1. Quickly read the question
and the answer choices to get a feel for what the question is
specifically asking.
2. Read the question again
(on the GMAT you have nearly two minutes per math question, so
there is time to spare as long as you budget it properly--read
Chapter One for pacing information).
3. Translate the equation
to paper and translate the question into an expression with variables.
4. If you get a mental block
or see a shortcut, use Backsolving (take
numbers and feed them into the question--either answer choices
or numbers you choose).
5. If that does not work,
start eliminating answers that are outside of the ballpark; guess
and move on.
I. Review of
Word Problem Concepts
A. Percentages
B. Interest, Discount, and Markups
C. Progressions
D. Uniform Motion
E. Work
F. Ratio and Proportion
G. Grouping and Counting
H. Tables, Charts, and Graphs (Data Interpretation)
I. Symbols
J. Progressions
A. Percentages
The
word percent is abbreviated by the symbol % and is a fraction
whose denominator is 100. 26% is equivalent to the fraction 26/100.
To change a decimal number to a percent, we simply multiply by
100; the number 0.321 is equivalent to 32.1%. If a percentage
is given, move the decimal two places to the left to express
its equivalent decimal form.
Example 1
Convert 4% into a decimal and
a fraction in lowest terms.
Solution
To convert 4% into a decimal, we move the decimal point two places
to the left:
4% = 0.04
To express 4% as a fraction, we divide by 100:
4/100 = 1/25
Hence,
4% = 0.04 = 1/25
Example 2
If the price of a stock falls from $50 to $40, what is the percentage
of decrease?
Solution
First, subtract the numbers resulting in the decrease: 50
- 40 = 10. Then divide by the original amount:
(50 - 40) / 50 = 10 / 50 = .2
Convert to a percentage by moving
the decimal point two places to the right:
% decrease = 20%
Example 3
An employee is to mark
up a piece of jewelry 120%. If it cost $100, what should its
selling price be?
Solution
The amount of the markup is 1.2 × 100= $120
The selling price is then $100 + $120 = $220
Example 4
A college bookstore purchases
trade books on a 40% margin, i.e., it purchases a trade book
for 40% less than its retail price. What is the percentage markup
based on its wholesale price?
Solution
Since the retail price is not given, the percentage markup that
we seek must be the same for all trade books. Therefore, let
the retail price of a trade book be $100 (rather than the symbol
x). Then the bookstore's purchase price is
100 - 100 × 0.4 = 100 -
40 = $60
If a book sells for $100 and
costs $60, its percentage markup is
%markup = (100 - 60) / 60 × 100 = 40 / 60 x 100 = 66%
Example 5
Kathy buys a bike for $240 after
a 40% markdown. What was the original price?
Solution
Let P be the original price. Then
P - P × 0.4 = 240
0.6P = 240
divide both sides by .6
therefore, P = $400
Example 6
Find the number of residents
of a city if 20% of them, or 6,200 people, ride bicycles.
Solution
Let R be the number of residents. The equation that represents
the verbal statement is
0.2R = 6,200. R = 6200/.2 = 62000/2 = 31,000 people.
Example 7
Kent pays 20% taxes on
income between $10,000 and $20,000 and 30% on income over $20,000.
The first $10,000 is tax free. If he pays $14,000 in taxes, what
was his income?
Solution
Let Kent's income be L. Then the total tax is
0.2(20,000 - 10,000) + 0.3(L - 20,000) =14,000
2,000 + 0.3L - 6,000 = 14,000
0.3L = 14,000 + 4,000 = 18,000
L = 18,000/.3 = $60,000
Example 8
How many gallons of pure water must be added to 100 gallons
of a 4% saline solution to provide a 1% saline solution?
Solution
Let x be the gallons
of pure water to be added. There are 100 × 0.04 = 4 gallons
of salt and 96 gallons of pure water in a 4% saline solution.
The total number of gallons will be x + 100. The amount of salt
will remain constant. Hence,
0.01(x + 100) = 4
0.01x + 1 = 4
0.01x = 3
x = 3/.01 = 300 gallons
w B. Interest, Discount, and Markups
If you have any more questions or suggestions, email 24hourtutor@800score.com
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