If you have two straight sticks of length 7.5 feet and 3.25 feet, what is the minimum length can you measure?
- 0.05 foot
- 0.25 foot
- 1 foot
- 3.25 feet
Explanation: The minimum length that can be measured using both sticks is the highest common factor (HCF) of 7.5 and 3.25, which equals 0.25.
A simple mathematical operation in each number of the sequence 14, 18, 20, 24, 30, 32, ..... results in a sequence with respect to prime numbers. Which one of the following is the next number in the sequence?
Explanation: Subtracting 1 from each term yields prime numbers: 13, 17, 19, 23, 29, 31. The next prime is 37, so the corresponding term in the original sequence is 38.
One page is torn from a booklet whose pages are numbered in the usual manner starting from the first page as 1. The sum of the numbers on the remaining pages is 195. The torn page contains which of the following numbers?
Explanation: The sum of the first n natural numbers is n(n+1)/2. For n=20, the total is 210. The difference between 210 and 195 is 15, which must equal the sum of the two consecutive page numbers torn out. The pair that sums to 15 is 7 and 8.
Consider the following arrangement that has some missing letters: abab_b_bcb_dcdcded_d. The missing letters which complete the arrangement are
- a, b, c, d
- a, b, d, e
- a, c, c, e
- b, c, d, e
Explanation: The completed sequence follows the repeating patterns ababa, bcbcb, cdcdc, and deded. The missing letters that fit this structure are a, c, c, and e.
Let A3BC and DE2F be four-digit numbers where each letter represents a different digit greater than 3. If the sum of the numbers is 15902, then what is the difference between the values of A and D?
Explanation: Since C+F ends in 2 and each letter represents a distinct digit greater than 3, C must be 8 and F must be 4. With the carryover, B+2+1 ends in 0, so B=7. Then E+3+1 ends in 9, giving E=5. The remaining digits are 9 and 6, which sum to 15 for A+D. The difference between 9 and 6 is 3.
S1: There are not more than two figures on any page of a 51-page book. S2: There is at least one figure on every page. Are there more than 100 figures in that book? Which one of the following is correct in respect of the above Statements?
- Both S1 and S2 are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
- S1 alone is sufficient to answer the Question.
- S1 and S2 together are not sufficient to answer the Question.
- S2 alone is sufficient to answer the Question.
Explanation: Using S1 alone, the total number of figures could range from 0 to 102. Using S2 alone, the count could be any value from 51 upward. Even combined, the figures per page could be either 1 or 2, producing a total between 51 and 102. Because 102 is not definitively greater than 100, the statements together are insufficient.
A family of two generations consisting of six members P, Q, R, S, T and U has three males and three females. There are two married couples and two unmarried siblings. U is P's daughter and Q is R's mother-in-law. T is an unmarried male and S is a male. Which one of the following is correct?
- R is U's husband.
- R is S's wife.
- S is unmarried.
- None of the above
Explanation: Since Q is R's mother-in-law, Q belongs to the older generation and R is married into the family. With U being P's daughter and T an unmarried male, the two married couples are P-Q and S-R. Therefore, R is married to S.
If in a particular year 12th January is a Sunday, then which one of the following is correct?
- 15th July is a Sunday if the year is a leap year.
- 15th July is a Sunday if the year is not a leap year.
- 12th July is a Sunday if the year is a leap year.
- 12th July is not a Sunday if the year is a leap year.
Explanation: From January 12 to July 12 there are 181 days in a non-leap year, giving 6 odd days, which makes July 12 a Saturday. In a leap year, the extra day in February reduces the odd days to 0, making July 12 a Sunday.
A man walks down the backside of his house straight 25 meters, then turns to the right and walks 50 meters again; then he turns towards left and again walks 25 meters. If his house faces to the East, what is his direction from the starting point?
- South-East
- South-west
- North-East
- North-west
Explanation: The house faces East, so its backside points West. The man first walks 25 m West, then turns right toward North and walks 50 m, then turns left toward West and walks 25 m. His final displacement is 50 m North and 50 m West from the starting point, placing him in the North-west direction.
Statements: All numbers are divisible by 2. All numbers are divisible by 3. Conclusion-I: All numbers are divisible by 6. Conclusion-II: All numbers are divisible by 4. Which of the above Conclusions logically follows from the two given Statements?
- Only Conclusion-I
- Only Conclusion-II
- Neither Conclusion-I nor Conclusion-II
- Both Conclusion-I and Conclusion-II
Explanation: Any number divisible by both 2 and 3 must be divisible by 6, so the first conclusion follows. However, divisibility by 2 and 3 does not guarantee divisibility by 4, so the second conclusion does not follow.
