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Tables and Structured Data Notes for GATE CS

Tables and Structured Data notes for GATE CS: 12 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

tables and structured data notes

Chapter Roadmap: Data Interpretation — Tables and Structured Data

@keyframes fadeInUp { from { opacity: 0; transform: translateY(10px); } to { opacity: 1; transform: translateY(0); } } .roadmap-item { animation: fadeInUp 0.6s ease-out forwards; opacity: 0; } .roadmap-item:nth-child(1) { animation-delay: 0.1s; } .roadmap-item:nth-child(2) { animation-delay: 0.3s; } .roadmap-item:nth-child(3) { animation-delay: 0.5s; } Chapter Roadmap: Tables and Structured Data Topic 1: Commercial Tables and Percentage Calculations Master cost price, selling price, marked price, profit and loss percentages, and discounts within tabular formats. Learn to handle missing values using ratios and basic algebra. Weightage Hint: Foundational and High Frequency Topic 2: Recurrence Patterns in Tabular Data Identify arithmetic, geometric, or other logical sequences within rows and columns. Predict missing values based on observed patterns. Weightage Hint: Logical Reasoning Focus By the end of this chapter, you will be able to: Extract and compute financial metrics from complex tables. Solve for missing entries using proportional reasoning. Detect and extend numerical patterns in structured data.

The Anatomy of a Commercial Table

@keyframes highlightTerm { 0% { background-color: transparent; } 50% { background-color: color-mix(in srgb, var(--color-primary) 20%, transparent); } 100% { background-color: transparent; } } .term-highlight { animation: highlightTerm 2s ease-in-out infinite alternate; border-radius: 4px; padding: 0 4px; } The Anatomy of a Commercial Table Commercial tables organize transactional data. Each row represents an item or entity, and columns represent financial attributes. Key Terms Cost Price (CP): The original purchase price. Selling Price (SP): The final price at which the item is sold. Marked Price (MP): The price tagged on the item before any discount. Profit: S P - C P (when S P > C P) Loss: C P - S P (when C P > S P) Discount: M P - S P Core Relationships S P = C P + Profit S P = M P - Discount Profit % = \frac{Profit}{C P} \times 100 Discount % = \frac{Discount}{M P} \times 100 In exam questions, not all values are provided. You must use these relationships to find missing entries.

Solving for Missing Values Using Ratios

@keyframes revealStep { from { opacity: 0; transform: translateX(-10px); } to { opacity: 1; transform: translateX(0); } } .step { animation: revealStep 0.5s ease-out forwards; opacity: 0; } .step:nth-child(1) { animation-delay: 0.1s; } .step:nth-child(2) { animation-delay: 0.3s; } .step:nth-child(3) { animation-delay: 0.5s; } .step:nth-child(4) { animation-delay: 0.7s; } .step:nth-child(5) { animation-delay: 0.9s; } Solving for Missing Values Using Ratios When direct values are missing but ratios are given, introduce a proportionality constant. Step-by-Step Method Identify the Ratio: Look for statements like "Ratio of CP of A to B is m:n". Assign Variables: Let C P_{A} = m x and C P_{B} = n x . Use Other Data: Apply profit, loss, or discount formulas to create an equation involving x . Solve for x: Calculate the value of x . Compute Actual Values: Substitute x back to find the required CP, SP, or MP. Example Logic If C P_{P} : C P_{Q} = 3 : 4, then: C P_{P} = 3 x C P_{Q} = 4 x If Profit % for Q is given, use: S P_{Q} = C P_{Q} (1 + \frac{Profit %}{100}) And since S P_{Q} = M P_{Q} - Discount_{Q}, you can link everything together.

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Question 1

Level 1: Warm-up

An item has a fixed Selling Price of ₹500. Which of the following Marked Prices yields the minimum non-negative Discount Percentage, assuming the standard constraint M P \geq S P is strictly enforced?

Question 2

Level 1: Warm-up

According to the Rule of Three in the Pattern Hunting Checklist, which of the following pattern confirmations is impossible to be considered valid?

Question 3

Level 1: Warm-up

An item has a Selling Price of ₹400. What is the minimum Marked Price such that the Discount Percentage is at least 20%?

Question 4

Level 1: Warm-up

Consider the formula Discount = M P - S P . Which of the following statements is true if a commercial table provides Marked Price (MP) in ₹ and Selling Price (SP) in paise?

Question 5

Level 1: Warm-up

A table shows values where x is in meters and y is in centimeters: | x | y | |---|---| | 1 | 100 | | 2 | 200 | | 3 | 300 | Which statement is true?

