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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
II. The volume of hemisphere is 1500 cubic cm.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. |
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Answer» From statement I: The total surface area of hemisphere is 400 square CM. From here, we can FIND value of Radius and hence curved surface area of hemisphere. ∴ STATEMENT I alone is sufficient to ANSWER the question. From statement II: The volume of hemisphere is 1500 cubic cm. From here, we can find value of Radius and hence curved surface area of hemisphere. ∴ Statement II alone is sufficient to answer the question. |
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| 2. |
1). if the data given in statement I alone is sufficient to answer the question whereas the data given in statement II alone is not sufficient to answer the question.2). if the data given in statement II alone is sufficient to answer the questions whereas the data given in statement I alone is not sufficient to answer the question.3). if the data in either statement I alone or in statement II alone is sufficient to answer the question.4). if the data in both the statements I and II is not sufficient to answer the question. |
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Answer» Statement I just tells US about the average age of the class but as no. of students is missing it is not useful. Statement II gives the information about the average age of boys and girls, which is not sufficient to find the ratio, as NUMBER of boys and girls cannot be determined from this. On COMBINING both the statements, Let the required ratio be k ? 1 = B ? G ⇒ 15.8 = [k(16.4) + (15.4)) / (k + 1)] ⇒ 15.8k + 15.8 = 16.4k + 15.4 ⇒ 0.6k = 0.4 ⇒ K = 4/6 = 2/3 ∴ Required Ratio = 2 ? 3 ∴ Data given in both the statement I and II are necessary to ANSWER the question |
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| 3. |
Directions: The following questions are accompanied by three statement (A) or (I), (B) or (II), and (C) or (III). You must determine which statement(s) is/are sufficient/necessary to answer the questions.C. One-fourth of the work is done by 8 workers in 12.5 days.1). Any two of them2). Only B3). Either A or C only4). A and C together |
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Answer» Let, the WORK will be completed in = x days The worker’s efficiency = a/day A. from this we get, ⇒ 8 × 40 ×a = 40/100 ⇒ a = 1/800 According to PROBLEM, ⇒ 32 × x ×a = 1 ⇒ x = 800/32 ⇒ x = 25 ∴ 32 workers complete the work in = 25 days From A we get the value. B. from this we get, ⇒ 160 × 5 × a = 1 ⇒ a = 1/800 According to problem, ⇒ 32 × x × a = 1 ⇒ x = 800/32 ⇒ x = 25 ∴ 32 workers complete the work in = 25 days From B we get the value. C. from this we get, ⇒ 16 × 12.5 × a = ¼ ⇒ a = 1/800 According to problem, ⇒ 32 × x × a = 1 ⇒ x = 800/32 ⇒ x = 25 ∴ 32 workers complete the work in = 25 days From C we get the value. ∴ We can get the value from any of the three. |
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| 4. |
II: The difference between the ages of Arbaaz and Salman is 18 years.1). The data either in statement I alone or in statement II alone is sufficient to answer the question.2). The data in statement II alone are sufficient to answer the questions, while the data in statement I alone are not sufficient to answer the question.3). The data in Statement I alone are sufficient to answer the question, while the data in statements II alone are not sufficient to answer the question.4). The data even in both the statements I and II together is not sufficient to answer the question. |
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Answer» From STATEMENT I: Let the ratio of AGES Arbaaz and Salman be 2x and 5x respectively. From I and II: 5x - 2x = 18 ⇒ 3x = 18 ⇒ x = 6 years Arbaaz’s age = 6 × 2 = 12 years Salman’s age = 6 × 5 = 30 years Total ages of Arbaaz, Salman and Sohail at PRESENT = 30 × 3 = 90 - 15 = 75 years ∴ Present age of Sohail = 75 - (30 + 12) = 33 years. ∴ Both statements are required to ANSWER the question. |
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| 5. |
II. The truck covers a distance of 550 m in 1 minute and the bus covers a distance of 33 km in 45 minutes1). If the data given in statement I alone is sufficient to answer the question whereas the data given in statement II alone are not sufficient to answer the question.2). If the data given in statement II alone is sufficient to answer the question whereas the data given in statement I alone are not sufficient to answer the question.3). If the data in either statement I alone or in statement II alone is sufficient to answer the question.4). If the data in both the statements I and II is not sufficient to answer the question. |