Statements: All cats are black. Conclusion-I: All dogs are black. Conclusion-II: Some dogs are not black. Which of the above Conclusions logically follows from the two given Statements disregarding commonly known facts?
- Only Conclusion-I
- Only Conclusion-II
- Neither Conclusion-I nor Conclusion-II
- Both Conclusion-I and Conclusion-II
Explanation: The premise only establishes that all cats are black. It provides no information about dogs, so neither conclusion about dogs can be logically drawn.
A is 16th from the left end in a row of boys and V is 18th from the right end. Q is 11th from A towards the right and 3rd from V towards the right end. How many boys are there in the row?
- 40
- 41
- 42
- Cannot be determined due to insufficient data
Explanation: A has 15 boys to his left. Q is 11 positions to the right of A and 3 positions to the right of V, which places 7 boys between A and V and 2 boys between V and Q. With 14 boys to the right of Q, the total is 15 + 1 + 7 + 1 + 2 + 1 + 14 = 41.
S1: C is younger than D, but older than A and B. S2: D is the oldest. S3: A is older than B. Who among A, B, C and D is the youngest? Which one of the following is correct in respect of the above Statements and the Question?
- S1 alone is sufficient to answer the Question.
- S1 and S2 together are sufficient to answer the Question.
- S2 and S3 together are sufficient to answer the Question.
- S1 and S3 together are sufficient to answer the Question.
Explanation: S1 establishes that D is older than C, who is older than both A and B, but it does not rank A and B relative to each other. S3 states that A is older than B. Combining S1 and S3 yields the complete order D > C > A > B, making B the youngest.
How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4?
Explanation: Between 1 and 100 there are 19 integers containing the digit 4: 4, 14, 24, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 54, 64, 74, 84, and 94. Of these, 7 are divisible by 4: 4, 24, 40, 44, 48, 64, and 84. The remaining count is 19 - 7 = 12.
Let x, y be the volumes; m, n be the masses of two metallic cubes P and Q respectively. Each side of Q is two times that of P and mass of Q is two times that of P. Let u = m / x and v = n / y. Which one of the following is correct?
- u = 4v
- u = 2v
- v = u
- v = 4u
Explanation: Let the side of cube P be a. Then the side of cube Q is 2a, making its volume 8a^3 while P's volume is a^3. Since the mass of Q is twice that of P, substituting into the density formulas gives v * 8a^3 = 2 * u * a^3, which simplifies to u = 4v.
The average age of a teacher and three students is 20 years. If all the three students are of same age and the difference between the age of the teacher and each student is 20 years, then what is the age of the teacher?
- 25 years
- 30 years
- 35 years
- 45 years
Explanation: Let the teacher's age be T and each student's age be a. The average gives (T + 3a)/4 = 20, so T + 3a = 80. The age difference gives T - a = 20. Solving these equations simultaneously yields a = 15 and T = 35.
A person bought a car and sold it for Rs. 3,00,000. If he incurred a loss of 20%, then how much did he spend to buy the car?
- Rs. 3,60,000
- Rs. 3,65,000
- Rs. 3,70,000
- Rs. 3,75,000
Explanation: When the selling price is Rs. 3,00,000 with a 20% loss, the cost price is calculated as (100 / 80) * 3,00,000 = Rs. 3,75,000.
Passage: In India, over the last decade or so, labour has been departing agriculture, but is only going to construction and unregistered manufacturing which are not markedly better jobs. Services, where labour tends to be most productive, are not generating the additional jobs the country needs. India will need 24 million or so jobs over the next decade. The new sector, e-commerce, can at best close only half the jobs gap. Only those sectors that drive domestic demand such as health and education can comfortably fill the other half.
Which one of the following is best implied in the passage?
- Strong measures need to be taken to reduce the rural to urban migration of labour.
- The working condition in construction and unregistered manufacturing needs to be improved.
- Service sector has been reducing the problem of unemployment.
- Increased social sector spending is imperative for large-scale job creation.
Explanation: The passage states that services are not generating enough jobs and e-commerce can only fill half the gap. It concludes that only domestic demand sectors such as health and education can provide the remaining jobs, implying that substantial investment in these social sectors is necessary.
Passage: In India, the current focus on the right to privacy is based on some new realities of the digital age. A right is a substantive right only if it works in all situations, and for everyone. A right to free expression for an individual about her exploitation, for instance, is meaningless without actual availability of security that guarantees that private force cannot be used to thwart this right. The role of the State, therefore, is not just to abstain from preventing rightful free expression, but also to actively ensure that private parties are not able to block it.
On the basis of the above passage, the following assumptions have been made: 1. State should have some institutions to ensure its appropriate role in a digital society. 2. State should ensure that private parties do not violate the citizens' right to privacy. 3. Digital economy is not compatible with the idea of not violating the citizens' privacy. Which of the above assumptions is/are valid?
