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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: Ratio & Proportion
Table of Contents  
 
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A ratio is a fraction that compares two numbers. The ratio of x to y is written as x : y. It is a relationship of part to part.

RATIOS COMPARE PART TO PART, NOT PART TO WHOLE.

If the Yankees win 100 out of 169 games, what is their ratio of wins to losses?

If they win 100 games, they lost 69 games. So the win/loss ratio is 100:69. The fraction of games won would be 100/169.

Ratios are usually used to compare quantities of the same type, for example, the ratio of the length of a Toyota to the length of a Cadillac. We would not form the ratio of the length of a Toyota to the cost of a Cadillac.




Proportions

A proportion states that two ratios are equal. Two ratios involve four numbers: two numerators and two denominators. You can solve for one of these numbers by equaling the two ratios, such as:

 
2
15
=
 
6
x

The unknown x is then found by cross multiplying:
2x = 15(6)
therefore, x = 45

Two quantities are (directly) proportional if one is a constant multiplied by the other: x = cy (where c is a constant).

Automobile company profits are generally proportional to economic growth.


They are inversely proportional (or indirectly proportional) if one is a constant divided by the other: x = c/y, or equivalently, xy = c.
.

The interest rate a company pays is inversely proportional to its credit rating.

The unemployment rate is inversely proportional to GDP growth

To decide if two quantities are directly or inversely proportional, we ask the question, "Do the quantities both increase or decrease together or does one increase while the other decreases?". If they both increase or decrease at the same rate, they are directly proportional; if one increases while the other decreases, they are inversely proportional. To solve an equation that represents a direct proportion, such as x = cy, we set up the equation as:

 
x1
x1
=
 
y2
y2

where the subscript 1 refers to the first situation and the subscript 2 to the second situation. If the equation results from an inverse proportion, such as xy = c, we have:

 
x1
y1
=
 
x2
y2

To solve problems involving proportions, 3 of the 4 numbers will usually be known and the problem will be to calculate the fourth.

Example 1


Calculate x if 4:15 = 16:x



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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
 
Uniform Motion

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