Charts, Graphs and Visual Data Interpretation Short Notes for CAT: Concepts, Formulas, Worked Examples & Practice

Charts, Graphs and Visual Data Interpretation short notes for CAT: 5 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Exam Readiness: Research Chart Checklist

Draw the Matrix: Rows = Authors, Columns = Paper Types. Add totals for both.
Compute the Invariant: $Total Authorships = \sum (Column Total \times Authors per Paper)$
Validate Row Sums: Ensure $\sum (Row Totals) = Total Authorships$ .
Lock Absolute Constraints: Fill in "exactly $n$ " and "zero" cells first.
Beware the Trap: Never add a "3-author paper" as $+ 1$ to an author's total without remembering it consumes $3$ units of the column's authorship capacity.
Check Consistency: If a deduction forces an author to have more papers than the total available in a column, re-evaluate your earlier assumptions.

Topic Hero: Financial and Firm Performance Charts

Chapter: Charts, Graphs and Visual Data Interpretation

Financial and Firm Performance Charts

Decode how companies make money, grow, and trade — through tables, scatter plots, and candlesticks.

What you will learn here

Revenue, Cost, and Profit tables across multiple years and companies
Scatter plots showing PAT, Employee Strength, and R&D spend
Candlestick charts for share price action (Open, High, Low, Close)
Year-over-year comparisons, growth rates, and ratio traps

Core Idea: The Profit Equation

The Foundation

$Profit = Revenue - Cost$

Key Derived Ratios

Ratio	Formula	Meaning
Profit Margin	$\frac{Profit}{Revenue} \times 100$	% of revenue kept as profit
Cost Ratio	$\frac{Cost}{Revenue} \times 100$	% of revenue spent
Revenue Growth	$\frac{Rev _{new} - Rev _{old}}{Rev _{old}} \times 100$	Year-over-year change

Note

Profit Margin + Cost Ratio = 100%
A company can have high revenue but low profit if costs are high
Always check whether data is in absolute values (crores) or percentages

Topic Recap: Key Formulas and Checks

Quick Revision Checklist

1. Pollution Index (PI)

Formula: $P I = \sum w_{i} P M_{i}$
Constraint: Distinct values from a fixed set.

2. Sustainability Index (SI)

$S I_{n e w} = S I_{o l d} (1 + \frac{%Δ}{100})$
Check: Integer result, $1 \leq S I \leq 100$ .

3. Travel Stats

Total = Sum of regions.
Overlap: $N (A \cup B) = N (A) + N (B) - N (A \cap B)$ .
Constraint: Distinct countries per person.

Charts, Graphs and Visual Data Interpretation: Solved Questions with Step-by-Step Explanations (2 Problems)

Question 1 · Data Interpretation and Logical Reasoning MCQ

Four companies (Alpha, Beta, Gamma, Delta) reported their Revenue and Cost (in Rs. crores) for the years 2022 and 2023. Profit is defined as Revenue minus Cost.

The following facts are known:

The total profit of the four companies was exactly $100$ in 2022 and $120$ in 2023.
For each company, the Profit in 2022 was an even integer, and the Profit in 2023 was an odd integer.
For each company, the Profit strictly increased from 2022 to 2023.
The absolute increase in Profit ( $Profit_{2023} - Profit_{2022}$ ) was a distinct positive integer for all four companies.

Which of the following statements is/are NECESSARILY true?

i. The minimum absolute increase in Profit among the four companies was exactly $1$ .

ii. The maximum absolute increase in Profit among the four companies was at least $9$ .

iii. The sum of the absolute increases of the two companies with the highest increases was exactly $16$ .

A.
Only i and ii
B.
Only ii and iii
C.
Only i and iii
D.
i, ii, and iii

Correct Answer:

Step-by-Step Solution

Key idea: This is a logical deduction question relying on integer constraints and parity (odd/even properties).

Step 1: Determine the parity of the increases.

Let $P_{22}$ be the 2022 profit (even) and $P_{23}$ be the 2023 profit (odd).

The increase is $Δ = P_{23} - P_{22}$ .

Since $Odd - Even = Odd$ , every company's absolute increase in profit MUST be an odd integer.

Step 2: Set up the sum constraint.

Total increase in profit = $Total_{2023} - Total_{2022} = 120 - 100 = 20$ .

Let the four distinct positive odd increases be $a < b < c < d$ .

We know $a + b + c + d = 20$ .

Step 3: Find all valid sets of ${a, b, c, d}$ .

The smallest distinct positive odd integers are $1, 3, 5, 7$ (Sum = $16$ ).

To reach a sum of $20$ , we must add $4$ to these base values while keeping them distinct and odd.

Possible sets:

Set 1: Add $4$ to the largest $\to {1, 3, 5, 11}$ . (Sum = $20$ )
Set 2: Add $2$ to the third and $2$ to the largest $\to {1, 3, 7, 9}$ . (Sum = $20$ )
Set 3: Add $4$ to the second $\to {1, 7, 5, 7}$ (Invalid, not distinct).
Any higher starting values (e.g., $3, 5, 7, 9$ ) sum to $24 > 20$ .

Thus, the ONLY possible sets of increases are ${1, 3, 5, 11}$ and ${1, 3, 7, 9}$ .

Step 4: Evaluate the statements against both valid sets.

i. Minimum is exactly $1$ : True for both ${1, 3, 5, 11}$ and ${1, 3, 7, 9}$ .
ii. Maximum is at least $9$ : True ( $11 \geq 9$ and $9 \geq 9$ ).
iii. Sum of the two highest is exactly $16$ : For Set 1, $5 + 11 = 16$ . For Set 2, $7 + 9 = 16$ . True for both.

All three statements are necessarily true.

