Caselets & Data Sufficiency — CAT DILR

A caselet is Data Interpretation dressed as a short paragraph rather than a table — the same percentages, ratios and comparisons are present, but buried in sentences instead of laid out in rows and columns. Data sufficiency questions test a genuinely different skill: judging whether a question COULD be answered from the given statements, without actually answering it.

1. Converting a caselet into a table

The first and only mandatory step for any caselet is extracting its numbers into a small table or list, exactly as if it had been given as one. A paragraph describing "Amit spends twice as much as Bina, and together they spend ₹900" contains the same information as a two-row table with a ratio column and a total column — writing it that way removes the need to re-read the prose for every one of the set's 4-6 questions.

A caselet's sentences are often given in an order that is not the order needed for computation, and the extraction step is what reorders the information usefully. A detail mentioned in the caselet's second sentence might only become usable once combined with a fact from the fourth sentence — the table makes this combination visible; re-reading the prose repeatedly does not.

Some caselets describe conditional or branching scenarios ("if the discount exceeds 20%, an additional loyalty benefit applies") rather than a single fixed set of numbers. These are solved by first checking which branch of the condition actually holds for the given data, then applying only that branch's rule — attempting to apply every stated rule simultaneously, rather than selecting the one branch that is actually triggered, is the standard error on this caselet sub-type.

2. The data sufficiency framework

A data sufficiency (DS) question gives a question and two statements, and asks not for the answer but for which statement(s) would let you compute it. The five standard answer choices are:

The discipline that makes DS fast is stopping the instant sufficiency is established, without computing the actual numeric answer. If Statement I pins down a unique value for what's being asked, the question is answered as "Statement I is sufficient" — actually calculating that value is unnecessary work that DS questions do not reward.

3. Testing each statement independently first

Always evaluate Statement I completely alone, forgetting Statement II exists, before looking at Statement II at all — and vice versa. The most common DS error is letting information from one statement "leak" into the evaluation of the other, silently treating a statement as sufficient because of a fact that only the other statement actually supplies.

Once both statements have been tested alone: if neither alone is sufficient, test them together as a last step, not before.

Sufficiency is a stronger requirement than mere relevance. A statement can be entirely true and directly related to the question's subject while still failing to pin down a single answer — "sufficient" specifically means the statement (or combination) determines exactly one value or a definite yes/no, not merely that it narrows the possibilities somewhat.

A statement narrowing a question from infinitely many possible values down to, say, three remaining candidates is still not sufficient, since more than one answer remains genuinely possible.

4. Common data-sufficiency traps

Trap. A statement can look irrelevant to the question and still be exactly sufficient, or look directly relevant and still fail. "Is $x$ an even integer?" with Statement I "$x/2$ is an integer" is sufficient alone (if $x/2$ is an integer, $x$ must be even) — despite not mentioning "even" at all. Judge sufficiency by what a statement logically implies, never by how closely its wording matches the question.

Two statements can independently give the same underlying fact through different wording, in which case having both together adds nothing beyond having either one — a genuine "even together, not sufficient" case arises when both statements, however phrased, pin down the same incomplete information rather than complementary pieces of it.

A statement giving an equation with two valid solutions (like $x^2=16$) is not automatically insufficient — if a second statement or an implicit constraint (such as "$x$ is positive") eliminates one of the two solutions, sufficiency can still be reached; the check is always "does exactly one value survive," not "does the statement look like a full equation."

Worked Examples

Example 1 (caselet extraction — medium). A caselet states: "Amit spends twice as much as Bina every month. Together, they spend ₹900. Chitra spends ₹150 more than Bina." Find each person's monthly spending.

Extract into variables: let Bina $=x$. Amit $=2x$. Chitra $=x+150$. From "Amit and Bina together spend ₹900": $2x+x=900\Rightarrow 3x=900\Rightarrow x=300$. So Bina $=₹300$, Amit $=₹600$, Chitra $=300+150=₹450$.

Example 2 (DS, either alone sufficient — medium). Is $x$ an even integer? Statement I: $x/2$ is an integer. Statement II: $x^2$ is even.

Statement I alone: if $x/2$ is an integer, $x$ is exactly twice that integer, so $x$ is even. Sufficient alone.

Statement II alone: if $x^2$ is even, $x$ cannot be odd (an odd number squared is always odd), so $x$ must be even. Sufficient alone.

Since each statement alone answers the question, the answer is: either statement alone is sufficient.

Example 3 (DS, both needed — easy). Find the value of $x$. Statement I: $x^2=16$. Statement II: $x>0$.

Statement I alone: $x=4$ or $x=-4$ — two possible values, not sufficient. Statement II alone: only says $x$ is positive, with no specific value — not sufficient. Both together: $x^2=16$ and $x>0$ together give exactly $x=4$. Sufficient only when combined.

Example 4 (DS, even together not sufficient — hard). Find the two-digit number $N$. Statement I: the sum of $N$'s digits is 9. Statement II: $N$ is divisible by 9.

Statement I alone: many two-digit numbers have digit sum 9 (18, 27, 36, ..., 90) — not sufficient. Statement II alone: many two-digit numbers are divisible by 9 (18, 27, ..., 99) — not sufficient.

Both together: every two-digit number whose digits sum to 9 is automatically divisible by 9 (the standard divisibility rule), so Statement II adds no new information beyond Statement I — the same list of candidates (18, 27, 36, 45, 54, 63, 72, 81, 90) remains. Even together, not sufficient.

Example 5 (caselet with a derived total — hard). A caselet states: "In a class, the number of girls is 20 more than the number of boys. If there are 100 students in total, find the number of boys and girls."

Let boys $=b$, girls $=b+20$. Total: $b+(b+20)=100\Rightarrow 2b=80\Rightarrow b=40$. Boys $=40$, girls $=60$.

Example 6 (caselet, conditional branching — hard). A store's policy: if a customer's bill exceeds ₹2,000, a flat 15% discount applies; otherwise, a flat 5% discount applies. Priya's bill before discount is ₹2,400. Find her final bill.

Check which branch applies: ₹2,400 exceeds ₹2,000, so the 15% branch applies (not the 5% one). Final bill $=2400\times 0.85=₹2,040$. Applying the 5% rule instead — the branch that does not actually hold — would give the wrong final amount of ₹2,280.

Summary

Extract a caselet's numbers into a table or a small set of variables immediately — this single step, done once, replaces re-reading the prose for every question in the set.

Data sufficiency rewards judging whether a statement determines a unique answer, not computing that answer — stop the moment sufficiency is established.

Evaluate each statement completely alone before considering the other, and only test them together as a genuinely last step if neither alone suffices.

Sufficiency is a logical property, not a wording match — a statement that never mentions the question's exact term can still be sufficient, and two differently worded statements can still carry the same underlying information, making "even both together, not sufficient" a real and recurring answer choice.