- 1 and 2
- 3 Only
- 1 and 3
- 2 only
Explanation: The passage argues that the state must actively ensure private parties do not block rights, which supports the assumption that institutions are needed for this role and that the state should prevent privacy violations by private parties. The passage does not claim that the digital economy is inherently incompatible with privacy, so the third assumption is not valid.
Passage: One of the biggest ironies around water is that it comes from rivers and other wetlands. Yet it is seen as divorced from them. While water is used as a resource, public policy does not always grasp that it is a part of the natural ecosystem. Efforts at engineering water systems are thus efforts at augmenting water supply rather than strengthening the capacities of ecological systems.
Which one of the following is the most logical and rational inference that can be made from the above passage?
- Rivers and other wetlands should be protected under Ramsar Convention.
- Engineering water systems should be modernized and further augmented.
- Wetlands need to be reinforced as more than just open sources or water.
- Water supply should not be free of cost so as to prevent its misuse or overuse.
Explanation: The passage criticizes the disconnect between water policy and the ecological systems that produce it, arguing that engineering focuses only on supply augmentation. It therefore implies that wetlands must be valued beyond mere water sources and their ecological capacity strengthened.
Passage: Asset allocation is the most important investment decision we will ever make, and sadly, most of us do not give that decision the importance it deserves. We are adamant about seeking predictability with our future. We tend to think of investing in risky assets as extremely volatile and value eroding. We also dislike fluctuating returns and the loss of control of investment. We think our money is best left idle unproductive but safe. There is no asset that is risk-free. We could lose our jobs, our homes can lose value, our banks can go bankrupt, our bonds can default, the government can collapse and companies we chose fondly may cease to exist. But we cannot live life assuming that all these extreme events are waiting to happen, and all at the same time. All these extreme forms or risks we know will not manifest at the same time.
Which one of the following statements best implies the suggestion given by the author of the passage?
- Distribute your wealth across different kinds of assets so that your risks would be minimized.
- Risk-taking behaviour should be a necessary component of your Personality if you want to generate wealth.
- While making investments, find a trustworthy asset management organization which would manage your wealth for you.
- You should know that investing your money is a risky business.
Explanation: The author stresses that no single asset is risk-free, yet extreme risks are unlikely to occur simultaneously. The logical suggestion is to spread investments across different asset classes so that losses in one may be offset by stability in others, thereby minimizing overall risk.
Passage: Although most of the Genetically Modified (GM) crops cultivated now are genetically engineered for a single trait, in future, crops genetically engineered for more than one trait will be the norm. Thus, biotechnology's role in agriculture and the regulation or the same cannot be understood solely in the context of the current generation of GM crops. Instead, there is a need to take a comprehensive look, taking into account various aspects, including socio-economic impacts, so that the potential or the technology can be harnessed while minimizing negative impacts. Given the importance of biotechnology in developing varieties that can help in climate change mitigation and adaptation, not using biotechnology as a part of the climate change action plan cannot be an option. Domestic regulation of biotechnology cannot be viewed in isolation of trade policy and obligations under various international treaties and conventions.
With reference to the above passage, the following assumptions have been made: 1. Biotechnology regulation is an evolving process. 2. Participation of people is needed in policy decisions regarding biotechnology regulation. 3. Biotechnology regulation should take into account socio-economic aspects in decision-making. 4. Wider involvement of political executive in biotechnology regulation improves its effectiveness in dealing with the country's trade policies and international obligations. Which of the above assumptions are valid?
- 1, 2 and 4 only
- 1 and 3 only
- 2, 3 and 4 only
- 1, 2, 3 and 4
Explanation: The passage describes biotechnology as constantly evolving, supports a comprehensive approach including socio-economic factors, and links regulation to trade policy and international obligations requiring political involvement. All four assumptions are therefore valid.
Passage: Although most of the Genetically Modified (GM) crops cultivated now are genetically engineered for a single trait, in future, crops genetically engineered for more than one trait will be the norm. Thus, biotechnology's role in agriculture and the regulation or the same cannot be understood solely in the context of the current generation of GM crops. Instead, there is a need to take a comprehensive look, taking into account various aspects, including socio-economic impacts, so that the potential or the technology can be harnessed while minimizing negative impacts. Given the importance of biotechnology in developing varieties that can help in climate change mitigation and adaptation, not using biotechnology as a part of the climate change action plan cannot be an option. Domestic regulation of biotechnology cannot be viewed in isolation of trade policy and obligations under various international treaties and conventions.
Which one of the following statements best implies the crux of the passage?
- Precautionary principle is not given importance in current debate on developing GM crops.
- Biotechnology is not currently used in climate change mitigation and adaptation mechanisms.
- Biotechnology's role is not confined to the current priorities of developing GM crops.