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Answer» Considering statement I: This statement is not sufficient to answer as we need the ratio of their SPEEDS and it doesn’t matter WHETHER they are travelling in the same direction or opposite. ∴ Statement I ALONE is not sufficient. Considering statement II: We know, Distance covered by TRUCK = 550 m = $(\frac{{550}}{{1000}}km)$ $(Speed = \frac{{Distance}}{{Time}})$ Speed of the truck$(\; = \frac{{550\;km}}{{1000\;min}})$ Speed of the bus$(\; = \frac{{33\;km}}{{45\;min}})$ Ratio of the speed of truck to bus$(\; = \frac{{550}}{{1000}} \times \frac{{45}}{{33}} = \frac{3}{4})$ ∴ Statement II ALONE is sufficient, but statement I alone is not sufficient. |
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| 6. |
1). The data in Statement I alone are sufficient to answer the question, while the data in statements II alone are not sufficient to answer the question.2). The data in statement II alone are sufficient to answer the questions, while the data in statement I alone are not sufficient to answer the question.3). The data in both the statements I and II together are necessary to answer the question.4). The data even in both the statements I and II together is not sufficient to answer the question. |
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Answer» From statement I: We only know that Fang will take twice as many days as Wang, but we cannot find the number of days that Zhang will take to complete the work. From statement II: TIME taken by Wang to do the whole work ALONE, ⇒ 1/20 - 1/30 = 1/60 = 60 days. But this statement alone is not sufficient to answer the question. Combining the two statements: Fang will take 120 days to complete the work. ⇒ 1/Z + 1/F = 1/30 ⇒ 1/Z + 1/120 = 1/30 ⇒ 1/Z = 1/30 - 1/120 = (4 - 1)/120 = 3/120 = 1/40 ∴ Zhang take 40 days to complete the work, working alone. ∴ Both statements are REQUIRED to answer the question |
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| 7. |
II. x is divisible by 91). If statement I alone is sufficient to answer the question, but statement II alone is not sufficient.2). If statement II alone is sufficient to answer the question, but statement I alone is not sufficient.3). If both the statements I and II together are needed to answer the question.4). If either statements I alone or statement II alone is sufficient to answer the question. |
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Answer» If 4X5X9X need to be DIVISIBLE by 9 then ⇒ 4 + X + 5 + X + 9 + X must be divisible by 9 ⇒ 18 + 3X must be divisible by 9 Now 18 is divisible by 9 we have to CHECK 3X If x is divisible by 3 then 3X will be divisible by 9 Statement II ∴ If x is divisible by 9 then 3X will be divisible by 9 ∴ EITHER statements I alone or statement II alone is sufficient to answer the question |
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| 8. |
1). If the data given in the statement I alone is sufficient to answer the question whereas the data given in statement II alone is not sufficient to answer the question.2). If the data given in the statement II alone is sufficient to answer the question whereas the data given in statement I alone is not sufficient to answer the question.3). If the data in either statement I alone or in statement II alone is sufficient to answer the question.4). If the data in either statement I & II is not sufficient to answer the question. |
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Answer» Let the 2-digit number be X Y. ∴ This number can be represented as 10 X + Y. By checking each statement individually- Statement I- The average of 2 individual DIGITS is 2 more than their addition. As average of 2 digits = (X + Y)/ 2 As per statement I- (X + Y)/2 = X + Y - 2 ∴ X + Y = (X + Y - 2) × 2 ∴ X + Y = 2 X + 2Y - 4 ∴ X + Y = 4 ---- (1) But statement I fail to give individual digits. ∴ Statement I alone can’t figure out 2-digit number. Statement II- The difference between 2 digits is 2 and 10th place digit is HIGHER than unit’s place digit. ∴ X – Y = 2 ---- (2) But statement II fail to give individual digits. ∴ Statement II alone can’t figure out 2-digit number. Combining information of both results- X + Y = 4 & X – Y = 2 Adding both results- (X + Y) + (X - Y) = 4 + 2 ∴ 2 X = 6 ∴ X = 3 Putting VALUE of X in 1st result- X + Y = 4 3 + Y = 4 ∴ Y = 1 ∴ 2-digit number is 31. ∴ Both STATEMENTS are essential to find 2-digit numbers. |
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| 9. |
1). The data either in statement I alone or in statement II alone is sufficient to answer the question.2). The data in statement II alone are sufficient to answer the questions, while the data in statement I alone are not sufficient to answer the question.3). The data in both the statements I and II together are necessary to answer the question.4). The data even in both the statements I and II together is not sufficient to answer the question. |
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Answer» From statement I: Share of PROFIT of P and Q will be in the RATIO of 4 : 7 After two years, Let the share of profit of Q be RS. y ∴ 4/7 = 95000/y ⇒ y = 95000 × 7/4 ⇒ y = Rs. 166250 ∴ Statement I alone is sufficient to answer. |