Question 6

Level 1: Warm-up

Consider the following two statements: Assertion (A): To find the total profit percentage of two items, we can simply add their individual profit percentages. Reason (R): Profit percentage is calculated on the Cost Price, which differs for each item. Which of the following options is correct?

Question 7

Level 1: Warm-up

Consider the following two statements: Assertion (A): If a table has the pattern Row 3 = Row 1 + Row 2, then each element in Row 3 is the sum of the corresponding elements in Row 1 and Row 2. Reason (R): The total sum of Row 3 equals the sum of totals of Row 1 and Row 2, so each element must also follow the same pattern. Which option is correct?

Question 8

Level 1: Warm-up

Estimate how many of the following row sequences in a table are Geometric Progressions? I. 2, 4, 8, 16 II. 3, 9, 27, 81 III. 5, 10, 15, 20 IV. 1, 5, 25, 125

Question 9

Level 2: Moderate

In the table below, the three entries in every row form an increasing arithmetic progression from left to right. In each column, the entry in Row 3 is the sum of the entries in Row 1 and Row 2. All entries are positive integers. R_{1} R_{2} R_{3} C_{1} - - 9 C_{2} - 7 - C_{3} 11 - x What is the minimum possible value of x ?

Question 10

Level 2: Moderate

An item has a Cost Price of ₹800. A shopkeeper wants to earn a profit of exactly 20% and offer a discount of at least 20%. What is the minimum Marked Price he must set, and is a Marked Price of ₹1000 sufficient to satisfy both conditions?

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Tables and Structured Data Notes for GATE CS

Tables and Structured Data notes for GATE CS: 12 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Chapter Roadmap: Data Interpretation — Tables and Structured Data

Chapter Roadmap: Tables and Structured Data

Topic 1: Commercial Tables and Percentage Calculations

Master cost price, selling price, marked price, profit and loss percentages, and discounts within tabular formats. Learn to handle missing values using ratios and basic algebra.

Weightage Hint: Foundational and High Frequency

Topic 2: Recurrence Patterns in Tabular Data

Identify arithmetic, geometric, or other logical sequences within rows and columns. Predict missing values based on observed patterns.

Weightage Hint: Logical Reasoning Focus

By the end of this chapter, you will be able to:

Extract and compute financial metrics from complex tables.
Solve for missing entries using proportional reasoning.
Detect and extend numerical patterns in structured data.

The Anatomy of a Commercial Table

Commercial tables organize transactional data. Each row represents an item or entity, and columns represent financial attributes.

Key Terms

Cost Price (CP): The original purchase price.
Selling Price (SP): The final price at which the item is sold.
Marked Price (MP): The price tagged on the item before any discount.
Profit: $S P - C P$ (when $S P > C P$ )
Loss: $C P - S P$ (when $C P > S P$ )
Discount: $M P - S P$

Core Relationships

S P = C P + Profit

S P = M P - Discount

Profit % = \frac{Profit}{C P} \times 100

Discount % = \frac{Discount}{M P} \times 100

In exam questions, not all values are provided. You must use these relationships to find missing entries.

Solving for Missing Values Using Ratios

When direct values are missing but ratios are given, introduce a proportionality constant.

Step-by-Step Method

Identify the Ratio: Look for statements like "Ratio of CP of A to B is m:n".
Assign Variables: Let $C P_{A} = m x$ and $C P_{B} = n x$ .
Use Other Data: Apply profit, loss, or discount formulas to create an equation involving $x$ .
Solve for x: Calculate the value of $x$ .
Compute Actual Values: Substitute $x$ back to find the required CP, SP, or MP.

Example Logic

If $C P_{P} : C P_{Q} = 3 : 4$ , then:

$C P_{P} = 3 x$
$C P_{Q} = 4 x$

If Profit % for Q is given, use:

S P_{Q} = C P_{Q} (1 + \frac{Profit %}{100})

And since $S P_{Q} = M P_{Q} - Discount_{Q}$ , you can link everything together.

Worked Example: Finding Cost Price from Ratio and Marked Price

Problem Statement

Items	Cost (₹)	Profit %	Marked Price (₹)
P	5,400	---	5,860
Q	---	25	10,000

The ratio of cost of item P to cost of item Q is 3:4. Find the discount offered on item Q.

