← Data Analysis & Interpretation · RITES Senior Technical Assistant Civil

Chapter 1 of 8

Tables & Data Sufficiency

In the RITES Senior Technical Assistant Civil syllabus under Data Analysis & Interpretation · 2 parts

Data Interpretation · Data Sufficiency

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📑 Contents (11 sections)

Part 1 of 2

Data Interpretation

Last reviewed 22 Sept 2026 · 5 min read

What a DI set really tests

Not arithmetic — reading. Nearly every mark lost in this section comes from one of four things: the unit in the heading (lakh, crore, thousand), the row or column read one line off, "percentage increase" mistaken for "percentage point", or an average taken over the wrong number of years.

Read in this order: title → unit → row and column headings → the question. Only then look at the numbers.

The four presentations

Type	What it is good at	Watch out for
Table	exact values, several variables	which way the years run
Bar chart	comparing quantities	the scale, and bars that do not start at zero
Line graph	trend over time	a broken axis exaggerating a rise
Pie chart	shares of one whole	two pies with different totals

A caselet presents the same data as a paragraph of prose; convert it into a small table before answering anything.

The five questions

FormulaThe recurring calculations

Total of a row or column — plain addition
Average $= \frac{total}{number of entries}$ (count the entries, do not assume five)
Ratio — reduce before dividing
Percentage share $= \frac{part}{whole} \times 100$
Percentage change $= \frac{new - old}{old} \times 100$ — always over the old value

For pie charts: $1% = 3.6°$ , so a sector of $54°$ is $15%$ . Two pie charts can only be compared in absolute terms if both totals are given.

Working quickly

Keep the unit out of the arithmetic: if everything is "₹ lakh", work in plain numbers and put the unit back at the end.
Use fraction equivalents rather than long division: $\frac{1}{8} = 12.5%$ , $\frac{1}{7} \approx 14.3%$ , $\frac{1}{6} \approx 16.7%$ , $\frac{1}{3} \approx 33.3%$ .
When options are far apart, approximate: $\frac{85}{180}$ is a little under half, so 47% is right and 43% is not.
Do not recompute a total you already worked out for the previous question — DI sets are built so each answer feeds the next.

A worked set

The table shows the sales of two products, in ₹ lakh.

Year	Product A	Product B	Total
2021	40	60	100
2022	55	65	120
2023	70	80	150
2024	60	90	150
2025	85	95	180

Worked ExampleQuestion 1 — total

What are the total sales of product A over the five years?

Solution. $40 + 55 + 70 + 60 + 85 =$ ₹ 310 lakh.

Worked ExampleQuestion 2 — average

Find the average annual sales of product B.

Solution. $\frac{60 + 65 + 80 + 90 + 95}{5} = \frac{390}{5} =$ ₹ 78 lakh.

Worked ExampleQuestion 3 — percentage change

By what percent did the total sales grow from 2021 to 2025?

Solution. $\frac{180 - 100}{100} \times 100 =$ 80%.

Worked ExampleQuestion 4 — percentage share

In which year was product A's share of the total the highest?

Solution. Shares: $40%$ , $45.8%$ , $46.7%$ , $40%$ , $47.2%$ → 2025.

Worked ExampleQuestion 5 — ratio

Find the ratio of the sales of A to B in 2023.

Solution. $70 : 80 =$ 7 : 8.

Worked ExampleQuestion 6 — year-on-year growth

Find the percentage increase in the sales of A from 2022 to 2023.

Solution. $\frac{70 - 55}{55} \times 100 = \frac{15}{55} \times 100 \approx$ 27.3%.

Worked ExampleQuestion 7 — a trap

Product A's share rose from 40% in 2024 to 47.2% in 2025. Is that a rise of 7.2% or of 7.2 percentage points?

Solution. 7.2 percentage points. As a percentage increase it is $\frac{7.2}{40} \times 100 = 18%$ . The two are different numbers and the options will contain both.

Worked ExampleQuestion 8 — as a pie chart

If the 2025 sales are drawn as a pie chart, what angle does product A occupy?

Solution. $\frac{85}{180} \times 360° =$ 170°.

Worked ExampleQuestion 9 — a year below the average

In how many years were product A's sales below their own five-year average?

Solution. Average $= 310/5 = 62$ → 2021 (40), 2022 (55) and 2024 (60) are below it: 3 years.

Worked ExampleQuestion 10 — combining rows

If the company earns a profit of 20% on A and 15% on B, what is the profit in 2024?

Solution. $0.20 \times 60 + 0.15 \times 90 = 12 + 13.5 =$ ₹ 25.5 lakh.

Frequently tested points

Read the unit in the heading before any calculation.
Percentage change is over the old value; a share in percent changes by percentage points.
Average needs the count of entries actually being averaged.
Pie chart: $1% = 3.6°$ ; comparing two pies needs both totals.
A bar chart whose axis does not start at zero exaggerates differences.
Reduce ratios before dividing, and reuse totals already computed.
Approximate when the options are far apart; compute exactly only when they are close.

