Quantitative Aptitude

Data Sufficiency

149 Questions
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Data Sufficiency Questions

Multiple choice

At a large manufacturing plant, the assembly line's output speed is measured and forecast at various times of the day. At 3:00 p.m. on a certain day, was the forecast output speed exactly 120 units per hour? (1) At 12:00 noon, the forecast output speed was 105 units per hour, and at 4:00 p.m., it was forecast to be 125 units per hour. (2) The forecast output speed followed a uniform linear trend throughout the day.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement 1 gives two points. Statement 2 confirms a linear trend. With a linear trend, two points define the line, allowing calculation of the value at any time. Both are needed.

Multiple choice

Machines A, B, and C, each working alone at their constant rates, produce 1 gadget in p minutes, q minutes, and 3 minutes, respectively. If Machines A, B, and C work simultaneously at their respective constant rates, will they take less than 1 hour to produce a total of 60 gadgets? (1) p q < 1.5

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Nora drove past three toll booths: Booth P, Booth Q, and Booth R in that order, at a constant speed. What was Nora's speed when she passed Booth Q? (1) Nora covered the 75 kilometers between Booth P and Booth Q in 1 hour 15 minutes. (2) Nora covered the 48 kilometers between Booth Q and Booth R in 48 minutes.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Speed is distance divided by time. Statement 1 gives speed between P and Q. Statement 2 gives speed between Q and R. Since the speed is constant, either statement is sufficient to find the speed at Booth Q.

Multiple choice

A boat takes 36 minutes to travel from Harbor A to Harbor B along a fixed route. How long does it take for the boat to return from Harbor B to Harbor A along the same route? (1) The boat's average speed from A to B is 80% of its average speed from B to A. (2) The distance between the harbors is 9 nautical miles.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The time taken for a trip depends on speed and distance. Statement (1) provides the ratio of speeds, which allows us to relate the time taken for the return trip to the time taken for the initial trip. Statement (2) is irrelevant because the actual distance cancels out when calculating the time ratio.

Multiple choice

Three machines, D, E, and F, operating at constant rates, can together produce a batch of components in 8 hours. How long would machines E and F, working together, take to produce the same batch? (1) Machine D produces twice as many components per hour as machine E, and machine E produces twice as many components per hour as machine F. (2) The time machine D takes to produce 12 components is the same as the time machines E and F together take to produce 9 components.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let rates be D, E, F. D+E+F = 1/8. (1) D=2E, E=2F => D=4F, E=2F. 4F+2F+F = 1/8 => 7F = 1/8 => F=1/56. E=2/56. E+F = 3/56. Time = 56/3 hours. (2) D/12 = (E+F)/9 => 9D = 12(E+F) => 3D = 4(E+F). Since D+E+F=1/8, E+F = 1/8 - D. 3D = 4(1/8 - D) => 7D = 0.5 => D=1/14. E+F = 1/8 - 1/14 = 3/56. Both are sufficient.

Multiple choice

Passage

1786100_passage_1535797315_hindi.htm

What is the ratio of the speed of boat in still water to the speed of stream? I. A boat went downstream for 120 km and immediately returned and it took the boat 15 hours to complete the round trip. II. A boat went downstream for 96 km and immediately returned and it took the boat 12 hours to complete the round trip. III. If the speed of the river was twice as high, the trip downstream and back would take 12 hours.

  1. All I, II and III together are sufficient

  2. Both II and III together are sufficient

  3. Either I and III or II and III together are sufficient

  4. Both I and II together are sufficient

  5. Both I and III together are sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let u be boat speed and v be stream speed. Round trip time = d/(u+v) + d/(u-v). With two equations (I and II), we have two variables (u, v) and the ratio d is known, but we need the ratio u/v. Statement III provides a third scenario to solve for the ratio.

Multiple choice

Passage

Directions: The following question is accompanied by three statements - (A) or (I), (B) or (II) and (C) or (III). You have to determine the statement(s) which is/are sufficient/necessary to answer the question.

What is the speed of the stream? A. The boat covers 80 km in 20 hours moving upstream. B. The boat covers 80 km in 10 hours moving downstream. C. The ratio between the speeds of the boat and the stream is 6 : 2, respectively.

