Data Sufficiency for CSAT

Data sufficiency questions give you a question plus two numbered statements, and ask whether those statements, alone or together, contain enough information to answer it. The twist is that you must judge sufficiency, not produce the solution: deciding the data is enough is the whole task. Because Paper II is qualifying at 33 percent, this is a gift of a topic once the method is fixed, since every question uses the same four-option format.

The format and the four verdicts

Every data sufficiency item has the same skeleton: a question, Statement 1 and Statement 2, and four options. Your verdict is always one of four: Statement 1 alone is sufficient; Statement 2 alone is sufficient; both together are sufficient but neither alone is; or even both together are not sufficient. Memorise this table, because UPSC never changes the wording, only the numbers.

Note the discipline hidden in the table: you must test each statement alone before combining them. A statement that looks weak on its own may be fully sufficient, and combining too early is how the (c)-trap catches people who never checked (a) or (b).

The golden rule: sufficiency, not solution

The sufficiency-not-solution rule says you stop the moment you know the answer is determined, without computing it. If Statement 1 gives a linear equation in one unknown, the value is fixed and you mark (a); there is no need to solve it. This rule is also a time-saver in reverse: if a statement leaves two or more live possibilities, it is insufficient, and you move on. Examiners exploit the urge to keep calculating, so train yourself to stop at 'determined'.

Test alone first: the solving order

Follow the fixed order every time. First, pretend Statement 2 does not exist and ask whether Statement 1 alone fixes the answer; if yes, the answer is (a). If not, forget Statement 1 and test Statement 2 alone; if yes, the answer is (b). Only if both fail alone do you combine them: if the pair fixes the answer, mark (c), otherwise (d). This order matters because the commonest error is marking (c) for a question where one statement already sufficed, which is really (a) or (b).

Worked examples

Example 1. Question: What is Ravi's age? Statement 1: Ravi is 5 years older than Sita. Statement 2: Sita is 20 years old. Statement 1 alone gives only a difference, so it fails. Statement 2 alone says nothing about Ravi, so it fails. Together they fix Ravi at 25, so the verdict is (c): both together are sufficient.

Example 2. Question: Is n a prime number? Statement 1: n is odd. Statement 2: n is less than 10. Statement 1 alone fails (9 is odd but not prime). Statement 2 alone fails (4, 6, 8 are below 10 but not prime). Together they still fail: n could be 3, 5 or 7 (prime) or 1 or 9 (not prime). Verdict (d). This is the classic hidden-multiple-values trap.

Example 3. Question: What is the two-digit number? Statement 1: the sum of its digits is 9. Statement 2: the difference of its digits is 3. Statement 1 alone leaves 18, 27, 36, 45, 54, 63, 72, 81 and 90. Statement 2 alone leaves many pairs. Together, the digits must sum to 9 and differ by 3, giving the pairs (6,3) and (3,6): the number could be 63 or 36. Two live possibilities remain, so the verdict is (d), even though it feels like 'almost enough'.

Example 4. Question: What is the remainder when n is divided by 6? Statement 1: n is a multiple of 3. Statement 2: n is even. Statement 1 alone fails: multiples of 3 leave remainders 0 or 3 on division by 6. Statement 2 alone fails: even numbers leave 0, 2 or 4. Together, n is a multiple of both 2 and 3, hence of 6, so the remainder is fixed at 0. Verdict (c).

The sufficiency traps

Examiners reuse a small set of traps. The hidden second value trap (Example 3) leaves exactly two possibilities, tempting a (c) that should be (d). The domain trap forgets that variables may be fractions or negatives unless stated to be integers. The 'at least' trap: 'n is at least 5' never fixes n. The degenerate case trap: a statement like 'x squared equals 4' gives two values, x = 2 or x = -2, so it cannot fix x. And the unnecessary-combination trap: marking (c) without ever testing the statements alone.

Speed tips

Three habits speed you up. One, never solve fully: the instant the answer is determined, mark and move. Two, test extreme and boundary values when a statement gives a range: if both extremes keep the answer the same, the statement may still fail on a middle value, so enumerate small cases. Three, use the AD/BCE split mentally: first decide 'is one statement alone enough' (A or B territory) versus 'do I need both or is it hopeless' (C or D territory); that first split eliminates half the options in seconds.

Key Terms

• Data sufficiency: a question format giving a question plus two statements, asking whether the statements provide enough information to answer it.
• Statement 1 / Statement 2: the two pieces of information supplied; each must be tested alone before they are combined.
• Sufficiency: the property of information that determines the answer uniquely; it does not require the answer to be computed.
• Necessary condition: information the answer depends on; a statement supplying only necessary conditions is usually insufficient.
• Unique value: a single fixed answer; sufficiency means the data pins the answer down to exactly one value (or one yes/no).
• Degenerate case: a lurking extra possibility, such as x = -2 alongside x = 2, or a zero divisor, that destroys sufficiency.

Practice questions