Data Sufficiency & Eligibility

Study Materials › Reasoning › Data Sufficiency

Both question types here test the same discipline: applying given rules to given facts without importing anything of your own. In data sufficiency you must judge whether the information determines an answer — not what the answer is. In eligibility questions you check a candidate against a checklist, and the trap is usually a fact the question never supplies.

Data Sufficiency: The Standard Options

(1) Statement I alone is sufficient.

(2) Statement II alone is sufficient.

(3) Both statements together are sufficient.

(4) Both together are still not sufficient.

Never solve the problem. You only need to know whether a unique answer could be determined. Candidates lose time here by computing values they were never asked for.

The Test for Insufficiency

A statement is insufficient if you can construct two different answers that both satisfy it. Finding one counter-example settles the matter instantly — this is far faster than trying to prove sufficiency.

Worked Examples from Real Papers

TS Police SI 2022 — Q65

Is the product xy an irrational number?
I. x is an irrational number.
II. y is an irrational number.

I alone: if y = 0 the product is 0, which is rational; if y = 1 with x = √2 the product is irrational. Two different answers → insufficient.
II alone: the same argument with the roles swapped → insufficient.
Both together: √2 × √2 = 2 is rational, while √2 × √3 = √6 is irrational. Both cases satisfy I and II, yet give opposite answers.
Answer: both statements together are still not sufficient.
Key idea: irrational numbers are not closed under multiplication. That single fact decides the whole question.

TS Police SI 2022 — Q66

What is the perimeter of the circle?
I. The centre (0,0) of the circle is at a distance of 5 units from the point P(3, 4).
II. The images of P with respect to both the x-axis and the y-axis lie on the circle.

I alone: gives the centre and tells us P is 5 units away — but never says P lies on the circle, so the radius stays unknown. Insufficient.
II alone: places the points (3, −4) and (−3, 4) on the circle, but with no centre the radius is not fixed. Insufficient.
Both together: centre (0,0) and the point (3, −4) on the circle give radius √(9 + 16) = 5, so the perimeter is 10π. Sufficient.
Answer: both statements together are sufficient.
The trap in I: "at a distance of 5 from P" feels like it gives the radius. It does not — read carefully whether the point is stated to be on the circle.

Eligibility & Conditional Selection

These give a list of conditions, one or two exception clauses, and a rule such as "if any information is not known, refer the case upward". Work down the checklist marking each condition met, failed or unknown — the unknowns are what the question is really testing.

TS Police SI 2022 — Q67

Conditions for a manager's post: (a) graduate with at least 60% (b) under 30 years as on 1 July 2022 (c) at least 50% in class X (d) a diploma, degree or PG in management (e) at least 1 year work experience. If any information is not known, the case is referred to the CEO.
Mr. X was born on 15 August 1995, has a graduation and a PG in management, has 1½ years of work experience, and scored 75% throughout his academic career from class XI onwards.

(b) On 1 July 2022 he is 26 — under 30. Met.
(a) 75% as a graduate, above 60%. Met.
(d) PG in management. Met.
(e) 1½ years, above the 1-year minimum. Met.
(c) Class X marks — his record is given only "from class XI onwards", so his class X percentage is never stated.
One condition is unknown, so the rule applies: he will be referred to the CEO.
This is the whole point of the question. Four conditions are comfortably met, which tempts you to select him. The phrase "from class XI" is doing all the work.

TS Police SI 2022 — Q68

Same conditions. Mr. Y was a first-class student throughout his academic career, completed his 25th birthday on 2 September 2017, worked as an assistant manager from 1 July 2018 to 3 August 2019, and holds a diploma in management from IIM.

(b) Turning 25 on 2 September 2017 makes him 29 on 1 July 2022 — under 30. Met.
(a) and (c) First class throughout covers both the graduation and class X thresholds. Met.
(d) Diploma in management. Met.
(e) 1 July 2018 to 3 August 2019 is about 1 year 1 month — above the minimum. Met.
Every condition is satisfied, so he can be appointed as manager.
Note: the exception clauses never come into play here. They exist only for candidates who fail exactly one specified condition — check the main list first.

Compute the age against the stated cut-off date, not today. These questions always fix a date such as "as on 1 July 2022", and candidates who are borderline are borderline by design.

Also see: Statement & Arguments · Assumptions & Conclusions · Assertion & Reason