Question 1

The 21st letter of the English alphabet is a consonant. How should this statement be evaluated?

Accepted Answer

Introduction / Context: This is a straightforward verification of truth question about the English alphabet. You are asked to judge whether a specific claim about the position of a letter and its type as a consonant or vowel is correct. Such questions test both factual knowledge and careful counting. Given Data / Assumptions: - The English alphabet has 26 letters in the standard order from A to Z. - The statement claims that the 21st letter of the alphabet is a consonant. - We must recall or count the letters and identify the 21st. - Letters are classified as vowels (A, E, I, O, U) or consonants (all others). Concept / Approach: To evaluate the statement, count the letters in order until you reach the 21st position. Then determine whether that letter is one of the five main vowels. If it is a vowel, the statement is incorrect; if it is not, the statement is correct. The task is a simple but precise counting exercise, where a small miscount can lead to an incorrect answer, so care is essential. Step-by-Step Solution: Step 1: Write or mentally list the letters in order, grouping them if needed for easier counting. Step 2: From A onward, count positions: A is 1, B is 2, C is 3, D is 4, E is 5, F is 6, G is 7, H is 8, I is 9, J is 10. Step 3: Continue counting: K is 11, L is 12, M is 13, N is 14, O is 15, P is 16, Q is 17, R is 18, S is 19, T is 20. Step 4: The next letter, U, is therefore the 21st letter. Step 5: Check whether U is a vowel or a consonant. U is one of the five main vowels (A, E, I, O, U). Step 6: Since the statement calls the 21st letter a consonant, but the 21st letter U is actually a vowel, the statement is incorrect. Verification / Alternative check: As an additional check, remember common facts: A is 1st, E is 5th, I is 9th, O is 15th and U is 21st. This pattern shows that every fourth vowel after A comes at positions 5, 9, 15 and 21. Recognising this pattern confirms that U is indeed the 21st letter and that it is a vowel. This backs up the earlier step by step count, so there is no doubt about the classification. Why Other Options Are Wrong: Correct: This would be true only if the 21st letter were a consonant, which it is not. Information insufficient: The question gives full information by specifying the alphabet and the letter position; nothing else is required. Not applicable: This option does not address the factual nature of the statement and is irrelevant to the task. Common Pitfalls: Students may miscount if they rush or skip letters, especially around the middle of the alphabet. Another potential mistake is mixing up the positions of T and U, since T is 20th and U is 21st. To avoid errors, it can help to group letters in sets of five or to write them down briefly in rough work during an exam. Remembering that U is the fifth vowel and the 21st letter can also act as a mental shortcut. Final Answer: The statement is incorrect, because the 21st letter U is a vowel, not a consonant.

Question 2

Which of the following sentences is capitalized correctly according to standard English conventions?

Accepted Answer

Introduction / Context: This question examines your ability to apply capitalization rules correctly. The sentence talks about observing the constellation Pisces in the night sky. You must choose the version that uses capital letters appropriately for sentence beginnings, proper nouns, and common nouns, while avoiding unnecessary capitals. Given Data / Assumptions: - The sentence structure is "On a cloudless night, I studied Pisces, a constellation in the northern sky." - Proper nouns like Pisces and the pronoun I should be capitalized. - The first letter of a sentence should be capitalized. - General directional adjectives such as northern, when used in phrases like northern sky, are usually written in lowercase. Concept / Approach: Standard capitalization rules state that the first word of a sentence must begin with a capital letter. The personal pronoun I is always capitalized. Proper names of constellations such as Pisces are capitalized, since they are specific names. However, in the phrase northern sky, northern acts as a common adjective, not a proper noun referring to a region like the North, so it is normally written with a lowercase initial. Applying these rules allows us to check each option systematically. Step-by-Step Solution: Step 1: Inspect option a: "on a cloudless night, I studied pisces, a constellation in the north sky." The first word on is not capitalized, which is incorrect. The constellation name pisces is in lowercase, which is also incorrect. The phrase north sky is not the usual expression, as we prefer northern sky. Step 2: Look at option b: "On a cloudless night, I studied Pisces, a constellation in the northern sky." Here, On begins with a capital letter, I is capitalized, Pisces is capitalized as a proper noun, and northern is correctly left in lowercase as a general descriptive term. Step 3: Consider option c: "on a Cloudless Night, i studied Pisces, a constellation in the North Sky." This sentence capitalizes Cloudless, Night and North and leaves i in lowercase, all of which violate standard rules. Step 4: Examine option d: "On a cloudless night, I studied pisces, a constellation in the north sky." The sentence correctly starts with On and correctly capitalizes I, but it keeps pisces in lowercase, which is wrong for a constellation name, and uses north sky instead of northern sky. Step 5: From this analysis, option b is the only one that follows capitalization rules correctly and uses the standard phrase northern sky. Verification / Alternative check: Compare the treatment of other constellation names in textbooks, such as Orion, Scorpius or Leo. These are always capitalized, just like country names. Also check sentences like "On a warm evening, I walked along the river." The first letter On is capitalized, while common adjectives like warm remain lowercase. Similarly, directional adjectives in phrases like southern ocean current or western horizon are lowercased. This pattern matches what we see in option b and confirms its correctness. Why Other Options Are Wrong: Option a: Fails to capitalize the first word and the proper noun Pisces. Option c: Over-capitalizes common words such as cloudless and night, leaves i in lowercase, and capitalizes North unnecessarily. Option d: Correctly begins the sentence and capitalizes I but fails to capitalize Pisces and uses the less natural phrase north sky. Common Pitfalls: Students often confuse when to capitalize directional words. North, South, East and West are capitalized only when used as proper names for regions, such as the North or the West. When they function as mere directions or adjectives, they remain lowercase. Similarly, they sometimes forget that specific astronomical objects like Mars, Jupiter and Pisces are treated as proper nouns. Reviewing these rules helps avoid losing marks on relatively easy capitalization questions. Final Answer: The sentence capitalized correctly is "On a cloudless night, I studied Pisces, a constellation in the northern sky."

