Ratio/Percentage based Sufficiency for Questions A ratio measures the relative size of two quantities, like the ratio of two similar objects or the ratio...
A ratio measures the relative size of two quantities, like the ratio of two similar objects or the ratio of two quantities with different units. A percentage expresses the relative size of one quantity compared to another, often expressed as a percentage.
In the context of data sufficiency, both ratios and percentages play crucial roles in determining whether a set of data can be formed from a given set. A set is sufficient if it can be formed from a smaller set through a finite number of operations, like addition, subtraction, multiplication, and division. This means that we can reconstruct the original set from the smaller set using these operations.
For example, consider the following two sets:
Set A: {3, 6, 9}
Set B: {1, 2, 4}
Set A can be formed from Set B through addition:
Therefore, Set A is sufficient for Set B.
Similarly, a set is perfectly sufficient if it can be formed from the original set with just one operation. For instance:
Set C: {1, 1.5, 2, 2.5}
Operations: Addition
Set C can be formed from Set A with addition, showing that it is perfectly sufficient for Set A.
While both ratios and percentages contribute to determining sufficiency, they are used in different scenarios. Ratios are often used in ratios, and percentages are often used in percentages.
Key points:
A set is sufficient if it can be formed from a smaller set using a finite number of operations.
A set is perfectly sufficient if it can be formed from the original set with just one operation.
Ratio is used when comparing the sizes of two quantities, while percentage is used when comparing the relative sizes of two quantities