Data sufficiency: Data Interpretation & Logical Reasoning Notes for MAT

Data Sufficiency – Study Notes

(MAT – Data Interpretation & Logical Reasoning)

1. Simple Explanation

Data Sufficiency is a question type that tests whether the given statements provide enough information to answer a question.

You never need to find the actual answer – only determine if the answer can be found.
The question is followed by two statements (Statement (1) and Statement (2)).
Each statement may contain a numerical value, an algebraic expression, a relationship, etc.
The answer choices are always:

Choice	Meaning
A	Statement (1) alone is sufficient, Statement (2) alone is not.
B	Statement (2) alone is sufficient, Statement (1) alone is not.
C	Both statements together are sufficient, but neither alone is sufficient.
D	Either statement alone is sufficient.
E	Neither statement alone nor together is sufficient.

Goal:

Analyze each statement independently.
Determine if it gives enough information to answer the question.
If both are required, verify that the combined data indeed resolves the problem.

2. Key Points (What to Look For)

#	What to Check	Why It Matters
1	Type of information (numeric value, inequality, relationship).	Determines if you can compute the required quantity.
2	Missing variables in the statement.	A statement might give a relation but not the actual numbers.
3	Logical implications (e.g., if `x > y` and we need to compare `x` vs `z`).	Even with inequalities, you may not have enough to deduce the final comparison.
4	Redundancy – if one statement already provides all needed data.	Avoid unnecessary work.
5	Combining statements – see if they complement each other.	Some problems require both to pin down a unique value.
6	‘Sufficiency only’ – you do not need to find the exact answer.	Saves time and prevents over‑analysis.
7	Avoid solving for variables that are not asked.	Focus on what the question actually requires.

3. Worked Example

Question

Let (p) and (q) be positive integers. Which of the following statements provides enough information to determine whether (p > q)?

(1) The product (pq) is greater than 12.
(2) The difference (p - q) is greater than 3.

Choose the correct answer.

Step‑by‑Step Analysis

Statement	What it says	Is it enough to decide (p > q)?
(1)	(pq > 12).	No. Eg: (p=2, q=7) gives (14 > 12) and (p<q). Eg: (p=4, q=4) gives (16 > 12) and (p=q). Thus (pq>12) does not fix the order.
(2)	(p - q > 3).	Yes. If (p - q > 3), then (p > q) automatically. No other possibilities.

Statement (2) alone is sufficient; statement (1) is not.
Therefore the correct choice is A.

Why Not Both Needed?

Even if we combine them, the answer would still be A: statement (2) alone already gives the answer. But for data‑sufficiency we only need to find the minimum information required.

4. Quick Revision Summary

Remember the answer choices: A, B, C, D, E – each has a precise meaning.
Always analyze each statement individually before combining them.
Focus on the question’s requirement (e.g., is it a comparison, an exact value, a range?).
Check for redundancy – if one statement already answers the question, you’re done.
Do not solve for the exact answer unless absolutely necessary; just determine if it can be found.
Practice with “impossible” scenarios – e.g., statements that give inequalities but not enough to determine sign.
Time‑management tip:
1. Read question → identify what is asked.
2. Skim both statements → note type (numeric, inequality, relation).
3. Decide if either alone is enough.
4. If not, test if together they fix the answer.
5. Pick the answer choice.

Pro Tip: Use a truth table mindset: list all possible values that satisfy each statement, then see if the question’s answer is the same across all possibilities. If it is, the statement is sufficient.

Good luck conquering Data Sufficiency!