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| 10. |
1). If the data in statement l 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 l alone is not sufficient to answer the question.3). If the data either in statement l alone or in statement Il alone is sufficient to answer the question.4). If the data given in both statements I and II together is not sufficient to answer the question. |
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Answer» Considering statement I: Let the selling price = SP = 4x and cost price = CP = 3x It is given that SP = Rs. 12,000 HENCE 4x = 12000 ⇒ x = 12000/4 ⇒ x = 3000 ⇒ 3x = 9000 Now that we know the CP and SP, where SP > CP (profit), we can place their values in the FORMULA for profit percent. $(Profit\% = \frac{{Profit}}{{CP}} \TIMES 100)$ $(= \frac{{SP - CP}}{{CP}} \times 100)$ $(= \frac{{12000 - 9000}}{{9000}} \times 100)$ = Rs. 33.33 ∴ Profit percent can be found by using statement I ALONE. Considering statement II: We do not know if its profit or loss. Hence we cannot find the percentage of it. ∴ Profit or loss percent cannot be found by using statement II alone. ∴ Statement I alone is sufficient, but statement II alone is not sufficient. |
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| 11. |
1). Statement I alone is sufficient to answer the question.2). Statement II alone is sufficient to answer the question.3). Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.4). Either Statement I or Statement II alone is sufficient to answer the question. |
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Answer» The RELATION between Distance travelled, Speed of travel and the Time taken to travel this distance is given by: Distance = Speed × Time---- (A) $(? Time = \;\frac{{Distance}}{{Speed}}\;)$---- (B) Let the LENGTH of the train be 'L' metres. According to the given information the train crosses the 120 metre platform in 'T' seconds. Using above formulae: Time taken to cross the platform = (TOTAL Distance covered)/Speed $(\therefore {\rm{\;T\;}} = \frac{{L + 120}}{{Speed}}\;)$---- (1) Consider Statement (I), according to which the train crosses a signal post in 'R' seconds Using above formulae: Time taken to cross the signal post = (Total Distance covered)/Speed $(\therefore {\rm{R\;}} = \frac{L}{{Speed}})$---- (2) The values of 'T' and 'R' are given values, so the only variables we need to solve for are 'L' and Speed. We have 2 equations to solve for 2 variables. ∴ Statement (I) is ENOUGH to find the length of the train. Now consider Statement (II),according to whichthe train moves at 90 km/hr. $(\therefore {\rm{Speed\;}} = {\rm{\;}}90\frac{{{\rm{km}}}}{{{\rm{hr}}}} = 90 \times \frac{5}{{18}}{\rm{m}}/{\rm{s\;}} = {\rm{\;}}25{\rm{\;m}}/{\rm{s}})$ Substituting this value in equation (1) we can get the length of the train. ∴ Statement (II) alone can give the length of the train. ∴ Both statements are individually sufficient to find the answer |
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| 12. |
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 question2). 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 in statement I alone or in statement II alone are sufficient to answer the question.4). The data in both the statement I and II are not sufficient to answer the question. |
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Answer» From STATEMENT I: The radius of the CIRCLE is equal to length of a RECTANGLE. Statement I alone is not SUFFICIENT to answer the QUESTION. From statement II: The breadth of the rectangle is equal to 25 cm. Statement II alone is not sufficient to answer the question. From statement I and II together: Radius of the circle = Length of rectangle Breadth of rectangle = 25 cm There is no information about the length of rectangle. Hence, the data in both the statement I and II are not sufficient to answer the question. |
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| 13. |
1). If the data given in the statement I alone is sufficient to answer the question whereas the data given in statement II alone are not sufficient to answer the question.2). If the data given in the statement II alone is sufficient to answer the question whereas the data given in statement I alone are not sufficient to answer the question.3). If the data given in either statement I or in statement II alone is sufficient to answer the question. 4). If the data given in both statement I and II is not sufficient to answer the question. |
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Answer» Simple Interest = Rs. 216 Statement I: Time = 3, Rate = 4% p.a. S.I. = $(\frac{{Prinicipal \times time \times Rate}}{{100}})$ $(\therefore Principal = \frac{{216 \times 100}}{{3 \times 4}} = 1800)$ Thus, statement I provides the sufficient DATA. Statement II: After one year S.I. = Rs. 72 $(\therefore 72 = \frac{{Principal \times 1 \times Rate}}{{100}})$ Thus, in Statement II provide insufficient data. |