  1. Only A and B together are sufficient.

  2. Any two of the three statements are sufficient.

  3. Only A and C together are sufficient.

  4. Only B and C together are sufficient.

  5. All A, B and C together are required.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A: Upstream speed = 80/20 = 4 km/hr. B: Downstream speed = 80/10 = 8 km/hr. C: Ratio of boat speed (b) to stream speed (s) is 6:2, or 3:1. With A and B, b-s=4 and b+s=8, so 2b=12, b=6, s=2. With A and C, b-s=4 and b/s=3, so 3s-s=4, 2s=4, s=2. With B and C, b+s=8 and b/s=3, so 3s+s=8, 4s=8, s=2. Any two statements are sufficient.

Multiple choice

Passage

In each of the following questions, a question & then two statements – I & II are given. You have to determine that the data provided in these statements is enough to answer the question or not. Study both the statement: निम्नलिखित प्रत्येक प्रश्न में एक प्रश्न और फिर दो कथन I और II दिए गए हैं। आपको यह निर्धारित करना है कि इन कथनों में प्रदान किया गया डेटा प्रश्न का उत्तर देने के लिए पर्याप्त है या नहीं। दोनों कथनों का अध्ययन करें:

what is the speed of the stream? धारा की गति क्या है? Statement I – A boat goes 12km upstream and 25 km downstream in 5 hours. Statement II – The boat goes 20 km upstream and 55 km downstream in 6.5 hours. कथन I - एक नाव 5 घंटे में 12 किमी धारा के प्रतिकूल और 25 किमी धारा के अनुकूल जाती है। कथन II - नाव 6.5 घंटे में 20 किमी धारा के प्रतिकूल और 55 किमी धारा के अनुकूल जाती है

  1. Only Statement I alone. केवल कथन I

  2. Only Statement II alone. केवल कथन II

  3. Both Statements I and II together. दोनों कथन I और II एक साथ

  4. Neither Statement I nor II is sufficient. न तो कथन I और न ही II पर्याप्त है।

  5. Either Statement I or II. या तो कथन I या II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed = b, stream speed = s. Upstream speed = b-s, downstream = b+s. Statement I: 12/(b-s) + 25/(b+s) = 5. Two unknowns, one equation - insufficient. Statement II: 20/(b-s) + 55/(b+s) = 6.5. Again two unknowns, one equation - insufficient alone. Together: Two equations with (b-s) and (b+s) as variables. Can solve for upstream and downstream speeds, then find s. Both needed.

Multiple choice

Passage

Each of the following questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer नीचे दिए गए प्रत्येक प्रश्न में एक प्रश्न और उसके नीचे दो कथन क्रमांक I और II दिए गए हैं। आपको यह तय करना है कि कथनों में दिया गया डेटा प्रश्न का उत्तर देने के लिए पर्याप्त है या नहीं। दोनों कथनों को पढ़िए और उत्तर दीजिए

Find the speed of boat in downstream? अनुप्रवाह में नाव की गति ज्ञात कीजिए? Statement I : Speed of boat in still water is 50% more than speed of boat in upstream. Statement II : Difference between time taken by boat to cover 32 km in upstream to that of in downstream in 2 hours. कथन I : शांत जल में नाव की गति धारा के प्रतिकूल नाव की गति से 50% अधिक है। कथन II: धारा के प्रतिकूल में 32 किमी की दूरी तय करने में नाव द्वारा लिए गए समय और धारा के अनुकूल लिए गये समय के बीच का अन्तर 2 घंटे है

  1. Statement I alone is sufficient to answer the question but statement II alone is not sufficient to answer the questions कथन I अकेले प्रश्न का उत्तर देने के लिए पर्याप्त है लेकिन कथन II अकेले प्रश्नों का उत्तर देने के लिए पर्याप्त नहीं है

  2. Statement II alone is sufficient to answer the question but statement I alone is not sufficient to answer the question. कथन II अकेले प्रश्न का उत्तर देने के लिए पर्याप्त है लेकिन केवल कथन I अकेले प्रश्न का उत्तर देने के लिए पर्याप्त नहीं है।

