Study Material — 5 PYQs (2023–2023) · Concept Notes · Shortcuts
SSC MTS Data Sufficiency — Maths is a frequently tested subtopic — 5 previous year questions from 2023–2023 papers are included below with concept notes, key rules and shortcut tricks.
Is x greater than 10?
Statement I: x + 5 = 18.
Statement II: x - 3 > 7.
Exam Q 32023Previous Year Pattern
A shopkeeper sells pens at a profit. What is the profit percentage?
Statement I: The cost price of each pen is ₹5.
Statement II: The selling price of each pen is ₹7.
Exam Q 42023Previous Year Pattern
What is the average of five consecutive even numbers?
Statement I: The smallest number is 12.
Statement II: The largest number is 20.
Exam Q 52023Previous Year Pattern
How many students passed the exam?
Statement I: 60% of the students passed.
Statement II: 120 students failed the exam.
Concept Notes
Data Sufficiency — Maths— Rules & Concept
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Core Concept
Read this first — the foundation of the topic
→Core Concept
Data Sufficiency questions give you a problem followed by two statements (I and II). Your job is to determine which statement(s) provide enough information to solve the problem
→You have 5 standard answer choices
(A) Statement I alone is sufficient, (B) Statement II alone is sufficient, (C) Both statements together are sufficient, (D) Each statement alone is sufficient, (E) Both statements together are insufficient
💡Key Rules
First, read the question carefully and identify what you need to find. Then examine each statement separately. Check if Statement I alone gives enough data. Next, check if Statement II alone gives enough data.
If neither works alone, see if combining both statements helps. Remember, you're not calculating the final answer - just checking if calculation is possible.
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Exam Patterns
What examiners ask — read before attempting PYQs
SSC CGL regularly tests data sufficiency with topics like ages, profit-loss, time-work, geometry, and averages. Common question types include finding unknown values, comparing quantities, or determining relationships between variables. Most questions follow the standard 5-option format.
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Shortcuts
Use these to save 30–60 seconds per question
Use the 'Elimination Method'. Start by checking if each statement individually has enough unique information. If Statement I gives multiple possible answers, it's insufficient.
If Statement II also gives multiple answers, check if combining both narrows it to one answer. This saves time over detailed calculations.
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Worked Example
Solve this step-by-step before moving on
1
Step 1
Identify what we need - Rahul's exact age.
2
Step 2
Check Statement I alone. 'Rahul is 5 years older than Priya' gives us R = P + 5, but we don't know P's value. This creates infinite possibilities. Statement I alone is insufficient.
3
Step 3
Check Statement II alone. 'Sum of ages is 35' gives us R + P = 35, but we don't know individual ages. Statement II alone is insufficient.
4
Step 4
Check both together. From I: R = P + 5. From II: R + P = 35. Substituting: (P + 5) + P = 35, so 2P = 30, P = 15, R = 20. Both statements together give unique answer.
Answer: (C) Both statements together are sufficient.
Common Mistake: Students often start calculating the complete answer instead of just checking sufficiency. Another trap is assuming additional information not given in statements. Stick only to provided data.
Key Points to Remember
Data sufficiency checks if given information can solve the problem, not the actual solution
Standard format has 5 answer choices about statement sufficiency combinations
Always test each statement individually before combining them
Insufficient means multiple answers are possible from given data
Sufficient means exactly one unique answer can be determined
Don't assume any information not explicitly stated in the statements
If both statements give same conclusion separately, answer is 'Each statement alone sufficient'
Focus on whether calculation is possible, not on doing the complete calculation
Exam-Specific Tips
SSC CGL typically includes 2-3 data sufficiency questions per paper
Standard answer format: (A) I alone, (B) II alone, (C) Both together, (D) Each alone, (E) Both insufficient
Most common topics tested are ages, profit-loss, time-work, and simple equations
Questions usually provide exactly 2 statements labeled as Statement I and Statement II
Data sufficiency questions carry same marks as regular quantitative aptitude questions
Time allocation should be 1-2 minutes per data sufficiency question
Geometry data sufficiency often involves finding area, perimeter, or angle measurements
Practice MCQs
Data Sufficiency — Maths — Practice Questions
12graded MCQs · easy to hard · full solution & trap analysis
What is the speed of a car?
Statement I: The car travels 150 km.
Statement II: The car travels for 3 hours.
Practice 2medium
A shopkeeper sells notebooks at ₹15 each. Statement I: He sold notebooks for a total of ₹450. Statement II: He made a profit of 20% on each notebook. What is the cost price of one notebook?