Solution

Find CP of Q using the ratio:
$C P_{P} : C P_{Q} = 3 : 4$
Given $C P_{P} = 5400$ :
$3 x = 5400 ⟹ x = 1800$
$C P_{Q} = 4 x = 4 \times 1800 = 7200$
Calculate SP of Q using Profit %:
$Profit % = 25%$
$S P_{Q} = C P_{Q} (1 + \frac{25}{100}) = 7200 \times 1.25$
$S P_{Q} = 9000$
Calculate Discount on Q:
$Discount = M P_{Q} - S P_{Q}$
$Discount = 10000 - 9000 = 1000$

Answer: The discount offered on item Q is ₹1000.

Tables and Structured Data: Solved Questions with Step-by-Step Explanations (10 Problems)

Question 1 · Quantitative Aptitude MCQ

An item has a fixed Selling Price of ₹500. Which of the following Marked Prices yields the minimum non-negative Discount Percentage, assuming the standard constraint $M P \geq S P$ is strictly enforced?

A.
₹450
B.
₹550
C.
₹500
D.
₹600

Correct Answer:

Step-by-Step Solution

Key idea: The constraint $M P \geq S P$ ensures that the Discount Percentage is non-negative.

Step 1: Recall the formula for Discount Percentage: $Discount % = \frac{M P - S P}{M P} \times 100$ .

Step 2: To minimize the non-negative discount, we need $M P - S P$ to be as small as possible, which means $M P$ should be as close to $S P$ as possible.

Step 3: Given the constraint $M P \geq S P$ , the minimum valid value for $M P$ is exactly $S P$ , i.e., $M P = 500$ .

Step 4: If $M P = 500$ , then $Discount % = \frac{500 - 500}{500} \times 100 = 0%$ .

Answer: ₹500

Question 2 · Quantitative Aptitude MCQ

According to the Rule of Three in the Pattern Hunting Checklist, which of the following pattern confirmations is impossible to be considered valid?

A.
A pattern verified across three known data points.
B.
A pattern assumed from only two known data points.
C.
A pattern verified by checking both row and column differences.
D.
A pattern verified by testing inter-row operations.

Correct Answer:

Step-by-Step Solution

Key idea: The Rule of Three prevents the "two-point illusion".

Step 1: Recall the Rule of Three from the Pattern Hunting Checklist. It states that a pattern must be verified across at least three known data points to be considered valid.

Step 2: Evaluate the options.

Step 3: Option A describes verifying across three points, which is valid.

Step 4: Option B describes assuming a pattern from only two points. This violates the Rule of Three and is therefore impossible to be considered valid.

Step 5: Options C and D describe valid verification methods (checking multiple directions or inter-row operations).

Answer: A pattern assumed from only two known data points.

Question 3 · Quantitative Aptitude MCQ

An item has a Selling Price of ₹400. What is the minimum Marked Price such that the Discount Percentage is at least 20%?

A.
₹480
B.
₹500
C.
₹520
D.
₹400

Correct Answer:

Step-by-Step Solution

Key idea: This is a constraint-based minimum problem. The Discount Percentage formula uses Marked Price as the base, not Selling Price.

Step 1: Write the Discount Percentage formula: $Discount % = \frac{M P - S P}{M P} \times 100$ .

Step 2: Apply the constraint: $\frac{M P - 400}{M P} \times 100 \geq 20$ .

Step 3: Simplify: $\frac{M P - 400}{M P} \geq 0.2$ .

Step 4: Multiply both sides by MP (positive): $M P - 400 \geq 0.2 \times M P$ .

Step 5: Rearrange: $M P - 0.2 \times M P \geq 400$ .

Step 6: Factor: $0.8 \times M P \geq 400$ .

Step 7: Solve: $M P \geq \frac{400}{0.8} = 500$ .

Step 8: The minimum Marked Price is ₹500.

Answer: ₹500

Question 4 · Quantitative Aptitude MCQ

Consider the formula $Discount = M P - S P$ . Which of the following statements is true if a commercial table provides Marked Price (MP) in ₹ and Selling Price (SP) in paise?

A.
The formula can be applied directly to find Discount in ₹.
B.
SP must be converted to ₹ before applying the formula to avoid unit mismatch.
C.
The formula will automatically yield the correct Discount in paise.
D.
Discount % will be unaffected by the unit mismatch.

Correct Answer:

Step-by-Step Solution

Key idea: Subtraction requires both operands to be in the same unit.

Step 1: The formula $Discount = M P - S P$ involves subtracting SP from MP.

Step 2: If MP is in ₹ and SP is in paise, they are in different units. Direct subtraction will yield a meaningless number.