Common MistakeCommon mistakes

Dividing by the new value in a percentage change.
Treating a rise from 40% to 47.2% as a 7.2% increase.
Averaging over five years when the question asks about four.
Comparing sectors of two pie charts as though the totals were equal.
Losing the unit — answering 310 when the answer is ₹ 310 lakh.

Revision SummaryChapter summary

Data interpretation rewards careful reading of the title, unit and headings before the numbers.
Tables, bar charts, line graphs, pie charts and caselets present the same kinds of data with different traps.
Five calculations — total, average, ratio, share and percentage change — cover almost every question asked.
Percentage change and percentage points are different, and both appear in the options.
Speed comes from fraction equivalents, approximation and reusing totals, not from faster long division.

Part 2 of 2

Data Sufficiency

Last reviewed 22 Sept 2026 · 5 min read

The question and the options

You are given a question and two (sometimes three) statements, and asked whether the statements are enough to answer it — not what the answer is.

The usual option set:

Option	Meaning
(a)	Statement I alone is sufficient, II alone is not
(b)	Statement II alone is sufficient, I alone is not
(c)	Each statement alone is sufficient
(d)	Both together are not sufficient
(e)	Both together are sufficient, but neither alone

Read the paper's own option list once — some papers order (d) and (e) the other way round.

The method

FormulaFour steps, in this order

Read the question and decide exactly what would settle it (a single value, a yes/no, a name).
Test Statement I alone, covering II with your hand.
Test Statement II alone, forgetting I completely.
Only if both fail individually, test them together.

Never compute more than you must. Sufficiency is reached the moment the answer is pinned to one possibility.

Exam TipA yes/no question is settled by a definite "no" too

If the question is "Is x greater than 5?", a statement forcing $x = 3$ is sufficient — it answers the question, even though the answer is no. Sufficiency is about certainty, not about a positive answer.

Where candidates lose marks

Carrying I into II. Once step 2 is done, statement I must be forgotten entirely.
Computing the answer. It wastes the time this question type is designed to save.
Accepting two possibilities. " $x^{2} = 16$ " gives $x = 4$ or $- 4$ — not sufficient for the value of $x$ , though sufficient for $∣ x ∣$ .
Assuming the obvious. A statement that ages are whole numbers, or that a person is male, must be given, not supposed.

Worked examples

Worked ExampleExample 1 — one statement enough

What is the value of $x$ ? I. $x + 5 = 12$ II. $x$ is a positive integer less than 10.

Solution. I gives $x = 7$ → sufficient. II allows 1 to 9 → not sufficient. Option (a).

Worked ExampleExample 2 — each alone

How old is Ravi? I. Ravi is twice as old as his sister, who is 12. II. Ravi was born in 2002 and it is now 2026.

Solution. I gives 24; II gives 24 → each alone is sufficient, option (c).

Worked ExampleExample 3 — both needed

What is the two-digit number? I. The sum of its digits is 9. II. The number is divisible by 5 and greater than 40.

Solution. I alone: 18, 27, 36, 45, 54, 63, 72, 81, 90. II alone: 45, 50, 55, … Together: 45 and 90 both fit → not sufficient even together, option (d).

Worked ExampleExample 4 — both together suffice

Who sits at the extreme left of a row of five? I. A sits third from the right. II. B sits to the immediate left of A, and C sits to the immediate left of B.

Solution. I places A at seat 3. II then places B at 2 and C at 1 → together they settle it; neither alone does → option (e).

Worked ExampleExample 5 — a yes/no question

Is $n$ an even number? I. $n$ is divisible by 6. II. $n$ is a prime number greater than 2.

Solution. I forces even → sufficient. II forces odd → also sufficient (the answer is "no", which is still an answer) → each alone, option (c).

Worked ExampleExample 6 — two possibilities

What is the value of $y$ ? I. $y^{2} = 49$ . II. $y$ is negative.

Solution. I gives $\pm 7$ → insufficient. II alone gives nothing. Together, $y = - 7$ → option (e).

Worked ExampleExample 7 — a relationship

How is P related to Q? I. P is the son of Q's brother. II. Q has only one brother.

Solution. I alone makes P Q's nephew — the brother's son, whether or not Q has other brothers → statement I alone is sufficient, option (a). II adds nothing.

Worked ExampleExample 8 — a statement that repeats the question

In which direction is X from Y? I. Y is to the north of X. II. X and Y are 5 km apart.

Solution. I answers it directly (X is south of Y) → sufficient. II gives distance only → option (a).

Worked ExampleExample 9 — coding

What is the code for "book"? I. In that code, "book my ticket" is written "sa ka na". II. In the same code, "my new ticket" is written "ka da na".

Solution. Together, the words common to both sentences are my and ticket, with common codes ka and na; so book is sa → sufficient together, neither alone → option (e).

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