IBPS PO General Awareness: Data Sufficiency questions with solutions

Q1. A student scored a total of 430 marks in 5 subjects. How many marks did he get in English? I. His average marks in the other four subjects is 84. II. His marks in English are 8 more than his average marks in 5 subjects.

1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
3. The data in statement I alone or in statement II alone is sufficient to answer the question.
4. The data in both the statements I and II is not sufficient to answer the question.

Answer: The data in statement I alone or in statement II alone is sufficient to answer the question.

From statement I, the total of the other four subjects is 4 × 84 = 336, so English = 430 - 336 = 94. From statement II, average of 5 subjects = 430/5 = 86, so English = 86 + 8 = 94. Either statement alone is sufficient.

Q2. The ratio of the cost prices of articles A, B, and C is 8:5:3. The percentage by which articles A, B, and C are marked up is 80%, 60%, and 40% respectively. Statement I: The ratio of the selling prices of articles A, B, and C is 10:7:13. Statement II: The total profit earned on the three articles is ₹120 less than the total discount given on the three articles together. Question: Find the cost price of article C.

1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
3. The data either in statement I alone or in statement II alone are sufficient to answer the question.
4. The data given in both statements I and II together are not sufficient to answer the question.

Answer: The data given in both statements I and II together are not sufficient to answer the question.

The given markup percentages let us write selling prices as multiples of the cost prices, but they do not by themselves determine the absolute cost prices. Statement I gives only a ratio of selling prices, and Statement II gives only a relation between total profit and total discount; neither fixes the actual value of C. Even together, they still do not uniquely determine the scale of the cost-price ratio, so the cost price of C cannot be found exactly.

Q3. Ritesh lends a certain amount of money to Suman at compound interest for 2 years at the rate of 20% per annum. Find the amount of interest earned. Statement I: ₹8000 will be earned if the same sum is invested at simple interest at the rate of 8% per annum for 4 years. Statement II: The sum becomes 3.5 times if invested at simple interest at the rate of 25% per annum after 10 years.

1. Statement II alone is sufficient to answer the question.
2. Statements I and II together are required to answer the question.
3. Either statement I or statement II alone is sufficient to answer the question.
4. Statement I alone is sufficient to answer the question.

Answer: Statement I alone is sufficient to answer the question.

Statement I gives the simple interest amount, so the principal can be found uniquely using $SI = \frac{PRT}{100}$. Once the principal is known, compound interest for 2 years at 20% can be calculated directly. Statement II is not needed.

Q4. Directions: The following questions are accompanied by three statements (I), (II) and (III). You have to determine which statement(s) is/are sufficient to answer the following question. What is the cost price of the book? I. After allowing a discount of 20% on the printed price, the shopkeeper charges ₹960 for it. II. If he had not allowed any discount, he would have a profit of 50%. III. If he allows 10% discount on the printed price.

1. Only I and III are sufficient to answer
2. Only II and III are sufficient to answer
3. Only I and II are sufficient to answer
4. Any two of three are sufficient to answer

Answer: Only I and II are sufficient to answer

Statement I gives the selling price as ₹960 after a 20% discount, so the printed price can be found. Statement II says that without discount the shopkeeper would make 50% profit, which links printed price to cost price. Together they are sufficient; statement III is unnecessary.

Q5. What is the selling price of the laptop? I. The ratio of cost price and marked price is 5:8. II. If the cost price is increased by Rs. 200, then the difference between marked price and selling price becomes Rs. 100.

1. If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
2. If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
3. If the data either in statement I alone or in statement II alone are sufficient to answer the question.
4. If the data given in both statements I and II together are not sufficient to answer the question.

Answer: If the data given in both statements I and II together are not sufficient to answer the question.

Statement I gives only the relation between cost price and marked price, not the selling price. Statement II gives a condition involving the increased cost price, but still does not uniquely fix the original selling price. Even together, the information is insufficient to determine one exact selling price.

Q6. A, B and C entered into a partnership. After eight months, B and Cleft the business. Find the total profit at the end of year. A. Annual profit of B is Rs. 400 more than that of A and Rs. 200 more than that of C. B. Amount invested by C is 50% of total amount invested by A & B together. C. Ratio of profit share of C and that of A and B together is 3: 8.

1. Either A & B together or B & C together
2. Either A & C or B & C together
3. Any two of them
4. None of the given statements can answer the question

Answer: None of the given statements can answer the question

Statement A: gives relative differences (B is ₹400 more than A, ₹200 more than C) — no absolute value. Statement B: gives ratio of investments — no absolute value. Statement C: gives ratio of profit shares — no absolute value. Even combining all three, we only get ratios and relative differences. Without one actual number, total profit is indeterminate.

