Basic Numeracy
There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the correct address. If the letters are randomly inserted into the envelopes, then consider the following statements:
1. It is possible that exactly one letter goes into an incorrect envelope.
2. There are only six ways in which only two letters can go into the correct envelopes.
Which of the statements given above is/are correct?
Three of the five positive integers p, q, r, s, t are even and two of them are odd (not necessarily in order). Consider the following :
1. p + q + r - s - t is definitely even.
2. 2p + q + 2r - 2s + t is definitely odd.
Which of the above statements is/are correct?
Consider the following in respect of prime number p and composite number c.
1. $\frac{\mathrm{p}+\mathrm{c}}{\mathrm{p}-\mathrm{c}}$ can be even.
2. 2p + c can be odd.
3. pc can be odd.
Which of the statements given above are correct?
A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so on. Consider the following statements:
1. The work will be finished on Thursday.
2. The work will be finished in 10 days.
Which of the above statements is/are correct?
A box contains 14 black balls, 20 blue balls, 26 green balls, 28 yellow balls, 38 red balls and 54 white balls. Consider the following statements:
1. The smallest number n such that any n balls drawn from the box randomly must contain one full group of at least one colour is 175.
2. The smallest number m such that any m balls drawn from the box randomly must contain at least one ball of each colour is 167.
Which of the above statements is/are correct?
Let pp, qq and rr be 2-digit numbers where p < q < r. If pp + qq + rr = tt0, where tt0 is a 3-digit number ending with zero, consider the following statements :
1. The number of possible values of p is 5.
2. The number of possible values of q is 6.
Which of the above statements is/are correct?
Question: Is (p + q - r) greater than (p - q + r), where p, q and r are integers ?
Statement-1: (p - q) is positive.
Statement-2: (p - r) is negative.
Which one of the following is correct in respect of the above Question and the Statements?
In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee. No one taking milk takes tea. Each person takes at least one drink.
Question: How many persons attended the party?
Statement-1: 50 persons took milk.
Statement-2: Number of persons who attended the party is five times the number of persons who took milk only.
Which one of the following is correct in respect of the above Question and the Statements?
Consider a 3-digit number.
Question: What is the number?
Statement-1: The sum of the digits of the number is equal to the product of the digits.
Statement-2: The number is divisible by the sum of the digits of the number.
Which one of the following is correct in respect of the above Question and the Statements?
For five children with ages a < b < c < d < e; any two successive ages differ by 2 years.
Question: What is the age of the youngest child ?
Statement-1: The age of the eldest is 3 times the youngest.
Statement-2: The average age of the children is 8 years.
Which one of the following is correct in respect of the above Question and the Statements?
There are large number of silver coins weighing 2 gm, 5 gm, 10 gm, 25 gm, 50 gm each. Consider the following statements:
1. To buy 78 gm of coins one must buy at least 7 coins.
2. To weigh 78 gm using these coins one can use less than 7 coins.
Which of the statements given above is/are correct?
A cuboid of dimensions 7 cm × 5 cm × 3 cm is painted red, green and blue colour on each pair of opposite faces of dimensions 7 cm × 5 cm, 5 cm × 3 cm, 7 cm × 3 cm respectively. Then the cuboid is cut and separated into various cubes each of side length 1 cm. Which of the following statements is/are correct ?
1. There are exactly 15 small cubes with no paint on any face.
2. There are exactly 6 small cubes with exactly two faces, one painted with blue and the other with green.
Select the correct answer using the code given below:
Comprehension
Based on the above passage, the following assumptions have been made:
1. Collection, processing and segregation of municipal waste should be with government agencies.
2. Resource recovery and recycling require technological inputs that can be best handled by private sector enterprises.
Which of the assumptions given above is/are correct?
Based on the above passage, the following assumptions have been made:
1. Organic farming is inherently unsafe for both farmers and consumers.
2. Farmers and consumers need to be educated about eco-friendly food.
Which of the assumptions given above is/are correct ?
Food consumption patterns have changed substantially in India over the past few decades. This has resulted in the disappearance of many nutritious foods such as millets. While food grain production has increased over five times since independence, it has not sufficiently addressed the issue of malnutrition. For long, the agriculture sector focussed on increasing food production particularly staples, which led to lower production and consumption of indigenous traditional crops/grains, fruits and other vegetables, impacting food and nutrition security in the process. Further, intensive, monoculture agriculture practices can perpetuate the food and nutrition security problem by degrading the quality of land, water and food derived through them.
Based on the above passage, the following assumptions have been made:
1. To implement the Sustainable Development Goals and to achieve zero-hunger goal, monoculture agriculture practices are inevitable even if they do not address malnutrition.
2. Dependence on a few crops has negative consequences for human health and the ecosystem.
3. Government policies regarding food planning need to incorporate nutritional security.
4. For the present monoculture agriculture practices, farmers receive subsidies in various ways and government offers remunerative prices for grains and therefore they do not tend to consider crop diversity.
Which of the above assumptions are valid?
