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Arithmetic : Ratio and Proportion

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A proportion is a statement that two ratios are equal.
The proportion a / b = c / d may be written in different ways such as a : b = c : d, or a : b :: c : d (read as 'a is to b as c is to d').

The terms on the outside, a and d, are called the extremes and the terms on the inside, b and c, are called the means.
Since a : b and c : d are ratios, b and d are nonzero.
On multiplying each side of the proportion by b d, the proportion becomes equivalent to the equation a d = b c.


MUST-KNOW : In a proportion, the product of the extremes equals the product of the means.


Determining the products of the extremes a d and the means b c is called cross-multiplication.
Cross-multiplying a proportion yields a new equality that may be used to solve a proportion involving an unknown.


If 5 : 8 = 12 : x, what is x?
Solution. In the given proportion, 5 and x are the extremes, and 8 and 12 are the means. Cross-multiplication gives 5 x = 96.
Dividing both sides by 5, x = 96/5 = 19.2

GMAT Math Review - Arithmetic : Index for Ratio & Proportion

GMAT Math Review - Arithmetic : Practice Exercise for Ratio & Proportion


10 more pages in GMAT Math Review

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