Data sufficiency in reasoning for LIC AAO

Data sufficiency asks a different question from the rest of reasoning. You are not asked for the answer. You are asked whether the statements given would let you find it. That sounds easier, and it is, until you realise that most wrong answers come from answering the question instead: using a fact from statement II while judging statement I, or assuming something neither statement says.

The five options

Most papers use a version of these options. Read the instructions each time, because the order of the options changes between papers.

The method

1. Read the question and decide what "an answer" looks like. A single name, a single floor, a single relation word, or a definite yes or no.
2. Test statement I alone. Cover statement II with your hand. Only I and general rules are allowed.
3. Test statement II alone. Now cover statement I.
4. Only if neither works alone, combine them.
5. Pick the option. If I works alone, you do not need to check whether "both together" works. It always would.

Two further rules save time:

• The statements never contradict each other. If you find a contradiction, you have made an error.
• A definite "no" is an answer. For a yes/no question, a statement that proves the answer is "no" is sufficient.

Worked examples

Example 1 (ages). Who is the oldest among P, Q, R and S?

I. P is older than Q, and S is older than R.
II. R is older than P.

• I alone: two separate pairs, P > Q and S > R. Either P or S could be the oldest. Not sufficient.
• II alone: nothing about Q or S. Not sufficient.
• Together: S > R > P > Q. S is the oldest. Both together are sufficient.

Example 2 (floors). In a five-floor building, with floor 1 at the bottom, on which floor does X live?

I. X lives on an even-numbered floor above floor 2.
II. X lives immediately above Y, who lives on floor 3.

• I alone: the even floors are 2 and 4, and above 2 leaves only floor 4. Sufficient.
• II alone: floor 4. Sufficient.
• Either alone is sufficient. Notice that both give the same floor. They always will, because the statements never contradict.

Example 3 (blood relation, with gender stated). How is P related to T?

I. T is the son of R, and R is the sister of P.
II. P is a woman.

• I alone: R is T's mother, and P is R's sibling. P is T's maternal uncle or maternal aunt, but P's gender is not given. Not sufficient.
• II alone: nothing links P to T. Not sufficient.
• Together: P is a woman and the sister of T's mother. P is T's maternal aunt. Both together are sufficient.

This is the heart of blood-relation DS. A statement can fix the family tree completely and still fail, because the relation word depends on a gender nobody stated.

Example 4 (blood relation, not sufficient). How is G related to H?

I. G's mother is H's sister.
II. H has two brothers.

• I alone: H is G's mother's sibling, so G is H's nephew or niece. G's gender is not given. Not sufficient.
• II alone: says nothing about G. Not sufficient.
• Together: we learn about H's brothers, but still nothing about G's gender. Neither is sufficient.

Example 5 (rank). In a class of 40, what is Q's rank from the top?

I. Q is five ranks below R, who is 12th from the top.
II. Q is 24th from the bottom.

• I alone: 12 + 5 = 17th. Sufficient.
• II alone: 40 − 24 + 1 = 17th. Sufficient.
• Either alone is sufficient. Both give 17, as they must.

Example 6 (yes or no). Is X the heaviest among X, Y and Z?

I. Y is heavier than X.
II. Z is lighter than X.

• I alone: someone is heavier than X, so the answer is a definite no. Sufficient.
• II alone: X > Z, but Y could be heavier or lighter than X. Not sufficient.
• I alone is sufficient.

Example 7 (direction). In which direction is village M from village N?

I. M is 5 km south of village O.
II. O is 5 km west of N.

• I alone: nothing about N. II alone: nothing about M.
• Together: put N at (0, 0). O is at (−5, 0), and M is at (−5, −5). M is south-west of N. Both together are sufficient.

Common traps

• Leakage. Using what you learnt from statement I while testing II. Cover the other statement physically.
• Solving instead of judging. You need to know that one answer exists, not what it is. Stop working once it is fixed.
• Missing the total. A position from one end is not sufficient for the position from the other end unless the total is known.
• Treating "probably" as "definitely". Two cases means not sufficient.
• Forgetting that "no" is an answer in yes/no questions.

Practice set

1. What is the code for "safe"? I. "safe policy" is written as "ka mo". II. "policy term" is written as "mo ri".
2. Is M taller than N? I. M is taller than O. II. O is taller than N.
3. A meeting is held on one day from Monday to Friday. On which day? I. It is held after Wednesday. II. It is not held on Friday.
4. In a row of 30, what is R's position from the left? I. R is 11th from the right. II. There are 19 people to the left of R.
5. How is U related to V? I. U is a grandchild of W. II. V is W's only son.
6. Is P the youngest of P, Q, R and S? I. P is older than S. II. Q and R are both older than P.
7. In a class of 25, what is Z's rank from the top? I. Z is eight ranks above Y. II. Y is 14th from the bottom.
8. Is K the sister of L? I. K is a woman. II. K and L are children of the same parents.

Answers

1. Both together. Together, "policy" is mo, so "safe" is ka. Alone, each statement leaves two possible codes.
2. Both together. M > O > N. Alone, each statement leaves N or M unplaced.
3. Both together. I leaves Thursday or Friday. II leaves Monday to Thursday. Together: Thursday.
4. Either alone. I: 30 − 11 + 1 = 20th. II: 19 + 1 = 20th.
5. Neither. U could be V's child, or the child of one of W's daughters, in which case V is U's maternal uncle. U's gender is also unknown.
6. I alone. S is younger than P, so the answer is a definite no. II alone leaves S unplaced.
7. Both together. Y is 25 − 14 + 1 = 12th from the top, so Z is 12 − 8 = 4th.
8. Both together. I alone gives no link to L. II alone gives a sibling of unknown gender. Together, K is L's sister.

What to do next

• Solve ten DS questions with a card covering the statement you are not testing.
• Revise how gender is fixed in blood relations before your next DS set.
• Compare this with data sufficiency in quant, which uses the same five options.
• Add a DS set to your weekly mains practice from reasoning for the LIC AAO mains.