- The negative Impacts of not biotechnology are properly understood.
Explanation: The passage emphasizes that biotechnology's present application in single-trait GM crops does not define its full potential. It must also address climate change, socio-economic impacts, and trade policy, indicating its role extends far beyond current GM crop development.
How many zeroes are there at the end of the following product? 1 × 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 × 55 × 60
Explanation: The product contains six factors of 10, eight factors of 5, and four factors of 2. The six 10s contribute six trailing zeroes. The remaining four 2s pair with four of the eight 5s to produce four additional zeroes. The total number of trailing zeroes is 6 + 4 = 10.
Let XYZ be a three-digit number, where (X + Y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by
Explanation: Expanding the three numbers gives XYZ + YZX + ZXY = 111(X + Y + Z) = 3 * 37 * (X + Y + Z). Because (X + Y + Z) is not a multiple of 3, the entire expression lacks the second factor of 3 needed for divisibility by 9, though it remains divisible by 3, 37, and (X + Y + Z).
Let p, q, r and s be natural numbers such that p - 2016 = q + 2017 = r - 2018 = s + 2019. Which one of the following is the largest natural number?
Explanation: From the given equalities, p - q = 4033 and r - q = 4035, which means r > p > q. Also, r - s = 4037, so r > s. Therefore, r is the largest of the four natural numbers.
How many five-digit prime numbers can be obtained by using all the digits 1, 2, 3, 4 and 5 without repetition of digits?
Explanation: The sum of the digits 1, 2, 3, 4, and 5 is 15, which is divisible by 3. Therefore, any five-digit number formed using these digits without repetition will be divisible by 3 and cannot be prime.
Passage: Private investment in general is volatile. Foreign private investment is more volatile because the available investment avenues are significantly greater (i.e., the entire world). Therefore, the responsibility of providing employment cannot be left to Foreign Direct investment (FDI). The current FDI inflows are volatile over time and across sectors and regions, which is a necessary consequence of their search for the highest returns. The adverse consequences are unstable employment and an accentuation of income and regional inequalities. A probable positive consequence of foreign investment is the inflow of new technology and its subsequent diffusion. However, the technology diffusion is not at all certain because the existing state of physical and human capital in India may prove inadequate for the diffusion.
With reference to the above passage, the following assumptions have been made: 1. Relying on foreign investment in the long run is not an economically sound policy. 2. Policies must be undertaken to reduce volatility in foreign private investment. 3. Policies must be undertaken to strengthen domestic private investment. 4. Public investment should be given priority over private investment. 5. Substantial public investment in education and health should be undertaken. Which of the above assumptions is/are valid?
- 1, 2 and 4
- 1, 3 and 5
- 2, 4 and 5
- 3 only
Explanation: The passage argues that employment generation cannot rely on FDI due to its inherent volatility, making long-term dependence on foreign investment unsound. It also notes that India's human capital deficiencies hinder technology diffusion, implying a need for public investment in education and health. While strengthening domestic investment is supported, reducing FDI volatility is deemed impossible because it is a necessary consequence of market behavior, and no comparison between public and private investment priority is made.
Passage: Many opportunities to harness the highly skewed, seasonal and spatial distribution of monsoon flows, which occur in a four-month period from June to September annually, have been lost. Since these few months account for most or the rainfall and consequent freshwater availability, the need for holding rainwater in reservoirs, for subsequently releasing it for use over the year, is a necessity nobody can afford to overlook. Climate change will continue to affect weather conditions and create water shortages and excesses. While millions suffer from droughts and floods, waters in the country's many rivers flow unutilized, and are discharged into the sea every year.
With reference to the above passage, which of the following could be the most rational and practical implications for India? 1. Inter-linking of rivers should be undertaken. 2. A network of dams and canals should be built across the country for proper distribution of water. 3. Farmers should be provided easy loans for digging borewells. 4. Usage of water for agriculture should be regulated by law. 5. Distribution of river water among regions should be regulated by the Union Government.
- 1 and 2
- 2, 4 and 5
- 1, 3 and 4
- 2, 3 and 5
Explanation: The passage highlights the loss of monsoon runoff into the sea and the need for reservoir storage. Inter-linking rivers can redistribute surplus water to deficit regions, while a dam and canal network can capture and distribute seasonal flows. Borewell loans and legal regulation of usage are not discussed in the passage.
Passage: People will invest in education whenever they are granted the economic freedom to fully enjoy benefits Again, this is for the obvious reason that the return on education increases as the level of economic freedom rises. When people, thanks to lower tax rates, are allowed to retain of the higher income that they gain from incremental level of education, it makes sense to invest in education. On the other hand, when the government decides to tax the higher income of educated individuals at even higher rates, it makes very little sense to invest in educating oneself further. The same incentives apply to parents who decide on whether to invest in their children's education.
