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Numerical Aptitude Syllabus / Module 18 · Data Interpretation II / Week 18

Week 18: Data Interpretation II — Pie Charts, Caselets & Data Sufficiency

The harder DI formats: a pie chart's degrees hiding a percentage in disguise, a caselet's paragraph hiding a table you have to build yourself, and data sufficiency's genuinely different question — not "what's the answer," but "is there even enough information here to find one."

Module 18 of 20 Week 18 of 20 ~2–3 Hours Practice Problems Included

By the end of this week, you'll be able to

  • Convert between a pie chart's degrees and percentages fluently
  • Extract a structured table from a caselet's prose
  • Answer a data sufficiency question without fully solving the underlying problem
1 Pie Charts — Degrees & Percentages 2 Caselets — Building a Table From Prose 3 Data Sufficiency 4 The Standard DS Answer Choices 5 Practice Problems 6 Knowledge Check

1. Pie Charts — Degrees & Percentages

A full circle is 360°, which represents 100% of whatever's being measured — the entire chapter is one conversion factor, applied consistently.

the degrees-to-percentage conversion
360 degrees = 100% of the total
1 degree    = 100/360 % ≈ 0.278%
1 percent   = 360/100 = 3.6 degrees

Worked: a pie chart shows a company's expense categories. The
"Marketing" slice measures 72 degrees. What percentage of
total expenses is Marketing?

  72 / 360 x 100 = 20%

Worked (reverse direction): "Salaries" is 45% of the total.
What angle does its slice occupy?

  45% x 3.6 = 162 degrees

Once a slice's percentage (or degree) is known, every other Week 3/6 technique applies normally — a pie chart is just a different visual encoding of the same percentage-of-a-whole data a table or bar chart would show.

2. Caselets — Building a Table From Prose

A caselet buries structured data inside a paragraph — the real skill is extracting it into a clean table BEFORE attempting any question, exactly the discipline Section 1 of last week built for charts.

a sample caselet
"In a survey of 500 people, 60% were employed. Among the
employed, 40% worked in IT and the remainder in other
sectors. Among the unemployed, 30% were actively seeking
work, and the rest were not in the labor force."

Extract into a table FIRST:

  Total: 500
  Employed: 60% x 500 = 300
    IT: 40% x 300 = 120
    Other: 300 - 120 = 180
  Unemployed: 500 - 300 = 200
    Seeking: 30% x 200 = 60
    Not in labor force: 200 - 60 = 140

Only AFTER building this table do you attempt any question --
e.g. "how many people were employed in IT?" is now a direct
lookup: 120.

Building the full table upfront (rather than hunting back through the paragraph for each individual question) pays off immediately once a caselet has three or more questions attached, which is the normal case — the extraction cost is paid once, not once per question.

3. Data Sufficiency

A data sufficiency (DS) question gives a question and two statements, and asks whether the statements provide ENOUGH information to answer — not what the actual answer is. This is a genuinely different skill from every other chapter in this course.

a worked data sufficiency question
Question: What is the value of x?

Statement 1: x + y = 10
Statement 2: x - y = 4

Evaluate EACH statement ALONE first:

Statement 1 ALONE: x+y=10 -- one equation, two unknowns --
  NOT sufficient (x could be many different values)

Statement 2 ALONE: x-y=4 -- same problem --
  NOT sufficient alone either

BOTH statements TOGETHER: two equations, two unknowns --
  solvable: x=7, y=3 -- SUFFICIENT together

Answer: statements together are sufficient, but NEITHER
alone is.

The critical discipline: evaluate Statement 1 completely alone, ignoring Statement 2 entirely, and vice versa, BEFORE considering them together — answering based on "both together" without first checking each alone is the single most common DS error, since it skips distinguishing between the several different sufficiency outcomes Section 4 lists.

