This document provides an overview of topics related to fractions, decimals, percentages, and profit/loss calculation. It includes definitions of proper and improper fractions, comparing fractions, converting between fractions, decimals and percentages. It also discusses calculating percentage changes, successive increases/decreases, product constancy, and profit/loss concepts like markup, discount, and using formulas to solve related problems. The document contains examples and practice problems for each topic.

1. GRE
Concept Session: Fractions, decimals and
Percentages
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2. Topics
• Proper and Improper
Fractions
• Union of Sets
• Recurring Decimals
• Percentages
• Successive
Increases/decreases
• Product Constancy
• Profit and loss
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3. Proper and Improper fractions
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Proper Fraction
The numerator is less than the denominator
Improper Fraction
The numerator is greater than (or equal to) the
denominator
Mixed Fractions
A whole number and proper fraction together
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4. Comparing Fractions
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Method of cross-multiplication
Which is greater?
1. 14/9 or 17/13
2. 4/25 or 7/29
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5. Comparing Fractions
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Percentage comparison
Which is greater?
1. 147/290 or 171/330
2. 651/215 or 840/299
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6. Problems
From the total number of students studying at 8th grade in St.
Anthony School, 2/7 passed in all subjects, 1/5 failed in exactly one
subject, 1/3 failed in exactly two subjects, and the remaining 57
failed in 3 or more subjects. How many students are there in 8th
grade in the School?
A. 100
B. 150
C. 200
D. 250
E. 315
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Answer : Option E

7. Union of Sets
n(A U B) = n(A) + n(B) - n(A ∩ B)
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8. Problems
If 3/5 of all the cookies have nuts and 3/4 of all the cookies have
fruits, at least what fraction of the cookies with nuts also have
fruits?
A. 7/15
B. 7/12
C. 1/3
D. 2/15
E. Cannot be determined
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Answer : Option B

9. Recurring Decimals
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Pure recurring decimals Mixed recurring decimals
Shortcut for pure recurring
decimals
Shortcut for mixed recurring
decimals
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10. Percentages
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What does percentage mean?
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11. Fractions, decimals and percentages conversion
• Fractions/decimals to percentages
• Percentages to fractions
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12. Fractions, decimals and percentages
conversion
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13. Percentage change representation
 As fractions  As decimals
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14. Problems
If John’s salary were 20% higher, it would be 20% less than
Smith’s. If Smith’s salary is $120,000, what is John’s salary?
(A) $36,000
(B) $80,000
(C) $60,500
(D) $42,850
(E) $60,000
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Answer : Option B

15. Percentage increase/decrease calculation
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 =
𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒𝑠
𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝑉𝑎𝑙𝑢𝑒
Example:
What is the percentage increase in
production from the year 2012 to
2013?
What is the percentage change in
production from 2013 to 2014?
43
55
60
50
0
10
20
30
40
50
60
70
2011 2012 2013 2014
Production ( in '000 units)
Production ( in '000 units)
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16. ‘Of’ and ‘than’
What percentage of A is B?
By what percentage is A less than B?
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17. Successive Increases/decreases
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18. www.georgeprep.com
If a number is increased by 20%, decreased by 15%, and increased
by 10%, the overall percent change is closest to
(A) 2% decrease
(B) 2% increase
(C) 9% increase
(D) 12% increase
(E) 14% increase
Problems
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Answer : Option D

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The price of a certain stock rose by 20% and decreased by d percent
to come back to its original price
A.Quantity A is greater.
B.Quantity B is greater.
C.The two quantities are equal.
D.The relationship cannot be determined from the information given.
Quantity A
d
Quantity B
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Problems
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Answer : Option B

20. Product constancy - concept
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21. Product constancy - problems
Rachel travels by her car from home to office everyday in the morning. If she
increases her usual speed by 20% she reaches 10 minutes early. If the distance
between her home and office is 60 miles, what is her usual speed? (in miles per
hour)
A. 40
B. 45
C. 50
D. 60
E. 75
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Answer : Option D

22. Profit and Loss
Terms
Marked Price or Listed Price (MP)
Sale Price(SP)
Cost Price(CP)
Discount
Profit(P)
Loss(L)
Markup
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23. Profit and Loss
MP
SP
CP
$ 200
$ 160
$ 100
discount
Profit
$ 100
$ 60
Markup
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$ 40
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24. Profit/loss/discount/markup percentage calculation
Formula
Profit % (SP-CP)/CP X
100
Loss % (CP-SP)/CP X
100
Discount % (MP-SP)/SP X
100
Markup % (MP-CP)/CP X
100
Formula Ratio required
Profit % (SP-CP)/CP X 100 SP/CP
Loss %
(CP-SP)/CP X 100 SP/CP
Discount %
(MP-SP)/MP X 100 MP/SP
Markup %
(MP-CP)/CP X 100 MP/CP
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25. Profit and Loss- problems
A computer that was discounted by 13% sold for $2175. What was the price of the
computer before the discount?
A. $2080.00
B. $2600.20
C. $2700.00
D. $2500.00
E. $2440.00
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Answer : Option D