With reference to the above passage, the following assumptions have been made: 1. Lower tax rates in a country invariably translate into greater investments in higher education. 2. Investment in the education of children ensures their economic freedom. 3. Economic freedom has a positive impact on building up human capital. Which of the above assumptions is/are valid?
- 1 only
- 2 only
- 3 only
- 1, 2 and 3
Explanation: The passage links lower tax rates to higher returns on education, supporting the assumption that reduced taxation encourages educational investment. It does not state that educating children guarantees their economic freedom, nor does it mention human capital, so the other two assumptions are not valid.
Passage: Our urban bodies cannot possibly ensure sustainable delivery of water in our cities unless financing mechanisms are put in place. Water delivery requires heavy investment in collecting it from a natural source, treating it to make it potable, and laying a distribution network of pipes for delivery to the users. It also requires investments in sewerage infrastructure and sewage treatment plants so that the sewers can carry the wastewater to these plants to ensure that no untreated sewage is discharged back into natural water bodies. If our cities were rich enough to meet the entire cost, water could be delivered free. They are not.
What is the most logical and crucial message conveyed by the passage?
- Urban local bodies must recover costs through user charges.
- Urban local bodies are not efficient enough to meet the water requirements of our cities.
- Water shortage in our cities is a perennial problem that cannot be solved.
- In view of the water crisis in our cities, there is an urgent need to limit the population of cities by adopting an upper limit of population size.
Explanation: The passage emphasizes the heavy investment required for water delivery and sewerage, and notes that cities are not rich enough to bear the entire cost. Therefore, the crucial message is that user charges must be used to recover costs and ensure sustainable delivery.
Passage: Our urban bodies cannot possibly ensure sustainable delivery of water in our cities unless financing mechanisms are put in place. Water delivery requires heavy investment in collecting it from a natural source, treating it to make it potable, and laying a distribution network of pipes for delivery to the users. It also requires investments in sewerage infrastructure and sewage treatment plants so that the sewers can carry the wastewater to these plants to ensure that no untreated sewage is discharged back into natural water bodies. If our cities were rich enough to meet the entire cost, water could be delivered free. They are not.
With reference to the above passage, the following assumptions have been made: 1. Rich cities only can ensure sustainable delivery of water. 2. Sustainable delivery of water in cities means much more than supplying water to households. Which of the above assumptions is/are valid?
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Explanation: The passage mentions that rich cities could supply water for free, but it does not claim that only rich cities can ensure sustainable delivery. It does describe sustainable delivery as encompassing sewerage and treatment infrastructure beyond mere household supply, so the second assumption is valid.
Passage: In India, agriculture still engages about half of workforce, and about 85 per cent of its farms small and marginal. Compared to China Vietnam, which have experienced fast structural and rural transformation, India's story is of slow transformation. As a result, poverty reduction in India was at a much slower pace during 1988-2014, compared to China and Vietnam. India's poverty reduction was slow during 1988-2005, but during 2005-2012, it accelerated dramatically-almost three times faster than during the earlier period. What did India do during this period? Research reveals that the relative price scenario changed significantly (by more than 50%) in favour of agriculture in the wake of rising global prices. This boosted private investments in agriculture by more than 50%. As a result, agri-GDP growth touched 4.1% during 2007-2012 as against 2.4% during 2002-2007. The net surplus or agri-trade touched $25 billion in 2013-2014: real farm wages rose by 7% per annum. All this led to unprecedented fall in poverty.
With reference to the above passage, the following assumptions have been made: 1. Structural and rural transformation is impossible when farms are mainly small and marginal. 2. A good price incentive can trigger investments in agriculture. 3. India needs to build value chains for high-value agri-products like livestock and horticulture. 4. Higher global prices of agricultural commodities are essential for India's poverty reduction. Which of the above assumptions are valid?
- 1 and 3
- 2 and 4
- 2 and 3
- 3 and 4
Explanation: The passage explicitly links favorable price incentives to increased agricultural investment and notes that rising global prices boosted farm incomes and reduced poverty. It does not claim that transformation is impossible with small farms, nor does it mention value chains for livestock or horticulture.
Passage: In India, agriculture still engages about half of workforce, and about 85 per cent of its farms small and marginal. Compared to China Vietnam, which have experienced fast structural and rural transformation, India's story is of slow transformation. As a result, poverty reduction in India was at a much slower pace during 1988-2014, compared to China and Vietnam. India's poverty reduction was slow during 1988-2005, but during 2005-2012, it accelerated dramatically-almost three times faster than during the earlier period. What did India do during this period? Research reveals that the relative price scenario changed significantly (by more than 50%) in favour of agriculture in the wake of rising global prices. This boosted private investments in agriculture by more than 50%. As a result, agri-GDP growth touched 4.1% during 2007-2012 as against 2.4% during 2002-2007. The net surplus or agri-trade touched $25 billion in 2013-2014: real farm wages rose by 7% per annum. All this led to unprecedented fall in poverty.