Step 3: To avoid unit mismatch, SP must be converted to ₹ (or MP to paise) before applying the formula.

Step 4: Converting SP to ₹ is the standard and most straightforward approach.

Answer: SP must be converted to ₹ before applying the formula to avoid unit mismatch.

Question 5 · Quantitative Aptitude MCQ

A table shows values where x is in meters and y is in centimeters:
| x | y |
|---|---|
| 1 | 100 |
| 2 | 200 |
| 3 | 300 |
Which statement is true?

A.
y = 100x is the pattern, and it correctly handles the unit conversion.
B.
y = x + 99 is the pattern, verified by three data points.
C.
The pattern cannot be determined because units are mismatched.
D.
y = 100x is the pattern, but x must first be converted to centimeters.

Correct Answer:

Step-by-Step Solution

Key idea: This is a pattern detection problem with unit awareness. The pattern itself can encode the unit conversion.

Step 1: Examine the data: x = 1, y = 100; x = 2, y = 200; x = 3, y = 300.

Step 2: Check for multiplicative pattern: y/x = 100/1 = 100, 200/2 = 100, 300/3 = 100. Constant ratio of 100.

Step 3: The pattern is y = 100x.

Step 4: Verify unit consistency: x is in meters, y is in centimeters. Since 1 meter = 100 centimeters, the pattern y = 100x correctly converts meters to centimeters.

Step 5: The pattern y = 100x inherently handles the unit conversion without needing a separate conversion step.

Answer: y = 100x is the pattern, and it correctly handles the unit conversion.

Question 6 · Quantitative Aptitude MCQ

Consider the following two statements:
Assertion (A): To find the total profit percentage of two items, we can simply add their individual profit percentages.
Reason (R): Profit percentage is calculated on the Cost Price, which differs for each item.
Which of the following options is correct?

A.
Both A and R are true and R is the correct explanation.
B.
Both A and R are true but R is not the correct explanation.
C.
A is false but R is true.
D.
A is true but R is false.

Correct Answer:

Step-by-Step Solution

Key idea: Profit percentage is a ratio relative to the Cost Price, not an absolute value.

Step 1: Evaluate Assertion (A). Profit % = (Profit / CP) * 100. Since CP is different for each item, adding the percentages does not give the total profit percentage. The total profit % must be calculated using total profit and total CP. Thus, A is false.

Step 2: Evaluate Reason (R). The formula for profit percentage explicitly uses Cost Price as the base. Since different items have different Cost Prices, R is true.

Step 3: Since A is false and R is true, the correct option is "A is false but R is true".

Answer: A is false but R is true.

Question 7 · Quantitative Aptitude MCQ

Consider the following two statements:
Assertion (A): If a table has the pattern Row 3 = Row 1 + Row 2, then each element in Row 3 is the sum of the corresponding elements in Row 1 and Row 2.
Reason (R): The total sum of Row 3 equals the sum of totals of Row 1 and Row 2, so each element must also follow the same pattern.
Which option is correct?

A.
Both A and R are true and R is the correct explanation.
B.
Both A and R are true but R is not the correct explanation.
C.
A is true but R is false.
D.
A is false but R is true.

Correct Answer:

Step-by-Step Solution

Key idea: This is an assertion-reason problem testing the difference between element-wise patterns and aggregate properties.

Step 1: Evaluate Assertion (A). The statement "Row 3 = Row 1 + Row 2" means each element in Row 3 is the sum of corresponding elements: $R 3_{i} = R 1_{i} + R 2_{i}$ . This is true by definition.

Step 2: Evaluate Reason (R). The statement claims that because the total sums match ( $\sum R 3 = \sum R 1 + \sum R 2$ ), each element must follow the pattern. This is false.

Step 3: The aggregate property (sum of totals) does not imply the element-wise property. For example:

Row 1: 1, 2, 3 (sum = 6)
Row 2: 4, 5, 6 (sum = 15)
Row 3: 5, 7, 9 (sum = 21 = 6 + 15)
Here, Row 3 = Row 1 + Row 2 element-wise.
But consider: Row 3': 6, 6, 9 (sum = 21 = 6 + 15)
The totals match, but Row 3' ≠ Row 1 + Row 2 element-wise.

Step 4: This is the aggregate fallacy (overcounting): assuming that because the aggregate follows a pattern, each individual element must also follow it.

Step 5: A is true, R is false.

Answer: A is true but R is false.