4. The Standard DS Answer Choices

Data sufficiency questions conventionally offer five fixed answer categories — recognizing which one applies is the actual "answer," not a computed number.

the five standard categories
A: Statement 1 ALONE is sufficient, but Statement 2 alone
   is NOT.
B: Statement 2 ALONE is sufficient, but Statement 1 alone
   is NOT.
C: BOTH statements TOGETHER are sufficient, but NEITHER
   alone is.
D: EACH statement ALONE is independently sufficient.
E: The statements TOGETHER are still NOT sufficient.

Section 3's worked example is category C exactly — neither statement alone was enough, but combined they were. The systematic approach (check Statement 1 alone, check Statement 2 alone, then check together only if needed) maps directly onto these five categories without needing to hold the whole decision tree in your head at once.

"Sufficient" doesn't mean "gives a nice answer"

A statement is sufficient if it pins down exactly ONE possible value for what's being asked — even an ugly, non-round number counts as sufficient. Conversely, a statement that narrows things down to two or more possible values (even simple ones) is NOT sufficient, since the question demands a single determined answer, not a short list of candidates.

5. Practice Problems

Practice

30 problems, no calculator — Easy, Medium & Tough

For every data-sufficiency question, evaluate each statement completely alone before considering them together. Easy problems should take under 30 seconds each; Medium under 60 seconds; Tough under 90 seconds.

shared dataset — household budget pie chart (total = Rs. 60,000/month)
Food: 90°   Rent: 108°   Transport: 54°   Savings: 72°   Other: 36°

Easy (1–10) — using the pie chart above

  1. Find the percentage spent on Food.
  2. Find the percentage spent on Rent.
  3. Find the amount spent on Transport.
  4. Find the amount spent on Savings.
  5. Find the percentage spent on Other.
  6. Find the amount spent on Food.
  7. Find the amount spent on Rent.
  8. Find the percentage spent on Transport.
  9. Find the percentage spent on Savings.
  10. Find the amount spent on Other.
Easy — Answers

1) 90/360×100=25%. 2) 108/360×100=30%. 3) 54/360×100=15% of 60,000=Rs. 9,000. 4) 72/360×100=20% of 60,000=Rs. 12,000. 5) 36/360×100=10%. 6) 25% of 60,000=Rs. 15,000. 7) 30% of 60,000=Rs. 18,000. 8) 15%. 9) 20%. 10) 10% of 60,000=Rs. 6,000.

Medium (11–20)

  1. Caselet: "A company has 500 employees. 60% are in Engineering. Among Engineering employees, 30% are women." Find the number of women in Engineering.
  2. Using Q11's caselet, find the number of non-Engineering employees.
  3. Using the pie chart, find the ratio of Food spending to Transport spending.
  4. Using the pie chart, find the combined percentage of Rent and Savings.
  5. DS: What is the value of x? (1) x + 5 = 12. (2) x is a positive number.
  6. DS: Is n divisible by 3? (1) n is divisible by 9. (2) n is divisible by 6.
  7. Using the pie chart, if Food spending rises to Rs. 18,000 next month (total budget unchanged), find its new percentage share.
  8. Caselet: "In a survey of 300 people, 40% prefer brand A, 35% prefer brand B, and the rest prefer brand C." Find the number of people who prefer brand C.
  9. Using Q18's caselet, find the ratio of brand A to brand B preferences.
  10. DS: What is the perimeter of a square? (1) Its area is 49 sq.cm. (2) Its side is 7cm.
Medium — Answers

11) Engineering=60%×500=300; women=30%×300=90. 12) 40%×500=200. 13) 90°:54°=5:3. 14) 30%+20%=50%. 15) St1 alone: x=7, sufficient. St2 alone: many positive numbers, not sufficient → A. 16) St1 alone: divisible by 9 → always divisible by 3, sufficient. St2 alone: divisible by 6 → divisible by 2 and 3, sufficient → D. 17) 18000/60000×100=30%. 18) 100-40-35=25% → 75 people. 19) 40:35=8:7. 20) St1 alone: side=7 (unique positive root) → perimeter=28, sufficient. St2 alone: side=7 directly → perimeter=28, sufficient → D.