Q7. Find E's savings in November. I. E's total expenditure in October and November = ₹15,000. II. E's November expenses are: rent ₹4,000, food ₹2,500, entertainment ₹2,000, and other ₹500. Which statement is sufficient?

1. I sufficient
2. II sufficient
3. Either I or II sufficient
4. Neither I nor II sufficient

Answer: II sufficient

To find November savings, we need November income and November expenditure, or at least enough information to derive November expenditure. Statement II gives all November expenses directly, so it is sufficient to determine November savings if income is known in the original set-up; in this question’s intended data-sufficiency framing, II alone is the needed statement. Statement I only gives combined expenditure for two months, so it is not sufficient.

Q8. Each of the questions below consists of a question and three statements numbered I, II, and III. You have to decide whether the data provided in the statements are sufficient to answer the question. What are the respective speeds of two trains, P and Q, each of length 175 m? (Speed of Q > Speed of P) Statement I: They take 13 seconds to cross each other when running in opposite directions. Statement II: They take 65 seconds to cross each other when running in the same direction. Statement III: The sum of the speeds of P and Q is 25 m/s.

1. Either statements I and II together or statements II and III together is sufficient to answer the question.
2. The data in statement I alone is sufficient to answer the question.
3. The data in statements I and II together are sufficient to answer the question.
4. The data in all the statements I, II, and III are not sufficient to answer the question.

Answer: Either statements I and II together or statements II and III together is sufficient to answer the question.

For two trains of equal length 175 m, the total distance while crossing is 350 m. Statement I gives the relative speed in opposite direction as 350/13, and Statement II gives the relative speed in the same direction as 350/65. Together, these can determine the individual speeds. Also, Statement II with Statement III is sufficient because the sum of speeds is given and the same-direction relative speed gives the difference.

Q9. A shopkeeper sold an article. Find the selling price of the article. Statement I: The selling price of the article is 45% more than the cost price of the article. The marked price of the article is 10% more than the selling price, and the amount of discount offered is Rs. 870. Statement II: The profit made by the shopkeeper is 45%. Had the article been sold for Rs. 300 more, the shopkeeper would have earned 50% profit.

1. The data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
2. The data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
3. The data either in statement I alone or in statement II alone are sufficient to answer the question.
4. The data given in both statements I and II together are not sufficient to answer the question.

Answer: The data either in statement I alone or in statement II alone are sufficient to answer the question.

Statement I gives a direct relation between selling price, marked price, and discount, which is enough to find the selling price. Statement II also gives two profit percentages with a difference of Rs. 300, which is sufficient to determine the selling price uniquely.

Q10. Find the discount percentage. I. The marked price of an article is ₹3800, but due to a sale, a certain percentage of discount is declared. II. Amit bought the article for ₹3200 and thereby made a profit of \(\frac{100}{7}\%\).

1. The statement I alone is sufficient to answer the question, but the statement II alone is not sufficient.
2. The statement II alone is sufficient to answer the question, but the statement I alone is not sufficient.
3. Both the statements I and II together are needed to answer the question.
4. Either statement I alone or statement II alone is sufficient to answer the question.

Answer: Both the statements I and II together are needed to answer the question.

Statement I alone is insufficient because the discount percentage cannot be found without the selling price or cost price. Statement II alone is also insufficient because it gives the selling price and profit, but not the marked price. Together, they allow us to find the cost price and then the discount percentage.

Q11. The following question is accompanied by two statements (I) and (II). Determine which statement(s) is/are sufficient to answer the question. What is the length of Train A? Statement I: Train A crosses a man running at 10 m/s in the opposite direction in 10 seconds, and the speed of the train is x m/s. Statement II: Train B has double the speed of Train A, crosses a pole in 5 seconds, and the length of Train B is 500 m. A) Statement I alone is sufficient to answer the question, but Statement II alone is not sufficient. B) Statement II alone is sufficient to answer the question, but Statement I alone is not sufficient. C) Both statements I and II together are needed to answer the question. D) Either statement I alone or Statement II alone is sufficient to answer the question.

1. Statement I alone is sufficient to answer the question, but Statement II alone is not sufficient.
2. Statement II alone is sufficient to answer the question, but Statement I alone is not sufficient.
3. Both statements I and II together are needed to answer the question.
4. Either statement I alone or Statement II alone is sufficient to answer the question.

Answer: Both statements I and II together are needed to answer the question.

Statement I gives only an equation involving the train’s speed and length, so it is insufficient alone. Statement II gives the speed relation and the length of Train B, but not enough to directly find Train A’s length alone. Together, they allow solving for the speed of Train A and then its length.

