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   GMAT Word Problems Guide
Ch 1: Word Problem Strategies
Ch 2: 5-Step Method
Ch 3: Functions & Symbols
Ch 4: Progressions & Sequences
Ch 5: Percentages
Ch 6: Interest
Ch 7: Ratio & Proportion
Ch 8: Uniform Motion
Ch 9: Work & Rate
Ch 10: Grouping & Counting
Ch 11: Data Interpretation
Ch 12: Averages & Median
 
 

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   Word Problems & Strategy Chapter 10: Grouping & Counting
Table of Contents  
 

Sets

A Set describes a group of items called an element or a member. Sets are usually marked off by these types of brackets {}. All the mammals of the world may be a set, of which dogs and cats are members, but lizards are a member of the reptiles group.

In mathematical terms, you can have a set of odd numbers less than 10 such as {1, 3, 5, 7,9} and a set of prime numbers less than 10 {2, 3, 5, 7} and the overlap is {3, 5, 7}.


Overlapping Sets

When a question relates to overlapping groups, try diagramming the problem with overlapping circles. This will make it easy to account for the overlap.

In group questions, you can add the two groups which represent "either" and subtract the group which represents "both" to get a total number of items in the two sets.

Example 1

If, in a certain school, 20 students play soccer, 10 play basketball, and 7 play both, how many students play basketball, soccer or both?

(A) 20
(B) 22
(C) 23
(D) 25
(E) 29

Solution

(C) Using the diagram above we have deduced some new facts:

3 play only basketball
13 only play soccer
7 play both
alone
alone
overlap

total of 23 players
Also, 20 + 10 - 7(both) = 23




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  Contents of Word Problems Chapter: Table of Contents
Chapter 1: Word Problems & Strategies
  Chapter 2: 5-Step Method
  Chapter 3: Functions & Symbols
  Chapter 4: Progressions & Sequences
  Chapter 5: Percentages
  Chapter 6: Interest, Discount & Markups
  Chapter 7:
Ratio & Proportion
  Chapter 8: Uniform Motion
  Chapter 9: Work & Rate
  Chapter 10:
Grouping & Counting
  Chapter 11: Data Interpretation
  Chapter 12: Averages & Mean
 
Data Interpretation

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