Which one of the following statements best reflects the critical message of the passage?
- India should create large-scale off-farm rural employment to reduce poverty in the near future.
- India should create a large number of farmer producer companies
- Private investment in agriculture should be given priority over public investment.
- Inclusive agricultural growth is key to reduce poverty in the near future.
Explanation: The passage correlates accelerated agricultural GDP growth with faster poverty reduction, emphasizing that agricultural growth is the key driver of poverty alleviation. It does not discuss off-farm employment, producer companies, or prioritizing private over public investment.
S1: R is greater than P as well as Q. S2: S is not the largest one. Among four numbers P, Q, R and S which one is the largest? Which one of the following is correct in respect of the above Statements and the Question?
- S1 alone is sufficient to answer the Question.
- S2 alone is sufficient to answer the Question.
- S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
- S1 and S2 together are not sufficient to answer the Question.
Explanation: S1 alone establishes R is greater than P and Q but does not compare R with S. S2 alone only eliminates S without ranking the others. Together, S2 eliminates S and S1 establishes R is greater than both P and Q, making R the largest.
S1: n is a prime number. S2: n leaves a remainder of 1 when divided by 4. If n is a unique natural number between 10 and 20, then what is n? Which one of the following is correct in respect of the above Statements and the Question?
- S1 alone is sufficient to answer the Question.
- S2 alone is sufficient to answer the Question.
- S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
- S1 and S2 together are not sufficient to answer the Question.
Explanation: S1 yields four primes between 10 and 20: 11, 13, 17, 19. S2 yields two candidates: 13 and 17. Even when combined, both 13 and 17 satisfy both conditions, so n cannot be uniquely determined.
S1: Their product is 21. S2: Their sum is 10. What are the two numbers? Which one of the following is correct in respect of the above Statements and the Question?
- S1 alone is sufficient to answer the Question.
- S2 alone is sufficient to answer the Question.
- S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
- S1 and S2 together are not sufficient to answer the Question.
Explanation: S1 alone allows multiple pairs such as (3,7) or (1.5,14). S2 alone allows many pairs summing to 10. Together they yield the quadratic a^2 - 10a + 21 = 0, giving the unique solution {3, 7}.
What is the greatest length x such that 3 1/2 m and 8 3/4 m are integral multiples of x?
- 1 1/2 m
- 1 1/3 m
- 1 1/4 m
- 1 3/4 m
Explanation: This requires finding the highest common factor of 7/2 and 35/4. Converting to quarters gives 14/4 and 35/4. The HCF of 14 and 35 is 7, so the result is 7/4 = 1 3/4 m.
The recurring decimal representation 1.272727... is equivalent to
- 13/11
- 14/11
- 127/99
- 137/99
Explanation: Let x = 1.272727... Then 100x = 127.272727... Subtracting the first equation from the second gives 99x = 126, so x = 126/99 = 14/11.
What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case?
Explanation: The LCM of 3, 4, 5, and 6 is 60. The least four-digit multiple of 60 is 1020. Adding the required remainder 2 gives 1022.
In adult population of a city, 40% men and 30% women are married. What is the percentage of married adult population if no man marries more than one woman and no woman marries more than one man; and there are no widows and widowers?
Explanation: Since the number of married men equals the number of married women, 0.4M = 0.3W, giving M/W = 3/4. Assuming 300 men and 400 women, there are 120 married couples. The married percentage is 240/700 = 24/7 % = 34 2/7 %.
What is the remainder when 51 × 27 × 35 × 62 × 75 is divided by 100?
Explanation: The remainder when dividing by 100 is determined by the last two digits of the product. Computing stepwise: 51×27=1377, ×35=48195, ×62=2988090, ×75=224106750. The final two digits are 50, so the remainder is 50.
A sum of Rs. 2,500 is distributed among X, Y and Z in the ratio 1/2 : 3/4 : 5/6. What is the difference between the maximum share and the minimum share?
- Rs. 300
- Rs. 350
- Rs. 400
- Rs. 450
Explanation: Multiplying the ratio by 12 to clear denominators gives 6:9:10. The total parts are 25, so each part equals 100. The shares are Rs. 600, 900, and 1000. The difference between the maximum and minimum is 1000 - 600 = 400.
For what value of n, the sum of digits in the number (10^n + 1) is 2?