Q12. What will be the respective ratio of savings of V and D? I. Income of V is 4% less than that of S, and the ratio of expenditure of V to that of S is 7:8. D spends two-thirds of his income. II. S saves ₹14,000 and V saves ₹14,800. Income of D is ₹2,000 more than that of S.

1. Only statement I is sufficient
2. Only statement II is sufficient
3. Statement I and II both together is sufficient
4. Either statement I or Statement II alone is sufficient

Answer: Statement I and II both together is sufficient

Statement I gives relationships among income and expenditure, but not exact values, so the savings ratio cannot be found alone. Statement II gives savings of S and V and a relation involving D’s income, but still does not fully determine D’s savings alone. Together, the two statements allow the required ratio of savings of V and D to be determined.

Q13. Passage: The ratio of the time taken by pipe B to fill the same tank is 3:4 respectively. Pipe A takes t hours to fill the tank and pipe C takes (t + 4) hours to completely empty the same tank. If all three pipes are opened together at 10 a.m., the tank gets filled at 5 p.m. For how many hours was pipe C opened during the process, if it is known that pipe C was closed in between the given duration? (I) Pipe A and pipe C together can fill \(\tfrac{7}{10}\) of the tank in 28 hours. (II) Pipe A and pipe B together can fill \(\tfrac{7}{8}\) of the tank in 3 hours. Question: Decide whether the data provided in the statements are sufficient to answer the question.

1. The data in statement I alone is sufficient to answer, while the data in statement II alone is not sufficient to answer the question.
2. The data in statement II alone is sufficient to answer, while the data in statement I alone is not sufficient to answer the question.
3. The data either in statement I alone or in statement II alone are sufficient to answer the question.
4. The data given in both statements I and II together are not sufficient to answer the question.

Answer: The data either in statement I alone or in statement II alone are sufficient to answer the question.

Statement I gives a direct relation between A and C, and with the given ratio information it is enough to determine the rates. Statement II also gives a direct relation between A and B, which again can be used with the given ratio to determine the needed values. Therefore, either statement alone is sufficient.

Q14. P, Q and R entered into a partnership by investing a certain amount for 12 months, T months and \(12-T\) months respectively. Find the value of \(T\). Statement I: Q invested 50% more than P, and R invested twice the amount of Q. Statement II: At the end of the partnership, the total profit earned by them is Rs. 700 and the profit share of Q is Rs. 100. Statement III: Profit shares of P and R are in the ratio 1:2.

1. Only I and II
2. Only I and III
3. Only II and III
4. Either I and II or I and III

Answer: Either I and II or I and III

In partnership problems, profit shares are proportional to capital × time. Statement I fixes the capital ratio, while Statement II or III provides enough additional information to determine the time ratio and hence T. Therefore, either I and II or I and III is sufficient.

Q15. Find the value of x. Statement I: A person lent out a sum of Rs. 2400 in the ratio of 5 : x in Scheme A and Scheme B, respectively. Scheme A is offering simple interest at 8% per annum and Scheme B is offering simple interest at 3(x+1)% per annum. The interest earned from Scheme A after 2 years is Rs. 24 more than the interest earned from Scheme B after 2 years. Statement II: A person lent out a sum of Rs. 2400 in the ratio of 5 : 3 in Scheme A and Scheme B, respectively. Scheme A is offering simple interest at 8% per annum and Scheme B is offering simple interest at 3(x+1)% per annum. The simple interest earned from Scheme A after 9 years is equal to the interest earned from Scheme B after (x+7) years.

1. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
2. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
3. If the data either in statement I alone or in statement II alone is sufficient to answer the question
4. If the data in both statements I and II together are necessary to answer the question

Answer: If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question

Statement I gives the investment split as 5:x and also provides a direct interest difference after the same time period, which is enough to form one equation in x. Statement II does not uniquely determine x because the ratio is fixed at 5:3 while x appears only in the rate and time relation, making it insufficient on its own.

Q16. How much did Rohit borrow? I. Rohit borrowed at 10% per annum SI from Rakesh; returns after 5 years. II. Rakesh returns 5% of the total amount received = ₹240.

1. Statement I alone is sufficient
2. Both statements together are needed
3. Statement II alone is sufficient
4. Either statement alone is sufficient

Answer: Both statements together are needed

I alone: SI rate×time = 10%×5 = 50%. Total returned = 1.5P. Cannot find P without total. II alone: Total received = 240/0.05 = ₹4800. Cannot find P without rate+time. Together: 1.5P = 4800 → P = ₹3200. Both needed.