  3. Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question. दोनों कथनों को मिलाकर प्रश्नों का उत्तर देना आवश्यक है, लेकिन इनमें से कोई भी कथन अकेले प्रश्न का उत्तर देने के लिए पर्याप्त नहीं है।

  4. Either statement I or statement II by itself is sufficient to answer the question. या तो कथन I या कथन II अपने आप में प्रश्न का उत्तर देने के लिए पर्याप्त है

  5. Statements I and II taken together are not sufficient to answer the quest
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed in still water = b, stream speed = s. Downstream speed = b+s, upstream speed = b-s. From Statement I: b = 1.5(b-s), so b = 1.5b - 1.5s, giving 0.5b = 1.5s or b = 3s. This gives ratio but not actual values. From Statement II: 32/(b-s) - 32/(b+s) = 2. Using b = 3s from Statement I, we can solve for s and then find b+s. Both statements are needed.

Multiple choice

Passage

Each of the following questions below consists of a question and two statements numbered I and II given. You have to decide whether the data provided in the statements is sufficient to answer the question.

What is the speed of boat in still water? I. Boat covers 15 km in upstream speed in 5 hours. II. Ratio of speed of downstream and upstream is 4: 3.

  1. statement, I alone is sufficient to Answer

  2. statement II alone is sufficient to Answer

  3. Either Statement I or Statement II is sufficient to answer the question

  4. neither statement I nor II is sufficient to answer the question.

  5. Both statements I and II together is necessary to answer the question.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Statement I: Upstream speed = 15/5 = 3 km/h = b - s. Statement II: Downstream/upstream = 4/3, so downstream speed = 4/3 × 3 = 4 km/h = b + s. From I and II together: b - s = 3, b + s = 4. Adding: 2b = 7, b = 3.5 km/h. Both statements necessary.

Multiple choice

Passage

Each of the questions below consists of a question and two statements given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer.

How many words are there in the page? I. Pavithra will take 5 minutes less to type the page at an average speed of 250 words per minute than the time taken to type the page at an average speed of 125 words per minute. II. Pavithra will take 14 minutes to type the first half of the page at an average speed of 130 words per minute.

  1. If Statement I alone is sufficient to answer the question

  2. If Statement II alone is sufficient to answer the question

  3. If Both the Statements I and II together are needed to answer the question.

  4. Either the Statement I alone or Statement II alone is sufficient to answer the question.

  5. Both statements together are not sufficient to answer
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I alone is sufficient: Let total words = W. At 125 wpm, time = W/125. At 250 wpm, time = W/250. Difference = W/125 - W/250 = 5 minutes, giving W = 1250 words. Statement II alone is also sufficient: (W/2)/130 = 14 gives W = 3640 words. Since both individually give the answer, option D is correct.

Multiple choice

Passage

Following questions contain two statements as statement I and statement II. You have to determine which statement/s is/are necessary to answer the question and give answer as, निम्नलिखित प्रश्नों में कथन I और कथन II के रूप में दो कथन शामिल हैं। आपको यह निर्धारित करना है कि प्रश्न का उत्तर देने के लिए कौन सा कथन / विवरण आवश्यक है ,

What is the speed (in meters per hour) of motorboat in still water? Statement I: The motorboat covers 100 km downstream in 10 hours. Statement II: The motorboat covers 60 km in upstream water in 10 hours. शांत जल में मोटरबोट की चाल (मीटर प्रति घंटा में) क्या है? कथन I: मोटरबोट 10 घंटे में धारा के अनुकूल 100 किमी की दूरी तय करती है। कथन II: मोटरबोट 10 घंटे में धारा के प्रतिकूल पानी में 60 किमी की दूरी तय करती है।

  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 कथन I के आंकड़े प्रश्न का उत्तर देने के लिए पर्याप्त है, जबकि कथन II का आंकड़े अकेले प्रश्न का उत्तर देने के लिए पर्याप्त नहीं है

  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 कथन II में आंकड़े प्रश्न का उत्तर देने के लिए पर्याप्त है, जबकि कथन I में आंकड़े प्रश्न का उत्तर देने के लिए पर्याप्त नहीं है