- For n=0 only
- For any whole number n
- For any positive integer n only
- For any real number n
Explanation: For n=0, 10^0+1=2 with digit sum 2. For any positive whole number n, 10^n is a 1 followed by n zeros, so 10^n+1 has digits 1, 0...0, 1, whose sum is 2. This does not hold for non-integer real numbers.
In a class, there are three groups A, B and C. If one student from group A and two students from group B are shifted to group C, then what happens to the average weight of the students of the class?
- It increases.
- It decreases.
- It remains the same.
- No conclusion can be drawn due to insufficient data.
Explanation: The total number of students and the total weight of the class remain unchanged because students are only moved between groups within the same class. Therefore the overall average weight stays the same.
How many different sums can be formed with the denominations Rs. 50, Rs. 100, Rs. 200, Rs. 500 and Rs. 2,000 taking at least three denominations at a time?
Explanation: The number of ways to choose at least 3 denominations from 5 is C(5,3) + C(5,4) + C(5,5) = 10 + 5 + 1 = 16. Each combination produces a unique sum because the denominations are distinct.
A person X can complete 20% of work in 8 days and another person Y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?
Explanation: X completes full work in 40 days (rate 1/40 per day). Y completes full work in 24 days (rate 1/24 per day). Combined rate is 1/40 + 1/24 = 1/15 per day. To complete 40% of the work: 0.4 / (1/15) = 6 days.
A car travels from a place X to place Y at an average speed of v km/hr, from Y to X at an average speed of 2v km/hr, again from X to Y at an average speed of 3v km/hr and again from Y to X at an average speed of 4v km/hr. Then the average speed of the car for the entire journey
- is less than v km/hr
- lies between v and 2v km/hr
- lies between 2v and 3v km/hr
- lies between 3v and 4v km/hr
Explanation: For equal distances, average speed equals total distance divided by total time. Let distance be a. Total distance = 4a. Total time = a/v + a/2v + a/3v + a/4v = 25a/12v. Average speed = 4a / (25a/12v) = 48v/25 = 1.92v, which lies between v and 2v.
Consider the following statements: 1. The minimum number of points of intersection of a square and a circle is 2. 2. The maximum number of points of intersection of a square and a circle is 8. Which of the above statements is/are correct?
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Explanation: A circle can intersect a square at a minimum of 2 points (entering and exiting through one side) and at a maximum of 8 points (crossing each of the four sides twice).
A man takes half time in rowing a certain distance downstream than upstream. What is the ratio of the speed in still water to the speed of current?
Explanation: Let speed in still water be s and current speed be c. Downstream speed is s+c and upstream is s-c. Since downstream time is half the upstream time for the same distance, s+c = 2(s-c). Solving gives s = 3c, so the ratio s:c is 3:1.
How many pairs of natural numbers are there such that the difference of whose squares is 63?
Explanation: Let a^2 - b^2 = 63, so (a+b)(a-b) = 63. The factor pairs of 63 are (63,1), (21,3), and (9,7). Solving each gives the pairs (32,31), (12,9), and (8,1). Thus there are exactly 3 pairs.
Which one of the following will have minimum change in its value if s is added to both numerator and the denominator of the fractions 2/3, 3/4, 4/5 and 5/6?
Explanation: Adding the same positive number to both numerator and denominator brings a fraction closer to 1. Therefore the fraction already closest to 1, which is 5/6, experiences the smallest relative change.
A digit n > 3 is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4?
Explanation: The only digit greater than 3 that is divisible by 3 but not by 6 is 9. Substituting n=9 gives 2n=18, 3n=27, 2n+4=22, and 3n+1=28. Only 28 is divisible by 4.
If 1 litre of water weighs 1 kg, then how many cubic millimeters of water will weigh 0.1 gm?
Explanation: Since 1 litre equals 10^6 cubic millimeters and weighs 1000 grams, 1 gram equals 1000 cubic millimeters. Therefore 0.1 gram equals 100 cubic millimeters.
A vessel full of water weighs 40 kg. If it is one-third filled, its weight becomes 20 kg. What is the weight of the empty vessel?
Explanation: Let vessel weight be v and full water weight be w. Then v + w = 40 and v + w/3 = 20. Subtracting gives 2w/3 = 20, so w = 30 kg. Substituting back yields v = 10 kg.
A frog tries to come out of a dried well 4.5 m deep with slippery walls. Every time the frog jumps 30 cm, slides down 15 cm. What is the number of jumps required for the frog to come out of the well?
Explanation: Each jump the frog gains a net 15 cm. After 28 jumps it reaches 420 cm. On the 29th jump it leaps 30 cm to reach 450 cm (4.5 m) and exits without sliding back.