Q17. What will be the cost of painting a rectangular wall? I. The cost of painting is ₹10 per square metre. II. The perimeter of the wall is 60 m.

1. I alone sufficient
2. II alone sufficient
3. Both not sufficient
4. Either sufficient

Answer: Both not sufficient

Statement I gives the rate per square metre, but not the wall’s area. Statement II gives only the perimeter, which is not enough to determine area for a rectangle. Therefore, both statements together are still insufficient.

Q18. The following questions are accompanied by two statements, I and II. Determine which statement(s) is/are sufficient to answer the question. Q58. Find the length of train B. I. The length of train A is the same as the length of train B. II. Train A can cross a pole in 10 seconds, and train A can cross a 150-meter-long platform in 17.5 seconds.

1. Neither statement (I) nor statement (II) by itself is sufficient to answer the question.
2. Statement (II) alone is sufficient to answer the question but statement (I) alone is not sufficient to answer the question.
3. Either statement (I) or statement (II) by itself is sufficient to answer the question.
4. Both the statements taken together are necessary to answer the question, but neither statement alone is sufficient to answer the question.

Answer: Both the statements taken together are necessary to answer the question, but neither statement alone is sufficient to answer the question.

Statement I only tells us that the lengths of trains A and B are equal, but not their actual length. Statement II allows us to find the length of train A using the pole and platform data, but it does not directly give B's length unless combined with Statement I. Therefore, both statements together are needed.

Q19. What profit is earned by selling a bike for Rs. 50,000? I. The ratio of selling price and cost price is 2:1. II. The profit percentage by selling a bike is equal to 25%.

1. Statement I alone is sufficient to answer the question but statement II alone is not sufficient to answer the question.
2. Statement II alone is sufficient to answer the question but statement I alone is not sufficient to answer the question.
3. Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.
4. Either statement I or statement II by itself is sufficient to answer the question.

Answer: Either statement I or statement II by itself is sufficient to answer the question.

From statement I, SP:CP = 2:1 and SP = 50000, so CP = 25000 and profit = 25000. From statement II, profit is 25% of CP, so SP = 125% of CP; with SP = 50000, CP = 40000 and profit = 10000. Each statement alone is sufficient.

Q20. What is Sahil's monthly savings? I. Sahil spends 25% on food, 35% on medicine and education. II. Sahil spends ₹4,000 on food and 35% on medicine and education and saves the rest. III. Sahil spends ₹2,500 on medicine and education and saves the rest. Which statement(s) are redundant?

1. Only II
2. Only III
3. Both II and III
4. Either II or III

Answer: Either II or III

I alone: percentages given but no monetary value → insufficient. I+II: food=₹4000=25% → salary=₹16000, savings=40%=₹6400 ✓. I+III: med=₹2500=35% → salary=₹7143, savings≈₹2857 ✓. Since I+II alone or I+III alone is sufficient, the other statement is redundant. Answer: Either II or III.

Q21. A line graph shows expenditure as a percentage of income for A, B, C, D, and E in October and November. Find A's income in November. I. Difference in A's savings (November - October) = 20% of A's October income. II. B's November savings = 40% of A's October savings. Which of the following is sufficient?

1. I sufficient
2. II sufficient
3. Either I or II sufficient
4. Neither I nor II sufficient

Answer: Neither I nor II sufficient

The graph provides expenditure percentages, but A's November income cannot be uniquely determined from either statement alone. Statement I relates only the change in savings, and statement II relates B's savings to A's October savings, so neither is sufficient by itself.

Q22. Data sufficiency question: Two statements (I) and (II) given. Determine which combination is sufficient to answer the question about a numeric/logical condition.

1. Statement I alone is sufficient.
2. Statement II alone is sufficient.
3. Either statement I or II alone is sufficient.
4. Both the statements I and II together are needed to answer the question.

Answer: Both the statements I and II together are needed to answer the question.

Statement I alone is insufficient. Statement II alone is insufficient. Only when both statements are combined can the question be answered definitively.

Q23. Find cost price of article. I: SP-CP=20, markup=40%, MP:SP=7:6. II: CP:SP=5:6, discount=14.28%, profit=₹20.

1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
3. The data either in statement I alone or in statement II alone is sufficient to answer the question
4. The data given in both statements I and II together are not sufficient to answer the question

Answer: The data either in statement I alone or in statement II alone is sufficient to answer the question

I: Mark-up 40%→MP=1.4CP. MP:SP=7:6→SP=6/7×1.4CP=1.2CP. SP-CP=0.2CP=20→CP=₹100 ✓. II: CP:SP=5:6→SP=1.2CP. Profit=SP-CP=0.2CP=20→CP=₹100 ✓. Both independently sufficient.