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Data Sufficiency

Quantitative Aptitude / DI · Advanced Quant / Data

Useful for: Railway RRB, IBPS Banking, KVS, NVS, OTET, BPSC TRE, UGC NET, EMRS

and 12 more exams

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Overview

Data sufficiency asks whether the given statements are enough to answer a question — you decide sufficiency, not the final value.

Key points

Standard options: I alone sufficient; II alone sufficient; either alone sufficient; both together needed; both together not sufficient.
Do not calculate the final answer if sufficiency is already clear.
A statement is sufficient only if it gives one definite answer.
Check each statement independently before combining them.
Hidden information in the question (e.g. "positive integers") counts.

Explanation

"Is x even?" — knowing x² is even is sufficient (x must be even).
Two equations in two unknowns are sufficient only if they are independent.
A range of values is insufficient when a single value is needed.
For yes/no questions, a definite "no" is also sufficient.

Step by step

Read the question and the exact value needed.
Test each statement alone, then together.
Pick the matching standard option.

Examples

Which is the larger of two positive integers? I: sum is 10; II: difference is 4 → both together give 7 and 3 → answer "both together needed".
What is Ravi’s age? I: Ravi is 5 years older than Sita; II: Sita is 20 → both together needed (25).
Is n divisible by 6? I: n is divisible by 12 → I alone sufficient (yes).

Traps and advanced points

Trap: Calculating fully when not needed.
Trap: Combining statements before testing each alone.
Trap: Treating a range as sufficient.

Quick revision

Test I, then II, then both.
One definite answer = sufficient.
A definite "no" is sufficient.

Practice MCQs

In data sufficiency, you must decide whether the statements are —
1. enough to answer the question
2. grammatically correct
3. long enough
4. true in real life
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Answer: (a) enough to answer the question. DS tests whether information is sufficient, not the actual answer value.
If statement I alone answers the question but II alone does not, the answer is —
1. neither is sufficient
2. I alone is sufficient
3. II alone is sufficient
4. both together are needed
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Answer: (b) I alone is sufficient. Only statement I works alone.
Before combining statements, you should first test —
1. both together
2. each statement alone
3. the options
4. nothing
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Answer: (b) each statement alone. Always check each statement separately first.
Question: Is x > 0? I: x² = 4. II: x³ = 8. Which is sufficient?
1. I alone
2. II alone
3. Both needed
4. Neither
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Answer: (b) II alone. x² = 4 gives ±2; x³ = 8 gives only 2.
Question: What is A’s age? I: A is 5 years older than B. II: B is 20. Which is sufficient?
1. Both together
2. Neither
3. I alone
4. II alone
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Answer: (a) Both together. Both are needed: A = 25.
If either statement alone answers the question, the answer is —
1. either statement alone is sufficient
2. neither
3. cannot say
4. both together needed
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Answer: (a) either statement alone is sufficient. Each one separately suffices.
If even both statements together cannot answer, the answer is —
1. neither is sufficient
2. I alone
3. II alone
4. both together
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Answer: (a) neither is sufficient. Insufficient even when combined.
In DS, a statement that gives two possible values for a unique-value question is —
1. irrelevant
2. sufficient
3. insufficient
4. always correct
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Answer: (c) insufficient. A unique answer is needed.
Using outside assumptions not given in statements in DS is —
1. a mistake
2. required
3. the best method
4. allowed
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Answer: (a) a mistake. Use only the given information.
During a classroom lesson on Decision Making, participants discuss how the concept applies in practice. which statement about Decision Making is NOT appropriate?
1. Educational decisions should combine goals, evidence, stakeholder impact, rules and feasibility.
2. A leader should decide only from personal preference.
3. Compare alternatives and document the reason for a major decision.
4. Decision Making should be interpreted according to its purpose and context.
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Answer: (b) A leader should decide only from personal preference.. Educational decisions should combine goals, evidence, stakeholder impact, rules and feasibility. Application: Compare alternatives and document the reason for a major decision. Common trap: A leader should decide only from personal preference.