Data sufficiency asks a strange question. You do not need the answer; you need to know whether the answer can be found. That sounds easier, and it would be, except that the options punish two habits: using a fact you assumed, and letting one statement leak into your check of the other.
In reasoning, DS questions borrow from every other topic: rankings, floors, blood relations, codes, directions and days. So each question is a small puzzle with a twist. You must stop the moment you know whether it can be solved.
The standard options
| Option | Meaning |
|---|---|
| (a) | Statement I alone is sufficient; II alone is not |
| (b) | Statement II alone is sufficient; I alone is not |
| (c) | Either statement alone is sufficient |
| (d) | Neither alone is sufficient, but both together are |
| (e) | Both together are still not sufficient |
The method
- Read the question and decide what "an answer" looks like: one name, one floor, one code.
- Check statement I alone. Can you fix that one answer?
- Check statement II alone. Cover statement I with your hand. Forget everything it said.
- Only if neither works alone, combine them.
- Choose the option from the table.
For a yes/no question ("Is R the heaviest?"), a definite "no" is just as sufficient as a definite "yes". The statement is insufficient only if it allows both.
Worked examples
Example 1: comparison
Who is the tallest among P, Q, R and S?
- I. P is taller than Q and R.
- II. S is taller than P.
I alone: P beats Q and R, but S is unknown. II alone: S beats P, but Q and R are unknown. Together: S > P > Q and R. S is the tallest. Answer (d).
Example 2: floors
A building has five floors, numbered 1 (bottom) to 5 (top). On which floor does A live?
- I. A lives on an odd-numbered floor above floor 2.
- II. A does not live on the top floor.
I alone: floor 3 or 5. II alone: floors 1 to 4. Together: floor 3. Answer (d).
Example 3: a gender trap
How is M related to N?
- I. M is the son of N's father.
- II. N is female.
I alone: M is male and a child of N's father, so M is N's brother. N's gender does not matter, because the question asks what M is to N. Answer (a).
Example 4: a code
What is the code for "sun"?
- I. "sun is hot" is coded "la pa ta", and "sun sets" is coded "ta ra".
- II. "is hot" is coded "pa la".
I alone: "sun" is the only common word and "ta" the only common code, so "sun" is "ta". II alone says nothing about "sun". Answer (a).
Example 5: a yes/no question
Is R the heaviest among P, Q, R and S?
- I. R is heavier than P and Q.
- II. S is heavier than R.
I alone: R beats P and Q, but S might be heavier. Not sufficient. II alone: S is heavier than R, so R is not the heaviest. A definite "no" is sufficient. Answer (b).
Example 6: three statements
In which direction is point Q from point P?
- I. P is 5 m north of R.
- II. Q is 5 m east of R.
- III. S is 5 m west of Q.
Put R at (0, 0). I gives P (0, 5). II gives Q (5, 0). Together, Q is south-east of P. III places S but links neither P nor R. I and II together are sufficient; III is not needed.
Traps to avoid
| Trap | What it looks like | The fix |
|---|---|---|
| Assumed gender | Taking a name or letter as male or female | Only relation words give gender |
| Leaked statement | Using I's facts while checking II alone | Cover the other statement |
| Assumed numbering | Floor 1 is the bottom, positions start from the left | Use only what the question says |
| Picking (d) too early | Combining when one statement already worked | Always test each alone first |
| Solving too far | Working out every detail before choosing | Stop as soon as the answer is fixed or clearly not fixable |
| Treating "no" as insufficient | Rejecting a statement that proves the answer is no | A definite no is sufficient |
Practice set
- Which direction is X facing? I. X is facing the rising sun. II. In the morning, X's shadow falls directly behind X.
- Who is the heaviest of five people, A, B, C, D and E? I. A is heavier than B and C. II. D is heavier than A but lighter than E.
- What is P's rank from the top in a class of 30? I. P is 12th from the bottom. II. Q is 5 ranks above P.
- Is today Tuesday? I. The day after tomorrow is Thursday. II. Yesterday was Monday.
- What is the code for "fast"? I. "run fast now" is coded "ko mi sa". II. "run now today" is coded "sa ko ve".
- How is J related to K? I. J is the brother of L. II. L is the son of K.
- Five friends live on floors 1 (bottom) to 5 (top), one on each floor. Who lives on floor 4? I. A lives immediately above B, and B lives on floor 3. II. Only C lives above A.
Answers
- (c). The sun rises in the east, so I gives east. In the morning the shadow falls west; if it falls behind X, X faces east. Each alone is enough.
- (d). I alone leaves D and E unknown. II alone leaves B and C unknown. Together, E is heavier than D, who is heavier than A, who is heavier than B and C. E is the heaviest.
- (a). I gives 30 − 12 + 1 = 19th from the top. II alone gives nothing without Q's rank.
- (c). Each statement alone makes today Tuesday.
- (d). I alone cannot separate three words from three codes. II alone does not contain "fast". Together, "run" and "now" take "sa" and "ko", so "fast" is "mi".
- (d). I alone says nothing about K. II alone says nothing about J. Together, J is male (a brother) and a child of K, so J is K's son.
- (c). I places A on floor 4. II also places A on floor 4, since exactly one person lives above A. Either alone answers "A".
What to do next
- Redo the practice set, saying out loud "I alone", "II alone", "together" for each question.
- Solve five DS questions a day for a week, mixing ranking, blood relation and coding forms.
- Compare with data sufficiency in quant, which uses the same options, and revise blood relations for the gender rules that decide many DS questions.
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