Scientists studied the vernal window transition period from winter to the growing season. They found that warmer winters with less snow resulted in a longer lag time between spring events and a more protracted vernal window. This change in the spring timetable has ecological, social and economic consequences for agriculture, fisheries and tourism. As the ice melts earlier, the birds don't return, causing a delay, or lengthening in springtime ecological events.
With reference to the above passage, the following assumptions have been made:
1. Global warming is causing spring to come early and for longer durations.
2. Early spring and longer period of spring is not good for bird populations.
Which of the above assumptions is/are correct?
A global analysis of nitrogen use efficiency a measure of the amount of nitrogen a plant takes in to grow versus what is left behind as pollution says that using too much fertilizers will lead to increased pollution of waterways and the air. Currently, the global average for nitrogen use efficiency is approximately 0.4, meaning 40 per cent of the total nitrogen added to cropland goes into the harvested crop while 60 per cent is lost to the environment, says a study. More than half of the world's population is nourished by food grown with fertilizers containing synthetic nitrogen, which is needed to produce high crop yields. Plants take the nitrogen they need to grow, and the excess is left in the ground, water and air. This results in significant emissions of nitrous oxide, a potent greenhouse and ozone depleting gas, and other forms of nitrogen pollution, including eutrophication of lakes and rivers and contamination of river water.
Which one of the following statements best reflects the most logical, rational and crucial message implied by the passage?
Along with sustainable lifestyles, climate justice is regarded as a significant principle in environmental parlance. Both the principles have bearings on political and economic choices of the nation. So far, in our climate change summits or compacts, both the principles have eluded consensus among nations. Justice, in the judicial sense, is well defined. However, in the context of climate change, it has scientific as well as socio-political connotations. The crucial question in the next few years will be how resources, technologies and regulations are used to support the victims of climate change. Justice in climate is not confined to actions relating to mitigation, but includes the wider notion of support for adaptation to climate change and compensation for loss and damage.
Which one of the following statements best reflects the most logical, rational and crucial message conveyed by the passage?
Sourcing food from non-agricultural lands (uncultivated systems such as forests, wetlands, pastures, etc) in addition to agricultural lands enables a systemic approach to food consumption. It allows rural and tribal communities to sustain themselves for the whole year and steer clear of natural disasters and season-induced shortfalls of agricultural food. Since the productivity of trees is often more resilient to adverse weather conditions than annual crops, forest foods often provide a safety net during periods of food shortages caused by crop failure; forest foods also make important contributions during seasonal crop production gaps.
Which one of the following statements best reflects the most logical and rational message conveyed by the author of the passage?
While awareness on use/misuse and abuse of antibiotics is common knowledge, as is the impact of dosing poultry with antibiotics, the environmental impact of antibiotics-manufacturing companies not treating their waste has scarcely been discussed at any length or seriousness thus far. Pollution from antibiotics factories is fuelling the rise of drug-resistant infections. The occurrence of drug-resistant bacteria surrounding the pharma manufacturing plants is well known.
Which one of the following statements best reflects the most logical and practical message conveyed by the passage?
Benefits of good quality school education accrue only when students complete and leave school after having acquired the gateway skills. Like one learns to walk before running, similarly one picks up advanced skills only after picking the basic foundational skills. The advent of the knowledge economy poses new challenges, and one of the severe consequences of having an uneducated workforce will be our inability to keep pace with the global economy. Without a strong learning foundation at the primary level, there can be no improvement in higher education or skill development.
Which one of the following statements best reflects the crux of the passage?
The paradox of choice is illustrated by the story of Buridan's ass. Jean Buridan, the 14th century philosopher, wrote about free will and the inability to choose due to numerous choices and uncertainties. In the story, a donkey stands between two equally appealing stacks of hay. Unable to decide which to eat, it starves to death. Changes in technology and innovations such as smart phones and tablets only exacerbate our glut of choices. Constant connectivity and overconsumption of real-time data and social media can leave little room for self-reflection and rest, making decisions more difficult. Life is about choices. Many people are overwhelmed with attractive life choices, yet find themselves unhappy and anxious.
Which one of the following statements best reflects the most logical message implied by the above passage?
Household finance in India is unique. We have a tendency to invest heavily in physical assets such as gold and property. Steps to encourage the financialization of savings are critical. A populace accustomed to traditional processes will not simply jump into financialization. Hurdles to change include onerous bureaucracy, a scepticism of organized financial institutions, a lack of basic information about which of the myriad basic information about which of the myriad services and providers is best for each family, and how (and even if) one can make the transition between them if necessary.
Regarding the financialization of household savings, which of the following statements best reflect the solutions that are implied by the passage?
1. A flexible environment is needed to develop solutions.
2. Households need customised solutions.
3. Innovations in financial technology are required.
Select the correct answer using the code given below:
Pharmaceutical patents grant protection to the patentee for the duration of the patent term. The patentees enjoy the liberty to determine the prices of medicines, which is time-limited to the period of monopoly, but could be unaffordable to the public. Such patent protection offered to the patentees is believed to benefit the public over the longer term through innovations and research and development (R&D), although it comes at a cost, in the nature of higher prices for the patented medicine. The patent regime and price protection - through a legally validated high price for the medicine during the currency of the patent - provide the patentee with a legitimate mechanism to get returns on the costs incurred in innovation and research.