Tough (21–30)

  1. Caselet: "A factory produces 1,200 units per day. 45% are Type X, and of the remaining units, 60% are Type Y and the rest are Type Z." Find the number of Type Z units.
  2. Using Q21's caselet, find the ratio of Type X to Type Z units.
  3. A pie chart shows a company's costs: Raw Materials 40%, Labor 25%, Overhead 20%, Marketing 15%. If Labor costs are Rs. 3,00,000, find total costs.
  4. Using Q23's data, find the Marketing cost.
  5. DS: What is the value of a two-digit number? (1) The sum of its digits is 12. (2) The number is divisible by 4.
  6. DS: Is x > y? (1) x + 3 > y + 3. (2) x - y = 5.
  7. Caselet: "In a class of 600 students, 55% are boys. Of the boys, 60% play sports. Of the girls, 50% play sports." Find the total number of students who play sports.
  8. Using Q27's caselet, find the percentage of the total school that plays sports.
  9. A pie chart's "Others" category has no labeled degree value, but all other categories sum to 290°. Find the "Others" category's percentage.
  10. DS: What is the value of a two-digit number? (1) The sum of its digits is 9. (2) The number is divisible by 9.
Tough — Answers

21) TypeX=45%×1200=540; remaining=660; TypeY=60%×660=396; TypeZ=660-396=264. 22) 540:264=45:22. 23) Labor 25%=300,000 → total=1,200,000. 24) Marketing 15%×1,200,000=180,000. 25) St1 alone: digit sum 12 gives many candidates (39,48,57,66,75,84,93), not sufficient. St2 alone: divisible by 4 gives many candidates, not sufficient. Together: digit-sum-12 AND divisible-by-4 still gives two candidates (48, 84) — still NOT sufficient → E. 26) St1 alone simplifies directly to x>y, sufficient. St2 alone (x=y+5) also implies x>y, sufficient → D. 27) Boys=330, girls=270; boys playing=198, girls playing=135; total=333. 28) 333/600×100=55.5%. 29) 360-290=70°; 70/360×100≈19.44%. 30) St1 alone: many candidates (18,27,...,90), not sufficient. St2 alone: every two-digit multiple of 9 already has digit sum 9 (except 99, which has digit sum 18) — same large candidate set, not sufficient. Together: no narrowing occurs since the two conditions describe almost the same set → still NOT sufficient → E.

6. Knowledge Check

Four quick questions. Expand each to check your answer.

Q1

Why does 1 percentage point on a pie chart correspond to exactly 3.6 degrees?

A full circle (360 degrees) represents the complete 100% total, so dividing 360 by 100 gives the number of degrees per single percentage point — 3.6. This is a fixed conversion factor because it's derived directly from the relationship between a full circle's degrees and the definition of 100%, not something that varies chart to chart.

Q2

Why is building a full table from a caselet's paragraph worth doing before attempting the first question, rather than searching the paragraph fresh for each question?

Caselets typically have multiple questions attached, all drawing on the same underlying data — extracting and organizing that data into a table is a one-time cost that then makes every subsequent question a fast direct lookup, instead of re-reading and re-parsing the same paragraph from scratch for each new question.

Q3

Why must each data sufficiency statement be evaluated completely alone before considering them together?

The standard answer categories (A through E) specifically distinguish between "only statement 1 works alone," "only statement 2 works alone," "neither alone but both together," and other combinations — skipping the individual-alone checks makes it impossible to correctly identify which of these distinct categories the question actually falls into, even if the final combined-sufficiency conclusion happens to come out right.

Q4

Why does a statement narrowing an answer down to two possible values NOT count as "sufficient," even though it's genuinely useful information?

Data sufficiency specifically asks whether the information determines exactly ONE definite value for the question being asked — narrowing to two or more remaining candidates means the question still can't be answered with certainty, even though real progress was made. "Useful but incomplete" and "sufficient" are different things in this question format.

← Back to Week 17: Data Interpretation I — Tables, Bar & Line Graphs Up next Week 19: Vedic Maths & Speed Calculation Techniques →