Data sufficiency in reasoning for IBPS Clerk

A data sufficiency question asks something, gives two statements, and asks whether the statements are enough to answer it. You do not need the answer itself. You need to know whether a single, definite answer exists.

That sounds easier than solving, and it can be. But the topic has its own trap: people solve with everything in front of them and forget to ask which statement did the work. The discipline below fixes that. It is the same every time, whether the question is about ranks, days, codes, blood relations or directions.

The five options

Almost every question uses these five choices, sometimes in a different order. Read the order in your paper before answering.

"Sufficient" means the statements give exactly one answer. If they leave two possibilities, they are not sufficient, even if one possibility seems more likely.

The method

1. Test statement I alone. Cover statement II with your hand. Is there exactly one answer?
2. Test statement II alone. Now forget statement I completely. Is there exactly one answer?
3. Only if neither works alone, test both together.
4. Match the result to the options. Two yeses give "either". One yes gives that statement alone. Two noes send you to step 3.

Worked examples

Example 1 (comparison). Who is the tallest among A, B and C?
I. A is taller than B. II. C is taller than A.

1. I alone: A is taller than B, but C is unknown. Not sufficient.
2. II alone: C is taller than A, but B is unknown. Not sufficient.
3. Together: C > A > B. C is the tallest.
4. Both together.

Example 2 (days). On which day of the week was the meeting held?
I. It was held after Tuesday but before Thursday. II. It was held on a weekday.

1. I alone: only Wednesday fits. Sufficient.
2. II alone: five weekdays remain. Not sufficient.
3. I alone.

Example 3 (numbers). Is x greater than y?
I. x = 2y. II. y is positive.

1. I alone: if y = 3, x = 6 and x > y. If y = −3, x = −6 and x < y. Two answers. Not sufficient.
2. II alone: nothing about x. Not sufficient.
3. Together: y is positive, so 2y > y, and x > y. One answer.
4. Both together.

Example 4 (ranking). In a row of 20 people, what is R's position from the left?
I. R is 8th from the right. II. There are 12 people to the left of R.

1. I alone: 20 + 1 − 8 = 13th. Sufficient.
2. II alone: 12 + 1 = 13th. Sufficient.
3. Either statement alone.

Example 5 (blood relations). How is M related to N?
I. M is the brother of O. II. O is the daughter of N.

1. I alone: nothing about N. Not sufficient.
2. II alone: nothing about M. Not sufficient.
3. Together: M is male ("brother") and a sibling of N's daughter, so M is N's son.
4. Both together.

Example 6 (direction). In which direction is P from Q?
I. P is 5 m north of R. II. R is 5 m east of Q.

1. I alone: Q is not mentioned. Not sufficient.
2. II alone: P is not mentioned. Not sufficient.
3. Together: from Q, go 5 m east to R, then 5 m north to P. P is north-east of Q.
4. Both together.

Example 7 (not enough). Who is the oldest among A, B, C and D?
I. A is older than B, and C is older than D. II. B is older than D.

1. I alone: two separate pairs. Not sufficient.
2. II alone: A and C unknown. Not sufficient.
3. Together: A > B > D and C > D. A and C are never compared, so either could be oldest.
4. Neither. Even both together are not sufficient.

Common traps

• Leaking information. Using a fact from statement I while you test statement II alone. Cover the other statement physically if you need to.
• Assuming what is not stated. That numbers are positive, that people have different heights, that a named person is male or female. Gender only comes from words like brother or daughter.
• Stopping at "both together" too early. Check each statement alone first, every time.
• Accepting "probably". Two possible answers means not sufficient, however unlikely the second one looks.
• Solving fully when you only need to know an answer exists. In example 4 you do not need to find 13th twice. You only need to see that each statement pins it down.

Practice

Aim for six minutes. Answer with: I alone, II alone, either, both together, or neither.

1. In which month is S's birthday? I. After March but before May. II. In a month with 30 days.
2. Is A the heaviest of A, B and C? I. A is heavier than B. II. A is heavier than both B and C.
3. What is the code for "go"? I. "go home now" is coded "ka la ma". II. "go out" is coded "ka ri".
4. How many people are in the row? I. R is 11th from the left. II. R is 9th from the left and 9th from the right.
5. How is K related to L? I. K and L are the children of M. II. K is male.
6. On which day did Q visit? I. After Monday but before Thursday. II. Not on Tuesday.
7. What is T's rank from the top in a class of 40? I. T is 15th from the bottom. II. 25 students rank above T.
8. What is the code for "sky"? I. "blue sky" is coded "na ta". II. "deep blue sky" is coded "ta ri na".

Answers:

1. I alone. I gives April. II gives four months (April, June, September, November).
2. II alone. II says outright that A is heavier than both. I leaves C unknown.
3. Both together. "go" is the only common word, and "ka" the only common code.
4. II alone. 9 + 9 − 1 = 17. I gives no second position.
5. Both together. I makes them siblings; II gives K's gender. Together, K is L's brother.
6. Both together. I leaves Tuesday or Wednesday. II removes Tuesday.
7. Either. I: 40 + 1 − 15 = 26th. II: 25 + 1 = 26th.
8. Neither. "blue" and "sky" appear in both sentences, and so do "na" and "ta", so they cannot be separated.

What to do next

• Do 10 data sufficiency questions a day for a week, and for each one write "I: yes/no, II: yes/no" before choosing.
• Mix the topics: one ranking, one blood relation, one code, one direction and one inequality in every set.
• Revise inequality as well, since "Is A greater than D?" questions are just inequality chains in disguise.