This page covers SSC CHSL Data Sufficiency โ Maths with complete concept notes, 25 graded practice MCQs, key points and exam-specific tips. Free to study.
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
โYou 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
๐กKey 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 โ 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 30โ60 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.
Test Data Sufficiency โ Maths under exam conditions
What is the value of y?
Statement I: 2y + 5 = 15
Statement II: y is a natural number less than 10.
(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 2easy
Is x a positive number?
Statement I: xยฒ = 25
Statement II: x > 0
(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 3easy
What is the area of a rectangle?
Statement I: The length of the rectangle is 12 cm.
Statement II: The perimeter of the rectangle is 40 cm.
(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 4easy
What is the cost price of an item?
Statement I: The selling price is โน500 and profit is 25%.
Statement II: The profit amount is โน100.
(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 5easy
What is the area of a rectangle?
Statement I: The length of the rectangle is 12 cm.
Statement II: The breadth of the rectangle is 8 cm.
(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 6easy
What is the average of three numbers?
Statement I: The sum of the three numbers is 45.
Statement II: The three numbers are consecutive integers.
(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 7easy
What is the price of one apple?
Statement I: 5 apples and 3 oranges cost โน110 together.
Statement II: 1 orange costs โน15.
Practice 8easy
What is the perimeter of a triangle?
Statement I: All three sides of the triangle are equal (equilateral triangle).
Statement II: Each side of the triangle is 6 cm.
(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 9medium
A train travels between two cities. The distance between the cities and the train's speed determine the travel time.
Statement I: The distance between the two cities is 480 kilometers, and the train travels at an average speed of 60 kilometers per hour.
Statement II: The train takes 8 hours to travel between the two cities.
Can we determine the average speed of the train?
Practice 10medium
A person invests money in two different schemes: Scheme A offers simple interest and Scheme B offers compound interest. The person invested a total of Rs. 50,000.
Statement I: Rs. 30,000 was invested in Scheme A at 8% per annum for 3 years, and Rs. 20,000 was invested in Scheme B at 10% per annum for 2 years (compounded annually).
Statement II: The total interest earned from both schemes combined is Rs. 9,200.
Can we determine the total amount (principal + interest) after the investment period?
Practice 11medium
A shopkeeper has apples and oranges in a basket. The total number of fruits and their individual prices determine the total value.
Statement I: There are 40 apples at Rs. 5 each and 60 oranges at Rs. 3 each in the basket.
Statement II: The total value of fruits in the basket is Rs. 380, and there are 100 fruits in total.
Can we determine the number of apples in the basket?
Practice 12medium
A rectangular tank has length, width, and height. Water is being filled into the tank at a constant rate.
Statement I: The tank's length is 10 meters, width is 8 meters, and height is 6 meters. Water is filled at 5 cubic meters per hour.
Statement II: The tank will be completely filled in 9.6 hours.
Can we determine the rate at which water is being filled?
Practice 13medium
A mixture contains milk and water. Statement I: The ratio of milk to water is 5:3. Statement II: If 8 liters of water is added, the ratio becomes 5:4. What is the original 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 14medium
A shopkeeper sells three types of items: A, B, and C. The cost price of A is Rs. 100. Statement I: The profit on A is 20% and the profit on B is 25%. Statement II: The selling price of B is Rs. 150. Is the cost price of B less than the cost price of 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 15medium
A train travels from Station X to Station Y. Statement I: The train travels at 60 km/h for the first half of the distance and 80 km/h for the second half. Statement II: The total distance between X and Y is 280 km. 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 16medium
A rectangular garden has a perimeter of P meters. Statement I: The length is 5 meters more than the width. Statement II: The area of the garden is 84 square meters. What is the perimeter of the garden?
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 17medium
A person invests money in two schemes: Scheme A and Scheme B. Statement I: The ratio of amounts invested in A to B is 3:2, and the total investment is Rs. 50,000. Statement II: Scheme A gives 8% annual interest and Scheme B gives 10% annual interest. What is the total annual interest earned?
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 18medium
A shopkeeper sells three types of items: pens, notebooks, and erasers. The cost price of a pen is Rs. 5, a notebook is Rs. 20, and an eraser is Rs. 2. In a particular transaction, the shopkeeper sold some items and made a profit of Rs. 100.
Statement I: The shopkeeper sold 10 pens, 5 notebooks, and 20 erasers at a markup of 40% on all items.
Statement II: The shopkeeper sold items with a total cost price of Rs. 500.
Is the given information sufficient to determine the profit made?
Practice 19hard
A man invests money in two schemes A and B. Scheme A offers compound interest at rate r% per annum, and Scheme B offers simple interest at rate s% per annum. After 2 years, the difference between the amounts is Rs. 480. What is the principal amount invested in Scheme A?
Statement I: The rate of interest in Scheme A is 20% per annum.
Statement II: The principal invested in Scheme A is twice the principal invested in Scheme B, and s = 10%.
Practice 20hard
A shopkeeper sells three types of items: X, Y, and Z. The cost price of X is Rs. 100. The shopkeeper makes a profit on X, a loss on Y, and breaks even on Z. What is the overall profit or loss percentage?
Statement I: The cost price of Y is Rs. 150, the cost price of Z is Rs. 200, and the profit on X is 20%.
Statement II: The selling price of X is Rs. 120, the selling price of Y is Rs. 120, and the selling price of Z is Rs. 200. The shopkeeper sells 2 units of X, 3 units of Y, and 1 unit of Z.
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