A question type, not a topic. You are given a question and two (sometimes three) numbered statements, and you must decide whether the statements are enough to answer, without necessarily computing the answer. The skill is judgement, not arithmetic. It tests the same quantitative content as number system and simplification and percentage ratio and average, but rewards knowing when you have enough information and stopping.
Most data-sufficiency sets use a fixed set of options. The two-statement form is the most common:
| Code |
Meaning |
| A |
Statement I alone is sufficient, but statement II alone is not |
| B |
Statement II alone is sufficient, but statement I alone is not |
| C |
Both statements together are sufficient, but neither alone is |
| D |
Each statement alone is sufficient |
| E |
Both together are still not sufficient |
Always read the option codes printed with the actual paper; the wording can vary, and some sets give three statements. The logic below is the same whatever the labels.
- Read the question and note exactly what is asked (a unique value, a yes or no, a comparison).
- Take statement I alone. Can it give a single definite answer? Mark it sufficient or not.
- Take statement II alone, fresh, ignoring statement I. Mark it.
- Only if neither alone works, combine them and test sufficiency together.
- Choose the code that matches.
- Do not solve for the number unless you must. Sufficiency means "is there exactly one answer", not "what is it".
- A statement is sufficient even if the answer it forces is "no". For a yes-or-no question, a definite "no" is just as sufficient as a definite "yes".
- Insufficiency means more than one answer is possible. If you can produce two different valid answers, the statement is not sufficient.
- Test each statement in isolation first; a common trap is to let information from statement I leak into your reading of statement II.
- Watch for hidden constraints: "x is a positive integer" can turn an otherwise loose statement into a sufficient one.
Question: What is the value of x?
Statement I: x + 5 = 12.
Statement II: x is an even number.
Statement I alone gives x = 7, a single value, so it is sufficient. Statement II alone allows 2, 4, 6, ..., many values, so it is not sufficient. The answer is code A (I alone sufficient, II alone not).
Question: What is the two-digit number?
Statement I: The sum of its digits is 9.
Statement II: The tens digit is twice the units digit.
Statement I alone allows 18, 27, 36, 45, ..., not unique. Statement II alone allows 21, 42, 63, 84, not unique. Together: digit sum 9 and tens = 2 times units gives units 3, tens 6, the number 63. Unique only when combined, so the answer is code C.
Question: Is the integer n even?
Statement I: n is the product of two consecutive integers.
The product of two consecutive integers is always even (one of them is even), so n is definitely even. The statement forces a definite "yes", so it is sufficient on its own.
Question: What is the perimeter of a square?
Statement I: The side is 6 cm.
Statement II: The area is 36 square cm.
Statement I gives perimeter 24 cm. Statement II gives side = √(36) = 6 cm, so perimeter 24 cm too. Each alone is sufficient, so the answer is code D.
Question: What is the age of the youngest of three children?
Statement I: Their average age is 10.
Statement II: The oldest is 14.
Statement I gives the total (30) but not the split. Statement II fixes one child only. Together we know two facts (sum 30, oldest 14) but the remaining two ages can still vary (for example 8 and 8, or 7 and 9). Not sufficient even together, so the answer is code E.
- Phrase the question as "is there exactly one answer", and stop the moment you can say yes or no to that.
- For yes-or-no questions, a consistent "no" is a sufficient answer; do not mistake "the answer is no" for "insufficient".
- Plug in two test values that satisfy a statement; if they give different answers, the statement is insufficient, and you have proved it quickly.
- Never carry a fact from one statement into the testing of the other; reset between steps.
- If both statements separately work, the answer is "each alone", not "both together"; read that distinction in the option codes carefully.
For each, decide which code (A, B, C, D, or E as defined above) applies.
- What is x? I: 2x = 10. II: x is prime.
- Is the number divisible by 6? I: It is divisible by 2. II: It is divisible by 3.
- What is the area of the rectangle? I: Its length is 8 cm. II: Its breadth is 5 cm.
- Is p greater than q? I: p = 7. II: q = 9.
- What is the average of five numbers? I: Their sum is 200. II: The largest is 60.
- Is the triangle right-angled? I: Its sides are 6, 8, 10. II: One angle is 90°.
- What is the speed of the car? I: It covers 120 km. II: It takes 2 hours.
- Is n a multiple of 4? I: n is even. II: n is divisible by 8.
- What is the cost of one pen? I: 5 pens cost 60 rupees. II: Pens cost more than pencils.
- How old is Ravi? I: Ravi is 3 years older than Sita. II: Sita is 12 years old.
Reveal the answer key and full worked solutions
- A. I gives x = 5 (unique). II alone allows many primes.
- C. Divisible by 6 needs both 2 and 3; neither statement alone settles it, both together do.
- C. Area needs both length and breadth; each alone is insufficient, together they give 40 square cm.
- C. p > q needs both values; together 7 is not greater than 9, a definite "no", which is sufficient only with both.
- A. Average = sum / 5 = 200/5 = 40; I alone suffices. II alone is irrelevant to the average.
- D. Sides 6, 8, 10 satisfy Pythagoras (a definite yes), and "one angle is 90°" is itself the definition; each alone suffices.
- C. Speed = distance / time needs both; each alone is insufficient, together 60 km/h.
- B. Divisible by 8 implies divisible by 4 (a definite yes). I alone (even) allows 2, 6, 10, which are not multiples of 4, so insufficient.
- A. 60/5 = 12 rupees per pen; I alone suffices. II gives no number.
- C. Ravi's age needs Sita's age plus the gap; together Ravi is 15, neither alone is enough.