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| 14. |
II. The train crosses another train 100 m long coming from the opposite direction at 72 km/hr in 6.4 sec.1). Only I2). Only II3). Both I and II4). Either I or II |
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Answer» Let the length of the train be ‘y’ m Considering statement I, Speed of train = length of train/time taken to cross signal post = (y/8) m/sec. Considering statement II, ? Another train is coming from opposite direction, the relative speed is the sum of the individual speeds Speed of other train = 72 km/hr = 72 × 5/18 = 20 m/sec. Using information from statement I, Relative speed = 20 + y/8 Time taken to cross the train = sum of the lengths of train/relative speed ⇒ 6.4 = (y + 100)/(20 + y/8) ⇒ 128 + 0.8y = y + 100 ⇒ 0.2y = 28 ⇒ y = 28/0.2 = 140 m ∴ Both the STATEMENTS are necessary to ANSWER the question |
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| 15. |
1). if the data given in statement I alone is sufficient to answer the question whereas the data given in statement II alone is not sufficient to answer the question.2). if the data given in statement II alone is sufficient to answer the questions whereas the data given in statement I alone is not sufficient to answer the question.3). if the data in either statement I alone or in statement II alone is sufficient to answer the question.4). if the data in both the statements I and II are not sufficient to answer the question. |
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Answer» From statement I, we can just get the rate of flow of outlet tap. From statement II alone it is not possible to get the answer. Now combining Statement I and II, Tap 1 takes 20 minutes and tap 2 takes 30 minutes ⇒ The time taken by both to fill the tank is given as follows, Let the total capacity of the tank be ( = LCM of 20 and 30) 60 units. ⇒ Tank filled by tap 1 in 1 minute = 60/20 = 3 units ⇒ Tank filled by tap 2 in 1 minute = 60/30 = 2 units ⇒ Tank filled by both the taps in 1 minute = 5 units ⇒ Tap 1 and 2 will require 60/5 = 12 minutes to fill the tank together and half of the tank in 6 minutes. From statement II, the outlet tap takes 24 minutes to fill the empty tank. ⇒ It takes (24 – 6) = 18 minutes to fill the tank when outlet tap is open. ∴ Hence the capacity of the tank is 18 × 100 = 1800 liters. ∴ Data given in both the statement I and II are necessary to answer the question. |
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| 16. |
II. Ambani invested Rs. 4000 more than Tata and Tata invested Rs. 5000 more than Birla.1). The data in Statement I alone are sufficient to answer the question, while the data in statements II alone are not sufficient to answer the question.2). The data in statement II alone are sufficient to answer the questions, while the data in statement I alone are not sufficient to answer the question.3). The data in both the statements I and II together are necessary to answer the question.4). The data even in both the statements I and II together is not sufficient to answer the question. |
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Answer» From statement II: Let BIRLA invested Rs. x Then, TATA = x + 5000 And Ambani = x + 5000 + 4000 = x + 9000 ∴ Their total INVESTMENT = Rs. (x + x + 5000 + x + 9000) From I and II: (x + x + 5000 + x + 9000) = 50000 ⇒ 3x = 36000 ⇒ x = 12000 Ratio of their investment = Ambani : Tata : Birla = 21000 : 17000 : 12000 = 21 : 17 : 12 ∴ Ambani’s share = 35000 × 21/50 = Rs. 14700 ∴ Both statements are required to answer the question. |
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| 17. |
II. Six years from now, sum of ages of Lance and Robin will be 77 years.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. |
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Answer» From statement I: Five years back, the RATIO of ages of Lance and Robin was 6:5. Knowing the ratio, age of Lance cannot be determined. ∴ Statement I alone is not sufficient to answer the question. From statement II: Six years from now, sum of ages of Lance and Robin will be 77 years. ⇒ Present sum of their ages = 77 – 2 × 6 = 65. But, age of Lance individually cannot be found. ∴ Statement II alone is not sufficient to answer the question. From statements I and II together: Five years back, the ratio of ages of Lance and Robin was 6:5. Let the ages of Lance and Robin be 6t and 5t, RESPECTIVELY, five years back. Present age of Lance = 6t + 5 Present age of Robin = 5t + 5 Six years from now, sum of ages of Lance and Robin will be 77 years. ⇒ Present sum of their ages = 77 – 2 × 6 = 65. We can now find VALUE of t, and hence find age of Lance. With the present age of Lance, age of Lance three years from now can be found. ∴ USING both the statements together, we can answer the given question. |
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