  3. The data either in statement I alone or in statement II alone is sufficient to answer the question केवल कथन I या कथन II में दिए गए आंकड़े प्रश्न का उत्तर देने के लिए पर्याप्त है

  4. The data given in both statements I and II together are not sufficient to answer the question I और II दोनों कथनों में दिए गए आंकड़े प्रश्न का उत्तर देने के लिए पर्याप्त नहीं हैं

  5. The data given in both statements I and II together are necessary to answer the question. प्रश्न का उत्तर देने के लिए I और II दोनों कथनों में दिए गए आंकड़े आवश्यक हैं।
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

To find the speed of the motorboat in still water, we need both downstream and upstream speeds. Downstream speed = distance/time = 100 km/10 hr = 10 km/hr. Upstream speed = 60 km/10 hr = 6 km/hr. Still water speed = (downstream speed + upstream speed)/2 = (10 + 6)/2 = 8 km/hr = 8000 m/hr. Neither statement alone gives both speeds, so both are necessary.

Multiple choice

Passage

Each of the questions below consist of a question and two statements. You have to decide whether the data provided in the statements is sufficient to answer the questions. Read both the statements and then choose the appropriate option. नीचे दिए गए प्रत्येक प्रश्न में एक प्रश्न और दो कथन हैं। आपको यह तय करना है कि कथनों में दिया गया डेटा प्रश्नों का उत्तर देने के लिए पर्याप्त है या नहीं। दोनों कथनों को पढ़िए और उपयुक्त विकल्प का चयन कीजिए।

Find the speed of boat in still water? शांत जल में नाव की गति ज्ञात कीजिए? Statement I : Time taken by boat to cover 64 km in downstream, is half the time taken by same boat to cover same distance in still water. Statement II : Speed of stream is 5 km/hr. कथन I : नाव द्वारा धारा के अनुकूल 64 किमी की दूरी तय करने में लिया गया समय, शांत पानी में समान दूरी को तय करने में उसी नाव द्वारा लिए गए समय का आधा है। कथन II: धारा की गति 5 किमी/घंटा है।

  1. Statement I alone is sufficient to answer the question but statement II alone is not sufficient to answer the questions कथन I अकेले प्रश्न का उत्तर देने के लिए पर्याप्त है लेकिन कथन II अकेले प्रश्नों का उत्तर देने के लिए पर्याप्त नहीं है

  2. Statement II alone is sufficient to answer the question but statement I alone is not sufficient to answer the question. कथन II अकेले प्रश्न का उत्तर देने के लिए पर्याप्त है लेकिन केवल कथन I अकेले प्रश्न का उत्तर देने के लिए पर्याप्त नहीं है।

  3. Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question. दोनों कथनों को मिलाकर प्रश्नों का उत्तर देना आवश्यक है, लेकिन इनमें से कोई भी कथन अकेले प्रश्न का उत्तर देने के लिए पर्याप्त नहीं है।

  4. Either statement I or statement II by itself is sufficient to answer the question. या तो कथन I या कथन II अपने आप में प्रश्न का उत्तर देने के लिए पर्याप्त है

  5. Statements I and II taken together are not sufficient to answer the question. कथन I और II को मिलाकर प्रश्न का उत्तर देन
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let boat speed = b, stream speed = s. Statement I: Time downstream = half time in still water. Distance/speed_down = 0.5 × Distance/speed_still. So 64/(b+s) = 0.5 × 64/b, giving 2b = b+s or b = s. But we don't know s. Insufficient alone. Statement II: s = 5 km/hr. But no relation to boat speed. Insufficient alone. Combined: b = s = 5 km/hr. Sufficient.

Multiple choice

Passage

Directions: The following question is accompanied by statements (A), (B) and (C). You have to determine which of the following statements is/are sufficient/necessary to answer the question.

What is the speed of boat in still water and the speed of stream? (A) The speed of the stream is one-fifth that of the boat in still water. (B) The boat covers 24 km in 3 hours upstream. (C) The boat covers 48 km in 4 hours downstream.

  1. A and B together are sufficient

  2. A and C together are sufficient

  3. B and C together are sufficient

  4. A and either B or C are sufficient

  5. All A, B and C are sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer