Why This Chapter Matters
Data sufficiency tests decision quality more than arithmetic stamina. The winning habit is to stop the moment sufficiency is established.
Core Ideas
- Do not solve more than the question asks. You only need to decide whether the statements are enough.
- Check Statement I alone, then Statement II alone, then combine them only if needed.
- Use standard answer patterns consistently to avoid avoidable mistakes.
- Universal mathematical truths are allowed; outside factual knowledge is not.
- Sufficiency depends on uniqueness. A statement that gives two possible answers is still insufficient.
- A statement can be mathematically rich and still insufficient if it does not answer the exact question asked.
High-Value Formulas
| Concept | Formula / Rule |
|---|---|
| Standard coding A | Statement I alone is sufficient |
| Standard coding B | Statement II alone is sufficient |
| Standard coding C | Both together are sufficient, neither alone |
| Standard coding D | Either statement alone is sufficient |
| Standard coding E | Even both statements together are insufficient |
How To Approach Questions
- Read the question target carefully.
- Test Statement I without assuming anything extra.
- Test Statement II independently.
- Combine only if both alone fail but together may work.
- Use elimination once one statement is clearly sufficient or clearly insufficient.
- Check whether the question needs a value, a yes/no answer, or only a comparison direction.
Worked Examples
Example 1
Prompt: To find a unique value of a variable, a single linear equation in one variable is usually sufficient.
Approach: This type of structural observation often lets you decide sufficiency without calculating the final number.
Example 2
Prompt: To find a boat’s still-water speed, knowing only one downstream speed is usually not enough unless you also know the stream relation.
Approach: This is a classic data-sufficiency habit: identify the missing variable instead of rushing into arithmetic.
Example 3
Prompt: If the question asks "Is the number prime?" then a statement showing only that the number is odd is not sufficient.
Approach: Odd numbers can be prime or composite. The statement sounds useful, but it does not settle the target question.
Common Mistakes
- Using hidden assumptions not supplied in the statements.
- Combining statements too early.
- Solving completely when uniqueness or inequality direction is already clear.
- Ignoring the standard answer code and selecting the mathematical result instead.
- Treating a yes/no question like a value question and demanding more information than needed.
Quick Revision
The chapter is about control: test, stop, and classify.