Based on the above passage, the following assumptions have been made:
1. Patent protection given to patentees puts a huge burden on public's purchasing power in accessing patented medicines.
2. Dependence on other countries for pharmaceutical products is a huge burden for developing and poor countries.
3. Providing medicines to the public at affordable prices is a key goal during the public health policy design in many countries.
4. Governments need to find an appropriate balance between the rights of patentees and the requirements of the patients.
Which of the above assumptions are valid?
India should ensure the growth of the digital economy while keeping personal data of citizens secure and protected. No one will innovate in a surveillance-oriented environment or in a place where an individual's personal information is compromised. The ultimate control of data must reside with the individuals who generate it; they should be enabled to use, restrict or monetise it as they wish. Therefore, data protection laws should enable the right kind of innovation - one that is user-centric and privacy protecting.
Based on the above passage, the following assumptions have been made:
1. Protection of privacy is not just a right, but it has value to the economy.
2. There is a fundamental link between privacy and innovation.
Which of the above assumptions is/are valid?
In India, while the unemployment rate is a frequently used measure of poor performance of the economy, under conditions of rising school and college enrolment, it paints an inaccurate picture. The reported unemployment rate is dominated by the experience of younger Indians who face higher employment challenges and exhibit greater willingness to wait for the right job than their older peers. The unemployment challenge is greater for people with secondary or higher education, and rising education levels inflate unemployment challenges.
Which one of the following statements most likely reflects as to what the author of the passage intends to say?
"Science by itself is not enough, there must be a force and discipline outside the sciences to coordinate them and point to a goal. It is not possible to run a course aright when the goal itself has not been rightly placed. What science needs is philosophy the analysis of scientific method and the coordination of scientific purposes and results; without this, any science must be superficial. Government suffers, precisely like science, for lack of philosophy. Philosophy bears to science the same relationship which statesmanship bears to politics : movement guided by total knowledge and perspective, as against aimless and individual seeking. Just as the pursuit of knowledge becomes scholasticism when divorced from the actual needs of men and life, so the pursuit of politics becomes a destructive bedlam when divorced from science and philosophy."
Which one of the following statements best reflects the most rational, logical and practical message conveyed by the passage?
"The last end of the state is not to dominate men, nor to restrain them by fear; rather it is so to free each man from fear that he may live and act with full security and without injury to himself or his neighbour. The end of the state, I repeat, is not to make rational beings into brute beasts and machines. It is to enable their bodies and their minds to function safely. It is to lead men to live by, and to exercise, a free reason; that they may not waste their strength in hatred, anger and guile, nor act unfairly toward one another."
Based on the above passage, which one of the following terms best expresses the ultimate goal of the state?
Data Interpretation
Logical Reasoning and General Mental Ability
Consider the following statements :
1. A is older than B.
2. C and D are of the same age.
3. E is the youngest.
4. F is younger than D.
5. F is older than A.
How many statements given above are required to determine the oldest person/persons?
Consider the following including the Question and the Statements :
There are 5 members A, B, C, D, E in a family.
Question: What is the relation of E to B?
Statement-1: A and B are a married couple.
Statement-2: D is the father of C.
Statement-3: E is D's son.
Statement-4: A and C are sisters.
Which one of the following is correct in respect of the above Question and Statements?
What is the middle term of the sequence
Z, Z, Y, Y, Y, X, X, X, X, W, W, W, W, W ____, A?
Consider the following:
I. A + B means A is neither smaller nor equal to B.
II. A - B means A is not greater than B.
III. A × B means A is not smaller than B.
IV. A ÷ B means A is neither greater nor equal to B.
V. A ± B means A is neither smaller nor greater than B.
Statement: P × Q, P - T, T ÷ R, R ± S
Conclusion-1: Q ± T
Conclusion-2: S + Q
Which one of the following is correct in respect of the above Statement and the Conclusions?
Consider the sequence
ABC_ _ ABC_DABBCD_ABCD
that follows a certain pattern.
Which one of the following completes the sequence?
Consider the following statements in respect of five candidates P, Q, R, S and T. Two statements are true and one statement is false.
True Statement: One of P and Q was selected for the job.
False Statement: At least one of R and S was selected for the job.
True Statement: At most two of R, S and T were selected for the job.
Which of the following conclusions can be drawn?
1. At least four were selected for the job.
2. S was selected for the job.
Select the correct answer using the code given below:
Let P, Q, R, S and T be five statements such that:
I. If P is true, then both Q and S are true.
II. If R and S are true, then T is false.
Which of the following can be concluded?
1. If T is true, then at least one of P and R must be false.
2. If Q is true, then P is true.
Select the correct answer using the code given below: