upper graph, approximately 2,350,000 copies of newspapers were
sold.
35% of 2,350,000 are approximately 820,000 and therefore C is the answer.






7. What exactly is the difference between the number of copies that machine D and B
did
in 1982?
A. 550,000.
B. 420,000.
C. 270,000.
D. 45,000.
E. 0.

The best answer is E.
Go to the year 1982 in the bottom graph. You can see that machine D and B did the
same amount of work and therefore the difference must be zero.

8. By approximately what percent did the yield from machine A increase from 1977
to 1981?

A. 15%.
B. 40%.
C. 50%.
D. 60%.
E. 67%.

The best answer is E.
Let’s find the increase in the yield of machine A.
In 1977, machine A did 100% of the work, which are approximately 450,000 copies.
In 1981, machine A did 50% of the work, which is 50% of 1,500,000, thus 750,000
copies. The difference (or the increase) was by 300,000 copies and in terms of percent
the increase was (300/450 = 67%) and therefore E is the answer.

9. In how many years did machine C did the same amount of work as any other
machine from 1981 to 1990 inclusive?
A. 0.
B. 1.
C. 2.
D. 3.
E. 4.

The best answer is C.
Remember, intersections are do not count between the years, only when the exact
mark of the year comes. In other words there were 3 intersections only, in 1981, 1983
and in 1985.
The intersection between 193 and 1984 does not count as one.

10. Approximately what is the ratio between the numbers of newspapers that machine
D produced in 1987 to the number of newspapers that machines A and B produced in
1981?
A. 13:28.
B. 4:5.
C. 2:3.
D. 6:7.
E. 72:75.

The best answer is E.
Use both graphs to answer this question.
In 1987 machine D produced 60% (from bottom graph) of 2400 (upper graph), which
is 1,440,000. In 1981 both machine together produced a 100% of the newspapers that
were sold, thus 1,500,000. The ratio is 144 to 150; break it down into simpler
numbers.
Divide by 2: 72 to 75 and therefore answer E is the best.