Data sufficiency in reasoning for SBI PO

Data sufficiency asks a different question from every other reasoning topic. You are not asked for the answer. You are asked whether the information given is enough to find one. That changes how you work: you stop as soon as you know whether an answer is fixed, and you never need to finish the calculation.

Candidates lose marks here in two predictable ways. They let statement I leak into their test of statement II, and they assume things the statements never said, most often a person's gender or the size of a group. Both are fixed by the method below.

How it is asked

A question is followed by two statements, I and II, and the same five options every time. In reasoning DS the question can come from almost any topic: ranking, coding, direction, blood relations, comparisons, days and dates, or a small puzzle. Some mains papers have used three statements with a different set of options; read the options carefully when that happens. The number of DS questions varies by year.

The five options

"Sufficient" means the answer is fixed: one value, one person, or a definite yes or no. A definite "no" is still an answer. If the question is "Is A the tallest?" and the data proves A is not, the data is sufficient.

The three-step method

1. Test I alone. Cover statement II with your hand. Does I fix the answer?
2. Test II alone. Now cover I and forget everything it told you. Does II fix the answer?
3. Only if neither works alone, test both together. If they still do not fix the answer, choose (5).

Worked examples

Example 1: comparison. Among P, Q, R and S, who is the heaviest?

• I. P is heavier than Q, and R is heavier than S.
• II. S is heavier than P.

I alone gives two separate pairs and no link. II alone says nothing about Q or R. Together: R > S > P > Q, so R is the heaviest. (4) Both are needed.

Example 2: coding. In a code language, what is the code for "safe"?

• I. "safe bank" is coded "ta mo" and "bank loan" is coded "mo ki".
• II. "safe deposit" is coded "ta ri".

I: "bank" is common to both phrases and "mo" to both codes, so "bank" is mo and "safe" is ta. II alone: "safe" could be ta or ri. (1) I alone is sufficient.

Example 3: direction. Which direction is A facing?

• I. If A turns right, A will face north.
• II. If A turns left, A will face south.

I: a right turn to north means A faces west. II: a left turn to south also means A faces west. Each works alone, and they agree. (3) Either alone is sufficient.

Example 4: blood relation. Is K the grandson of J?

• I. K is the son of L.
• II. L is the daughter of J.

I alone does not mention J. II alone does not mention K. Together: K is the son of J's daughter, so K is J's grandson. "Son" states that K is male. (4) Both are needed.

If statement I had said "K is a child of L", even both together would not settle "grandson". K's gender would be unknown, and the answer would be (5).

Example 5: days. On which day of the week was the meeting held?

• I. It was held after Tuesday.
• II. It was held before Friday.

Each statement alone allows several days. Together they leave Wednesday or Thursday: still two days. (5) Even both together are not sufficient.

Example 6: distance. What is the shortest distance between P and Q?

• I. P is 4 km north of R.
• II. R is 3 km east of Q.

Neither alone connects P to Q. Together: P is 3 km east and 4 km north of Q, so the distance is √(9 + 16) = 5 km. (4) Both are needed. In DS you could stop at "the positions are fixed", but checking the arithmetic takes seconds.

Traps to watch for

• Assumed gender. A letter or a name tells you nothing. Only a word like son, sister or husband does.
• Assumed group size. "A is 7th from the left" says nothing about the right end unless the total is known.
• Assumed seat or direction. "Faces the centre" and "faces north" are different; so are "to the right" and "immediately to the right".
• Stopping at the first sufficient statement. If I works, still test II. The answer might be (3), not (1).
• Solving too far. Once you know the answer is fixed, move on.
• Statements that clash. In a well-set question, two statements that each work alone give the same answer. If yours disagree, re-read both.

Practice set

1. On which day is the event held? I. It is after Monday but before Wednesday. II. It is on a weekday.
2. What is A's rank in a class of 40 students? I. Exactly 12 students rank above A. II. Exactly 27 students rank below A.
3. Is X older than Y? I. X is older than Z. II. Z is older than Y.
4. How many people are standing in a queue? I. A is 7th from the front. II. A is 10th from the back.
5. In a code language, what is the code for "gold"? I. "gold ring" is coded "pa lu". II. "gold coin" is coded "pa ne".
6. Is T the aunt of V? I. T is the sister of U. II. U is the father of V.
7. In a row of people facing north, is J to the left of K? I. J is third from the left end. II. K is fourth from the right end.

Answers:

1. (1) I alone. The only day after Monday and before Wednesday is Tuesday. II allows five days.
2. (3) Either alone. I: 12 above means A is 13th. II: 27 below means A is 40 − 27 = 13th.
3. (4) Both together. X > Z > Y. Neither alone mentions both X and Y.
4. (4) Both together. 7 + 10 − 1 = 16 people. A is counted in both positions, so subtract one.
5. (4) Both together. Alone, "gold" could be either code in each statement. Together, "gold" is the common word and "pa" the common code.
6. (4) Both together. "Sister" makes T female; T is the sister of V's father, so T is V's aunt.
7. (5) Not sufficient. Without the number of people in the row, you cannot place K from the right end relative to J.

What to do next

• Solve 10 DS questions a day for a week, physically covering each statement while you test the other.
• Next to each answer, write the reason a statement failed: missing link, missing gender, missing total, or two possibilities.
• Revisit the topics DS draws on: blood relations, direction sense and coding–decoding.
• For the quant version, which uses similar options with numbers, see data sufficiency in quant.