This page covers IBPS RRB PO Data Sufficiency — Maths with complete concept notes, 12 graded practice MCQs, key points and exam-specific tips. Free to study.
Core ConceptRead 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.
Exam PatternsWhat 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.
ShortcutsUse 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.
Worked ExampleSolve 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.
Exam TrapsCommon mistakes students make — avoid these
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
Is the number x divisible by 12?
Statement I: x is divisible by 3 and x is divisible by 4.
Statement II: x is divisible by 2 and x is divisible by 6.
Practice 2easy
What is the simple interest earned on a principal amount?
Statement I: The principal is Rs. 5,000 and the rate of interest is 8% per annum.
Statement II: The time period is 3 years.
Practice 3easy
What is the cost price of an item if its selling price is Rs. 1,200?
Statement I: The profit percentage is 20%.
Statement II: The profit amount is Rs. 200.
Practice 4easy
How many students passed the exam in a class?
Statement I: There are 50 students in the class.
Statement II: 70% of the students passed the exam.
Practice 5easy
What is the average age of three friends A, B, and C?
Statement I: A's age is 24 years and B's age is 26 years.
Statement II: The sum of all three ages is 75 years.
Practice 6medium
What is the cost price of a shirt?
Statement I: The shirt is sold at a profit of 25%, and the selling price is ₹500.
Statement II: The cost price of the shirt is ₹100 less than the selling price.
Practice 7medium
What is the average age of three friends A, B, and C?
Statement I: A's age is 5 years more than B's age, and B's age is 3 years more than C's age.
Statement II: The sum of A's and C's ages is 40 years.
Practice 8medium
A shopkeeper sells two types of items: pens and notebooks. The cost price of a pen is Rs. 5 and the cost price of a notebook is Rs. 8. The shopkeeper sells pens at a profit of P% and notebooks at a profit of Q%. On a particular day, the shopkeeper sold a total of 100 items and made a total profit of Rs. 240.
Statement I: The shopkeeper sold 60 pens and 40 notebooks.
Statement II: The average profit per item sold was Rs. 2.40.
Which of the following statements is/are sufficient to find the individual profit percentages P and Q?
A) Statement I alone is sufficient, but Statement II alone is not sufficient.
B) Statement II alone is sufficient, but Statement I alone is not sufficient.
C) Both statements together are sufficient, but neither alone is sufficient.
D) Neither statement alone nor both together are sufficient.
Practice 9hard
A container has a mixture of milk and water. The ratio of milk to water is m:w. The container is filled to capacity V liters.
Statement I: The container has 15 liters of milk and 10 liters of water.
Statement II: The ratio of milk to water is 3:2, and the container's capacity is 25 liters.
Can we determine the ratio m:w and the volume of milk in the container?
(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 10hard
A rectangular tank has length L, width W, and height H (all in meters). Water is filled to a height h meters. A pipe fills the tank at rate r cubic meters per hour, and a drain empties it at rate d cubic meters per hour.
Statement I: The tank's volume is 120 cubic meters, and the net filling rate is 2 cubic meters per hour.
Statement II: The current water volume is 60 cubic meters, and it will take 30 hours to fill the tank completely.
Can we determine the individual values of r and d?
(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 11hard
A company has two projects, X and Y. The profit from project X is p% of its investment, and the profit from project Y is q% of its investment. The total investment is Rs. 10 lakhs.
Statement I: The profit from project X is Rs. 2 lakhs, and the profit from project Y is Rs. 1.5 lakhs.
Statement II: The investment in project X is Rs. 5 lakhs, and the investment in project Y is Rs. 5 lakhs.
Can we determine the individual values of p and q?
(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 12hard
A train travels from City P to City Q. The distance is d kilometers. The train travels the first half of the distance at speed s₁ km/hr and the second half at speed s₂ km/hr.
Statement I: The average speed for the entire journey is 48 km/hr, and s₁ = 40 km/hr.
Statement II: The time taken for the first half is 2.5 hours, and the time taken for the second half is 3 hours.
Can we determine the value of s₂?
(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
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