H. Tables,
Charts, and Graphs (Data Interpretation)
Graphs and charts show the relationship of numbers
and quantities in visual form. By looking at a graph, you can
see at a glance the relationship between two or more sets of
information. If such information were presented in written form,
it would be hard to read and understand.
Here are some things to remember
when doing problems based on data interpretation:
Example Set #28: Table Chart
Examples 1-5 are based on this Table Chart.
The following chart is a record
of the performance of a baseball team for the first seven weeks
of the season.
|
|
Games
Won |
Games
Lost |
Total
No.of Games Played |
|
First Week |
5 |
3 |
8 |
|
Second Week |
4 |
4 |
16 |
|
Third Week |
5 |
2 |
23 |
|
Fourth Week |
6 |
3 |
32 |
|
Fifth Week |
4 |
2 |
38 |
|
Sixth Week |
3 |
3 |
44 |
|
Seventh Week |
2 |
4 |
50 |
1. How many games did the
team win during the first seven weeks?
(A) 32
(B) 29
(C) 25
(D) 21
(E) 50
Choice B is correct. To find
the total number of games won, add the number of games won for
all the weeks, 5 + 4 + 5 + 6 + 4 + 3 + 2 = 29.
2. What percent of the games
did the team win?
(A) 75%
(B) 60%
(C) 58%
(D) 29%
(E) 80%
Choice C is correct. The team
won 29 out of 50 games or 58%.
3. According to the chart,
which week was the worst for the team?
(A) second week
(B) fourth week
(C) fifth week
(D) sixth week
(E) seventh week
Choice E is correct. The seventh
week was the only week that the team lost more games than it
won.
4. Which week was the best
week for the team?
(A) first week
(B) third week
(C) fourth week
(D) fifth week
(E) sixth week
Choice B is correct. During the
third week, the team won 5 games and lost 2, or it won about
70% of the games that week. Compared with the winning percentages
for other weeks, the third week's was the highest.
5. If there are fifty more
games to play in the season, how many more games must the team
win to end up winning 70% of the games?
(A) 39
(B) 35
(C) 41
(D) 34
(E) 32
Choice C is correct. To win 70%
of all the games, the team must win 70 out of 100. Since it won
29 games out of the first 50 games, it must win (70 - 29) or
41 games out of the next 50 games.
Example Set #29: Interpreting
Graphs
Answer the following questions based
on the graph above.
1. During what two-year period
did the company's earnings increase the most?
(A) 95-97
(B) 96-97
(C) 96-98
(D) 97-99
(E) 98-00
Reading from the graph, the company's
earnings increased from $5 million in 1996 to $10 million in
1997, and then to $12 million in 1998. The two-year increase
from '96 to '98 was $7 million--clearly the largest on the graph.
The answer is (C).
2. During the years 1996 through 1998, what were the average
earnings per year?
(A) 6 million
(B) 7.5 million
(C) 9 million
(D) 10 million
(E) 27 million
The graph yields the following
information:
Year Earnings
1996 $5 million
1997 $10 million
1998 $12 million
To figure out the average, add (5 + 10 + 12)/3 = 9. The answer
is (C).
3. In which year did earnings
increase by the greatest percentage over the previous year?
(A) 96
(B) 97
(C) 98
(D) 99
(E) 2000
To find the percentage increase
(or decrease), divide the numerical change by the original amount.
|
Year |
Earnings |
% increase from
year before |
|
1995 |
8 |
n/a |
|
1996 |
5 |
decrease |
|
1997 |
10 |
100% |
|
1998 |
12 |
20% |
|
1999 |
11 |
decrease |
|
2000 |
8 |
decrease |
The largest number in the right-hand column, 100%, corresponds
to the year 1997. The answer is (B).
4. If the company's earnings
are less than 10 percent of sales during a year, then the Chief
Operating Officer will get a 50% pay cut. How many times between
1995 and 2000 did the Chief Operating Officer take a pay cut?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Calculating 10 percent of the
sales for each year yields Year, 10% of Sales (millions), Earnings
(millions).
|
Year |
10% of sales |
Earnings |
is 10% of sales greater
than earnings? |
|
1995 |
.10 x 80 = 8 |
8 |
no cut |
|
1996 |
.10 x 70 = 7 |
5 |
cut |
|
1997 |
.10 x 50 = 5 |
10 |
no cut |
|
1998 |
.10 x 80 = 8 |
12 |
no cut |
|
1999 |
.10 x 90 = 9 |
11 |
no cut |
|
2000 |
.10 x 100 = 10 |
8 |
cut |
Comparing the right columns shows that earnings were less than
10 percent of sales in 1996 and 2000. The answer is (C).