Passage: India is at once among the fastest growing global economies and home to the largest number of malnourished children in the world. There are regions where malnutrition is not the exception but the norm. And across the country, malnutrition is the cause of death for roughly half the 1-3 million children who die before their fifth birthday each year. Even those children who survive suffer permanently from the damage that has already been done to their bodies and minds from not getting enough of the right foods and nutrients. Around 44 million children under 5 are stunted. That makes it harder for them to learn in school and subsequently earn a living as adults. Their lifetime earnings potential is almost a quarter less than that of their healthy peers.
With reference to the above passage, which of the following is/are the most rational and practical implication/Implications? 1. India's Public Distribution System should be monitored by the Union Government. 2. Girls should be encouraged to delay marriage and first pregnancy. 3. Mothers should be encouraged to breastfeed their children immediately after birth. 4. The supply of safe drinking water and proper sanitation facilities to all should be ensured. 5. Authorities should ensure the vaccination as prescribed.
- 1, 2, 3 and 4
- 2, 3, 4 and 5
- 1 only
- 3 and 5 only
Explanation: The passage focuses exclusively on malnutrition as a food supply problem. Only a monitored Public Distribution System directly addresses ensuring food access. Vaccination, water, sanitation, and breastfeeding are not discussed in the passage.
Passage: The pulse variety 'Pusa Arhar 16' has the potential to be grown in the paddy-growing of Punjab, Haryana and Uttar Pradesh and eventually in all of India. Its yield (about 2000 kg/hectare) will be significantly greater than those of the existing varieties and because its size will be uniform, it will be amenable to mechanical harvesting, an attractive feature for farmers in northern India who currently use this technology for paddy. Most important, Arhar straw, unlike paddy straw, is green and can be ploughed back into the soil. In Paddy straw, the problem is the high silica content, which does not allow for easy decomposition. In the case of Arhar, the farmer, even after combine harvesting, just needs to run a rotovator to cut the leftover straw into pieces, which can be ploughed back and will decompose very fast. All this is difficult with leftover paddy stalks that cannot be easily salvaged or ploughed back. Farmers, therefore, choose the easiest option of simply burning it.
Which of the following are the most rational inferences that can be made from the passage? 1. Farmers' income will be higher with pulse cultivation than with paddy cultivation. 2. Pulse cultivation causes less pollution as compared to paddy cultivation. 3. Pulse straw can be used to improve soil quality. 4. In the context of northern Indian agriculture, paddy straw has no usefulness. 5. Mechanized agriculture is the main cause for stubble burning.
- 2, 3 and 5
- 1, 4 and 5
- 2 and 3 only
- 1 and 4 only
Explanation: The passage states that Arhar straw decomposes easily and can be ploughed back, unlike paddy straw which is burned, supporting inferences 2 and 3. It does not directly compare farmer incomes, claim paddy straw is entirely useless, or identify mechanization as the main cause of burning.
Passage: In India, authorities always look to store the maximum amount of water in reservoirs during the monsoon season, which is then used for irrigation and generation of electricity during the summer months. It is an internationally accepted practice that the water level of a reservoir should be kept below a certain level before the onset of monsoon season. This is so that when monsoon rains come, there is space to store the excess rainwater and also so that water can be released in a regulated manner. But the authorities store the maximum amount of water in reservoirs even before the close of the monsoon, only to ensure greater electricity generation and irrigation.
With reference to the above passage, the following assumptions have been made: 1. High risks involved in holding maximum water in reservoirs are due to our over-dependence on hydro power projects. 2. Storage capacity of dams should not be fully used before or during monsoon season. 3. Role of dams in flood control is underestimated in India. Which of the above assumptions is/are valid?
- 1 and 2 only
- 2 only
- 3 only
- 1, 2 and 3
Explanation: The passage criticizes filling reservoirs before the monsoon ends, which implies that their role in absorbing excess rainwater and controlling floods is underestimated. It does not attribute this practice to over-dependence on hydro power, and statement 2 is contradicted because reservoirs must indeed be used during monsoon to store excess rainwater.
Passage: Economic liberalization in India was shaped largely by the economic problems of the government than by the economic priorities of the people or by the long-term development objectives. Thus, there were limitations in conception and design which have been subsequently validated by experience. Jobless growth, persistent poverty and rising inequality have mounted as problems since economic liberalization began. And all these years later, four quiet crises confront the economy: agriculture infrastructure, industrialization and education as constraints on the country's future prospects. These problems must be resolved if economic growth has to be sustained and transformed into meaningful development.
Which of the following is/are the most rational and logical Inference/Inferences that can be made from the passage? 1. It is essential to rethink and redefine the economic role of the state in the quest for development. 2. India has not made effective implementation of its policies in social sectors nor made sufficient investments in them.
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Explanation: The passage attributes current problems to the conception and design of liberalization rather than implementation failures. It implies that the state's economic role needs rethinking for meaningful development, but does not specifically fault implementation or underinvestment in social sectors.