Question 8 · Quantitative Aptitude MCQ

Estimate how many of the following row sequences in a table are Geometric Progressions?
I. 2, 4, 8, 16
II. 3, 9, 27, 81
III. 5, 10, 15, 20
IV. 1, 5, 25, 125

A.
1
B.
2
C.
3
D.
4

Correct Answer:

Step-by-Step Solution

Key idea: A Geometric Progression (GP) has a constant ratio between consecutive terms.

Step 1: Test Sequence I: 2, 4, 8, 16. Ratios: 4/2 = 2, 8/4 = 2, 16/8 = 2. Constant ratio. It is a GP.

Step 2: Test Sequence II: 3, 9, 27, 81. Ratios: 9/3 = 3, 27/9 = 3, 81/27 = 3. Constant ratio. It is a GP.

Step 3: Test Sequence III: 5, 10, 15, 20. Ratios: 10/5 = 2, 15/10 = 1.5. Not constant. (It is an AP with common difference 5). Not a GP.

Step 4: Test Sequence IV: 1, 5, 25, 125. Ratios: 5/1 = 5, 25/5 = 5, 125/25 = 5. Constant ratio. It is a GP.

Step 5: Count the GPs: I, II, and IV. There are 3 GPs.

Answer: 3

Question 9 · Quantitative Aptitude MCQ

In the table below, the three entries in every row form an increasing arithmetic progression from left to right. In each column, the entry in Row 3 is the sum of the entries in Row 1 and Row 2. All entries are positive integers.

$R_{1} R_{2} R_{3} C_{1} - - 9 C_{2} - 7 - C_{3} 11 - x$

What is the minimum possible value of $x$ ?

A.
17
B.
18
C.
19
D.
21

Correct Answer:

Step-by-Step Solution

Key idea: this is a constrained table-completion problem. Do not fill a blank from two visible neighbours; translate the row-wise AP condition and the column-wise sum condition into equations, then apply the increasing/integer constraints.

Step 1: Let the first entry of Row 1 be $a$ . Since Row 1 is an integer AP ending at $11$ , its middle entry is $\frac{a + 11}{2}$ . Hence $a$ must be odd.

Step 2: Let the first entry of Row 2 be $b$ . Its middle entry is $7$ , so its third entry is $14 - b$ because in an AP the middle term is the average of the first and third terms.

Step 3: Column 1 gives the additive condition:

$a + b = 9 ⟹ b = 9 - a .$

Therefore Row 2’s third entry is

$14 - (9 - a) = 5 + a .$

Step 4: Column 3 gives

$x = 11 + (5 + a) = 16 + a .$

Step 5: Apply the hidden constraints. Row 2 must be increasing:

$b < 7 ⟹ 9 - a < 7 ⟹ a > 2.$

Also $b > 0$ , so $a < 9$ . Since $a$ is a positive odd integer, $a \in {3, 5, 7}$ .

Step 6: Minimise $x = 16 + a$ by taking $a = 3$ :

$x = 16 + 3 = 19.$

Verification: for $a = 3$ , the completed rows are $3, 7, 11$ ; $6, 7, 8$ ; $9, 14, 19$ , which satisfy all conditions.

Answer: $19$ .

Question 10 · Quantitative Aptitude MCQ

An item has a Cost Price of ₹800. A shopkeeper wants to earn a profit of exactly 20% and offer a discount of at least 20%. What is the minimum Marked Price he must set, and is a Marked Price of ₹1000 sufficient to satisfy both conditions?

A.
₹1152, Yes
B.
₹1200, No
C.
₹1000, No
D.
₹1200, Yes

Correct Answer:

Step-by-Step Solution

Key idea: This is a constraint-based minimum problem where two conditions (exact profit and minimum discount) must be satisfied simultaneously. The discount is calculated on the Marked Price, not the Selling Price.

Step 1: Calculate the required Selling Price for exactly 20% profit.

$S P = C P \times (1 + \frac{20}{100}) = 800 \times 1.2 = 960$ .

Step 2: Apply the discount constraint. The discount must be at least 20%, so the Selling Price can be at most 80% of the Marked Price.

$S P \leq M P \times (1 - \frac{20}{100})$

$960 \leq M P \times 0.8$

Step 3: Solve for the minimum Marked Price.

$M P \geq \frac{960}{0.8} = 1200$ .

The minimum Marked Price is ₹1200.

Step 4: Check if ₹1000 is sufficient. Since $1000 < 1200$ , it is not sufficient to meet both conditions.

Answer: ₹1200, No

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