A) Statement I alone is sufficient
B) Statement II alone is sufficient
C) Both statements together are sufficient
D) Neither statement alone nor together is sufficient
Practice 3medium
A train travels from Station A to Station B. Statement I: The distance between A and B is 240 km. Statement II: The train takes 4 hours to travel from A to B. What is the average speed of the train?
A) Statement I alone is sufficient
B) Statement II alone is sufficient
C) Both statements together are sufficient
D) Neither statement alone nor together is sufficient
Practice 4medium
A person invests money in two schemes. Statement I: He invests ₹5,000 in Scheme A at 10% per annum simple interest. Statement II: He invests ₹3,000 in Scheme B at 8% per annum simple interest. What is the total interest earned after 2 years?
A) Statement I alone is sufficient
B) Statement II alone is sufficient
C) Both statements together are sufficient
D) Neither statement alone nor together is sufficient
Practice 5medium
A mixture contains milk and water. Statement I: The ratio of milk to water is 3:2. Statement II: The total quantity of the mixture is 50 liters. What is the quantity of milk in the mixture?
A) Statement I alone is sufficient
B) Statement II alone is sufficient
C) Both statements together are sufficient
D) Neither statement alone nor together is sufficient
Practice 6medium
A person's age is being determined. Statement I: The person's age is 5 years more than twice the age of their child. Statement II: The child's age is 10 years. What is the person's age?
A) Statement I alone is sufficient
B) Statement II alone is sufficient
C) Both statements together are sufficient
D) Neither statement alone nor together is sufficient
Practice 7hard
A rectangular tank has length L meters and width W meters. Water is filled to a height of h meters. The volume of water is 240 cubic meters.
Statement I: The perimeter of the base is 56 meters.
Statement II: The length is 4 meters more than the width, and the height is 3 meters.
Can we determine the exact dimensions (L, W, h) of the tank?
Practice 8hard
Two trains, A and B, start from the same station at the same time. Train A travels at a constant speed of x km/h and Train B travels at a constant speed of y km/h. After some time, Train A is 60 km ahead of Train B.
Statement I: Train A travels 15 km/h faster than Train B.
Statement II: The time elapsed is 4 hours.
Can we determine the individual speeds of trains A and B?
Practice 9hard
A shopkeeper has a mixture of two types of tea: Type X and Type Y. The cost price of Type X is ₹a per kg and Type Y is ₹b per kg. He mixes them in a certain ratio and sells the mixture at ₹150 per kg, making a profit of 25%.
Statement I: Type X costs ₹80 per kg and Type Y costs ₹120 per kg.
Statement II: The ratio of Type X to Type Y in the mixture is 3:2.
Can we determine the cost price of the mixture per kg?
Practice 10hard
A quadrilateral ABCD has sides AB, BC, CD, and DA. The perimeter is 60 meters. The quadrilateral is divided into two triangles by diagonal AC.
Statement I: Triangle ABC has sides AB = 12 m, BC = 16 m, and AC = 20 m. Triangle ACD has sides AC = 20 m, CD = 10 m, and DA = 8 m.
Statement II: The quadrilateral is a cyclic quadrilateral (inscribed in a circle).
Can we determine the area of quadrilateral ABCD?
Practice 11hard
A shopkeeper sells two types of items. The cost price of item A is ₹x per unit and item B is ₹y per unit. He sells item A at 20% profit and item B at 15% loss. In a particular transaction, he sold 5 units of A and 3 units of B for a total of ₹2,150.
Statement I: The cost price of item A is ₹200 per unit.
Statement II: The total cost price of all items sold is ₹1,900.
Is the data sufficient to find the individual cost prices of items A and B?
Practice 12hard
A person invests a sum of money in two schemes: Scheme P offers simple interest at r₁% per annum, and Scheme Q offers simple interest at r₂% per annum. The person invests ₹x in Scheme P and ₹y in Scheme Q for 2 years. The total interest earned is ₹4,800.
Statement I: The amount invested in Scheme P is ₹10,000 and in Scheme Q is ₹15,000.
Statement II: The interest rate of Scheme P is 12% per annum and Scheme Q is 16% per annum.
Can we determine the individual interest earned from each scheme?
60-Second Revision — Data Sufficiency — Maths
Remember: Check each statement individually first, then combine if needed
Trap: Don't calculate final answers, only check if calculation is possible
Formula: Sufficient = exactly one unique answer possible
Strategy: Use elimination method to save time on complex calculations
Warning: Never assume information not explicitly given in statements
Pattern: Most SSC questions test basic arithmetic and algebra concepts