This page covers SBI PO Data Sufficiency — Maths with complete concept notes, 14 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
14graded MCQs · easy to hard · full solution & trap analysis
What is the average age of three friends?
Statement I: The sum of ages of two friends is 48 years.
Statement II: The third friend is 6 years older than the average age of the first two friends.
Practice 2easy
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 3easy
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 4medium
A rectangular plot has length and width in a specific ratio. The perimeter of the plot is known to be 120 meters.
Statement I: The length is 20 meters more than the width.
Statement II: The ratio of length to width is 5:3.
What is the area of the rectangular plot?
Practice 5medium
A person invests money in two schemes: Scheme X (simple interest) and Scheme Y (compound interest). The principal amounts and rates are unknown.
Statement I: The principal in Scheme X is Rs. 5000 at 8% per annum for 3 years, and the principal in Scheme Y is Rs. 5000 at 8% per annum for 3 years (compounded annually).
Statement II: The difference between the compound interest and simple interest earned over 3 years is Rs. 98.56.
What is the total interest earned from both schemes combined?
Practice 6medium
A shopkeeper sells two types of items. The cost price of item A is Rs. 200 and item B is Rs. 300. He sells item A at a profit of 25% and item B at a loss of 10%. What is the total profit or loss percentage on the combined transaction?
Statement I: He sells 40 items of type A and 30 items of type B.
Statement II: The ratio of items sold is A:B = 4:3.
Which statement(s) is/are sufficient to answer the question?
Practice 7medium
A shopkeeper sells two types of items: notebooks and pens. The cost price of a notebook is Rs. 20 and the cost price of a pen is Rs. 5. He sells notebooks at a profit of P% and pens at a profit of Q%. In a particular transaction, he sells 15 notebooks and 40 pens for a total selling price of Rs. 525.
Statement I: The profit percentage on notebooks is 25%.
Statement II: The total profit earned on this transaction is Rs. 75.
Which statement(s) is/are sufficient to find the profit percentage on pens?
(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 8medium
A train travels from City X to City Y. The distance between the cities is unknown. The train travels at a constant speed for the entire journey.
Statement I: The train takes 5 hours to complete the journey and covers 80 km in the first hour.
Statement II: The train covers 320 km in the first 4 hours of the journey.
What is the total distance between City X and City Y?
Practice 9hard
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 25% profit and item B at 20% loss. In a particular transaction, he sells 40 units of A and 60 units of B, earning a net profit of ₹800.
Statement I: The cost price of item A is ₹100 per unit.
Statement II: The cost price of item B is ₹80 per unit.
Which statement(s) is/are sufficient to find the net profit percentage on the total transaction?
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 cylindrical tank has a base radius of r meters and height h meters. Water flows into the tank at a rate of A cubic meters per hour and flows out at a rate of B cubic meters per hour. The tank starts empty and reaches 75% capacity in exactly T hours.
Statement I: The radius is 2 meters, height is 5 meters, and the net inflow rate is 3 cubic meters per hour.
Statement II: The tank's volume is 60π cubic meters and the net inflow rate is 3 cubic meters per hour.
Which statement(s) is/are sufficient to determine the time T?
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 rectangular plot of land has length L meters and width W meters. A fence is built around the perimeter. The cost of fencing is ₹p per meter. Additionally, a diagonal path is laid across the plot at a cost of ₹q per meter. The total cost of fencing and the diagonal path is ₹12,000.
Statement I: The perimeter is 200 meters and the diagonal is 50√2 meters, with p = 40 and q = 60.
Statement II: The length is 60 meters, the width is 40 meters, and the total cost is ₹12,000.
Which statement(s) is/are sufficient to determine the individual costs of fencing and the diagonal path?
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 between P and Q is d kilometers. The train travels the first half of the distance at speed s₁ km/h and the second half at speed s₂ km/h. The average speed for the entire journey is 48 km/h.
Statement I: The first half is covered at 40 km/h and the second half at 60 km/h.
Statement II: The harmonic mean of the two speeds is 48 km/h.
Which statement(s) is/are sufficient to verify that the average speed is indeed 48 km/h?
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 13hard
A company manufactures two products: X and Y. The profit on product X is ₹m per unit and on product Y is ₹n per unit. In a given month, the company sells a units of X and b units of Y, generating a total profit of ₹50,000. The profit margin (profit as a percentage of cost price) on X is 25% and on Y is 20%.
Statement I: 25a + 20b = 50,000 and the cost price of X is ₹100 per unit.
Statement II: The selling price of X is ₹125 per unit and the selling price of Y is ₹120 per unit.
Which statement(s) is/are sufficient to determine the number of units of X sold (a)?
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 14hard
A shopkeeper sells two types of items: Type A and Type B. The profit margin on Type A is 25% and on Type B is 40%. Last month, the shopkeeper sold a total of 500 items and earned a total profit of ₹4,500.
Statement I: The cost price of Type A is ₹100 per item.
Statement II: The shopkeeper sold 200 items of Type B.
Which of the following is necessary to determine the number of Type A items sold?
(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) Both statements together are not sufficient to answer the question.
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