Number and Percetages

Question 1

True/False?

Increasing percentages =
increasing numbers.

Answer 1

False

% is a proportion of a total #
% is also a fraction of a total

i.e. 10% is 1/10

that means ; x% = ratio of a/b

if x% increased, it means ratio a/b also increased

Possible scenarios for % increase;
* #a increased while #b is same
* #b decreased while #a is same
* Both increased ; %/rate/proportion of increase of a&raquo_space; %/rate/proportion of increase of b.
* Both decreased; %/rate/proportion of decline of a &laquo_space; %/rate/proportion of decline of b.

*For example
“Auto manufacturer X increased their United States market share from 10%
last year to 25% this year. Therefore, Company X sold more cars in the
United States this year than last.”

This is true if the market size (denominator)
* stayed the same or
* became larger.

But if the size of the U.S. car
market decreased by enough, the argument would not be true,*

KEY - Find out what makes up the percentage ie numerator and denominator

Question 2

True/False?

Decreasing percentages =
decreasing numbers.

Answer 2

False

x% = a/b (100)
if x% decreases, it means the ratio a/b has decreased

Possible scenarios for % decrease are;
* #a decreases while #b is same
* #b increased while #a is same
* Both decrease; %/rate/proportion of decline of a&raquo_space; %/rate/proportion of decline of b
* Both increase: %/rate/proportion of increase of a &laquo_space; %/rate/proportion of increase of b

KEY - Find out what makes up the percentage ie numerator and denominator

Question 3

True/False?

Increasing numbers =
increasing percentages.

Answer 3

False

if x% = a/b ratio

if #a increases, possible scenarios are:

• # a increases while #b is same = % increases
• Both #a and #b increase but proportion of a increase is&raquo_space; proportion of b increase = % increases
• Both #a and #b increase but proportion of a increase is &laquo_space;proportion of b increase = % decreases

“The number of bicycle-related accidents rose dramatically from last month to this month. Therefore, bicycle-related accidents must make up a greater percentage of all road accidents this month.” This
conclusion can be true, but it does not have to be true,

KEY - Find out what makes up the percentage ie numerator and denominator

Question 4

True/False?

Decreasing numbers =
decreasing percentages.

Answer 4

False

Just because a number decreases does not necessarily mean that the corresponding
percentage must become smaller.

Question 5

True/False?

Large numbers = large percentages

small numbers = small percentages

Answer 5

False

Remember, the size of a number does not
reveal anything about the percentage that number represents unless you
know something about the size of the overall total that number is drawn
from.

you cant speak on % until you know the # of overall total .

Question 6

True/False?

Large percentages = large numbers

small percentages = small numbers.

Answer 6

False

You cant know the actual number size of the % unless you know the # Total

A figure such as 90% sounds impressively large, but if you have 90% of $5, that really
isn’t too impressive, is it?

Question 7

3 Elements of Numerical situations

Answer 7

• Overall Total
• a number within the total
• a percentage within the total

Question 8

Common Numerical tricks

Answer 8

GMAT problems will often give you one of the elements, but without at least two elements present, **you cannot make a definitive judgment about what is occurring with another element. **

• When you are given just a percentage information, you cannot make a judgment about numbers.
• Likewise, when you are given just a numerical information you cannot make a judgement about percentages.

Question 9

Numerical ideas indicators

Answer 9

Amount
Quantity
Sum
Total
Count
Tally

Question 10

Percentage ideas indicators

Answer 10

Percent
Portion
Proportion
Fraction
Ratio
Incidence
Likelihood
Probability
Segment
Share

Question 11

“More likely” indicates

Answer 11

> 50% probability

Question 12

“Least likely” indicates…

Answer 12

< 50% probability

Question 13

General number/percentage rules

If the stimulus contains percentage or proportion information only, avoid…

Answer 13

answers that contain hard numbers.

Please keep in mind that these rules are very general. You must read the stimulus closely and carefully to determine exactly what information is present

Question 14

General number/percentage rules

If the stimulus contains only numerical information, avoid…

Answer 14

answers that contain percentage or proportion information.

Please keep in mind that these rules are very general. You must read the stimulus closely and carefully to determine exactly what information is present

Question 15

General number/percentage rules

If the stimulus contains both percentage and numerical information…

Answer 15

any answer choice that contains numbers, percentages, or both may be true.

Please keep in mind that these rules are very general. You must read the stimulus closely and carefully to determine exactly what information is present

Question 16

Whats makes up the numerator and denominator for….

Market share

Answer 16

Market share is simply the portion of a market that a company controls. The
market share can be measured either in terms of
* revenues (sales) or
* units sold.

market share can change when factors in the market change.
For example, a company can gain market share (percentage) if the market shrinks and they maintain a constant size, or if they grow in an unchanging market.

Question 17

True or False?

Decreased market share = decreased sales

Answer 17

False

• a company losing market share does not mean that their sales decreased, only that they became a smaller entity in the market relative to the whole (the market grew and they stayed the same size, for example).

Question 18

True or False?

Decreased sales = decreased market share

Answer 18

False

a company could lose sales and
still gain market share if the overall market became smaller.

Question 19

Rumored declines in automobile-industry revenues are exaggerated. It is true that automobile manufacturers’ share of the industry’s revenues fell from 65 percent two years ago to 50 percent today,
but over the same period suppliers of automobile parts had their share increase from 15 percent to 20 percent and service companies (for example, distributors, dealers, and repairers) had their share
increase from 20 percent to 30 percent.
Which one of the following best indicates why the statistics given above provide by themselves no evidence for the conclusion they are intended to support?

(A) The possibility is left open that the statistics for manufacturers’ share of revenues come
from a different source than the other
statistics.

(B) No matter what changes the automobile industry’s overall revenues undergo, the total of all shares of these revenues must be 100 percent.

(C) No explanation is given for why the revenue shares of different sectors of the industry changed.

(D) Manufacturers and parts companies depend for their revenue on dealers’ success in selling cars.

(E) Revenues are an important factor but are not
the only factor in determining profits.

Answer 19

A. does not address the fundamental percentage-to-number error in the argument.

B. This is the correct answer. The answer reveals the error of the author: the changing market shares of different groups have no impact on the actual amount of revenues. In all instances, the market shares will add up to 100%, so a discussion of shifts within this 100% is meaningless as far as making a determination of whether revenues declined.

C. This is not a flaw of the argument.

D. The interrelationship of the groups named in the stimulus is not an issue in determining whether the conclusion is in error.

E. The argument is about revenues, and information about profits will not reveal the error in the reasoning.