Question 2 · Data Interpretation and Logical Reasoning MCQ

The Sustainability Index (SI) for three cities (X, Y, Z) is calculated using three parameters: Air (A), Water (W), and Soil (S).

Scores for each parameter are integers from 0 to 100.

The weights assigned to these parameters are $w_{A}, w_{W}, w_{S}$ such that $w_{A} + w_{W} + w_{S} = 1$ , and all weights are strictly positive.

The parameter scores for the cities are:

City X: A = 80, W = 60, S = 40
City Y: A = 50, W = 80, S = 70
City Z: A = 60, W = 50, S = 90

It is known that $S I (X) > S I (Y)$ and $S I (Y) > S I (Z)$ .

Which of the following statements is NECESSARILY TRUE?

A.
$w_{A} > 0.45$
B.
$w_{W} > 0.35$
C.
$w_{S} < 0.25$
D.
$w_{A} + w_{W} > 0.8$

Correct Answer:

Step-by-Step Solution

Key idea: This is a weighted average bounding question, recognisable by the unknown weights and strict inequality conditions between composite scores.

Why this method applies: We must translate the SI inequalities into a system of linear constraints on the weights, then find the feasible region to test the options.

Step 1: Formulate the SI equations.

Substitute $w_{S} = 1 - w_{A} - w_{W}$ to reduce variables.

$S I (X) = 80 w_{A} + 60 w_{W} + 40 (1 - w_{A} - w_{W}) = 40 + 40 w_{A} + 20 w_{W}$

$S I (Y) = 50 w_{A} + 80 w_{W} + 70 (1 - w_{A} - w_{W}) = 70 - 20 w_{A} + 10 w_{W}$

$S I (Z) = 60 w_{A} + 50 w_{W} + 90 (1 - w_{A} - w_{W}) = 90 - 30 w_{A} - 40 w_{W}$

Step 2: Apply Condition 1 ( $S I (X) > S I (Y)$ ).

$40 + 40 w_{A} + 20 w_{W} > 70 - 20 w_{A} + 10 w_{W}$

$60 w_{A} + 10 w_{W} > 30 ⟹ 6 w_{A} + w_{W} > 3$ (Ineq 1)

Step 3: Apply Condition 2 ( $S I (Y) > S I (Z)$ ).

$70 - 20 w_{A} + 10 w_{W} > 90 - 30 w_{A} - 40 w_{W}$

$10 w_{A} + 50 w_{W} > 20 ⟹ w_{A} + 5 w_{W} > 2$ (Ineq 2)

Step 4: Test the options against the feasible region defined by Ineq 1, Ineq 2, and $w_{A} + w_{W} < 1$ .

Option C claims $w_{S} < 0.25$ , which means $w_{A} + w_{W} > 0.75$ .

Let's find the minimum possible value of $w_{A} + w_{W}$ in the feasible region.

The vertices of the region formed by $6 w_{A} + w_{W} > 3$ , $w_{A} + 5 w_{W} > 2$ , and $w_{A} + w_{W} < 1$ are approximately:

V1 (Intersection of 1 & 3): $w_{A} = 0.4, w_{W} = 0.6 ⟹ S u m = 1.0$

V2 (Intersection of 2 & 3): $w_{A} = 0.75, w_{W} = 0.25 ⟹ S u m = 1.0$

V3 (Intersection of 1 & 2): $6 w_{A} + w_{W} = 3$ and $w_{A} + 5 w_{W} = 2$ .

Multiply second by 6: $6 w_{A} + 30 w_{W} = 12$ . Subtract first: $29 w_{W} = 9 ⟹ w_{W} = 9/29 \approx 0.31$ .

$w_{A} = 2 - 5 (9/29) = 13/29 \approx 0.448$ .

Sum at V3 = $22/29 \approx 0.758$ .

Since the minimum sum in the entire feasible region is $\approx 0.758$ , it is strictly greater than $0.75$ .

Therefore, $w_{A} + w_{W} > 0.75$ is necessarily true, which means $w_{S} < 0.25$ is necessarily true.

Answer: $w_{S} < 0.25$

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Charts, Graphs and Visual Data Interpretation Short Notes for CAT: Concepts, Formulas, Worked Examples & Practice

Charts, Graphs and Visual Data Interpretation short notes for CAT: 5 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice q

A question from this chapter

Question 1

Four companies (Alpha, Beta, Gamma, Delta) reported their Revenue and Cost (in Rs. crores) for the years 2022 and 2023. Profit is defined as Revenue minus Cost. The following facts are known: The total profit of the four companies was exactly 100 in 2022 and 120 in 2023. For each company, the Profit in 2022 was an even integer, and the Profit in 2023 was an odd integer. For each company, the Profit strictly increased from 2022 to 2023. The absolute increase in Profit (Profit_{2023} - Profit_{2022}) was a distinct positive integer for all four companies. Which of the following statements is/are NECESSARILY true? i. The minimum absolute increase in Profit among the four companies was exactly 1 . ii. The maximum absolute increase in Profit among the four companies was at least 9 . iii. The sum of the absolute increases of the two companies with the highest increases was exactly 16 .

Question 2

The Sustainability Index (SI) for three cities (X, Y, Z) is calculated using three parameters: Air (A), Water (W), and Soil (S). Scores for each parameter are integers from 0 to 100. The weights assigned to these parameters are w_{A}, w_{W}, w_{S} such that w_{A} + w_{W} + w_{S} = 1, and all weights are strictly positive. The parameter scores for the cities are: City X: A = 80, W = 60, S = 40 City Y: A = 50, W = 80, S = 70 City Z: A = 60, W = 50, S = 90 It is known that S I (X) > S I (Y) and S I (Y) > S I (Z) . Which of the following statements is NECESSARILY TRUE?

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