Question 3

The sentence "On BBC World News channel last night they showed an informative program about new innovations in medical imaging, which you would have found interesting" is wordy and awkward. Which of the following is the best revision in clear and co…

Accepted Answer

Introduction / Context: This question focuses on sentence improvement. The original sentence is slightly wordy and contains the redundant phrase new innovations. Your task is to choose the revision that is clearest and grammatically best while avoiding redundancy, vague pronoun references, and awkward structure. All options remove the initial prepositional phrase about the TV channel, so the emphasis is on how the core idea is expressed. Given Data / Assumptions: - The original idea is that an informative program about innovations in medical imaging was broadcast, and the listener would have found it interesting. - The revision should avoid redundancy such as new innovations, because innovations are by definition new. - It should also make clear what you would have found interesting without unclear use of they. Concept / Approach: Good sentence revisions aim for clear subject reference, avoid wordiness and redundancy, and maintain grammatical correctness. The phrase new innovations is redundant, so using innovations alone is better. Also, the pronoun they in the original sentence has a vague reference. A clearer construction is to state directly that there was an informative program and then restate program in a short appositive phrase to show that this program is what you would have found interesting. Step-by-Step Solution: Step 1: Examine option a: "there was an informative program about innovations in medical imaging, a program you would have found interesting." This version removes the word new, keeps innovations, and uses a program in apposition to clarify the object of your interest. Step 2: Option a is grammatically correct and very clear. It avoids the vague pronoun they and redundant new innovations. Step 3: Consider option b: "they showed an informative program about innovations in medical imaging, which you would have found interesting." Here, they may be unclear, because the subject is not explicitly introduced in the new sentence. Step 4: Option c says "new innovations" and uses that instead of which. The phrase new innovations remains redundant, and the combination that you would have found interesting is less smooth in this nonrestrictive context. Step 5: Option d also contains the redundant phrase new innovations and uses they without a clear prior subject. This makes it weaker than option a. Step 6: Comparing all options, option a gives the most concise, precise and grammatically strong revision. Verification / Alternative check: Test option a by reading it aloud: "There was an informative program about innovations in medical imaging, a program you would have found interesting." The meaning is explicit and unambiguous. You know what existed, what it was about, and that this same program is considered interesting to the listener. None of the other options improves clarity or correctness beyond this version, especially because they either retain redundancy or keep the unclear subject they. Why Other Options Are Wrong: Option b: Uses they without a clear antecedent and, although close to correct, is slightly less precise than repeating program. Option c: Retains the redundancy of new innovations and uses that where a nonrestrictive which or appositive structure would be more natural. Option d: Combines the weak pronoun they with the redundant phrase new innovations, making it the least improved of the choices. Common Pitfalls: Students often overlook redundancy in phrases like new innovations, past history or added bonus. In sentence improvement questions, exam setters frequently target such wording. Another trap is retaining vague pronouns like they when the subject is not clearly defined in the new version. To avoid these pitfalls, aim for sentences where each pronoun has a clear reference and every word adds meaning rather than repetition. Final Answer: The best revision is "there was an informative program about innovations in medical imaging, a program you would have found interesting."

Question 4

Is a cube a polygon? How should this statement be evaluated in basic geometry?

Accepted Answer

Introduction / Context: This question tests your understanding of basic geometric terms. It asks whether a cube, which is a familiar three dimensional solid, can be classified as a polygon. You must recall the precise definitions of polygon and cube and decide whether the classification in the question is correct or not. Given Data / Assumptions: - A polygon is a flat, two dimensional figure. - Polygons are made up of straight line segments joined end to end in a closed chain. - A cube is a solid, three dimensional shape with six square faces, twelve edges and eight vertices. - The statement under test says that a cube is a polygon. Concept / Approach: Because polygons are two dimensional and a cube is three dimensional, they belong to different categories in geometry. A cube is a polyhedron, not a polygon. While each face of a cube is a square, and a square is a polygon, the cube itself is not. To answer correctly, you must distinguish between the faces of the cube and the cube as a whole solid figure. Step-by-Step Solution: Step 1: Recall the definition of a polygon: it is a plane figure with three or more straight sides. Examples include triangles, rectangles, pentagons and so on. Step 2: Note that plane figure means the shape lies entirely in a single flat plane and has only two dimensions, length and breadth, with negligible thickness. Step 3: Consider what a cube is. A cube has length, breadth and height and occupies space in three dimensions. It is a solid object, not a flat figure. Step 4: In geometry, such three dimensional figures with flat faces are called polyhedra, not polygons. Step 5: Each of the six faces of a cube is a square, and a square is indeed a polygon, specifically a quadrilateral with equal sides and right angles. Step 6: However, the fact that the faces of a cube are polygons does not mean that the cube itself is a polygon. It is a solid built from polygons. Step 7: Therefore, classifying a cube as a polygon mixes up the categories of two dimensional shapes and three dimensional solids and is incorrect. Verification / Alternative check: Think of other geometric classifications. A sphere is not a circle, even though any cross section of a sphere can look like a circle. Similarly, a cylinder is not a rectangle, though unfolding its surface forms a rectangle. In each case, the solid object and the flat shape are related but belong to different geometric families. The relationship between cube and square is of the same kind: a cube is built from square faces, but it is not itself a square or any polygon. Why Other Options Are Wrong: Correct: This would only be acceptable if cubes were defined as polygons, which contradicts standard definitions. Information insufficient: Geometry gives precise definitions of polygons and cubes, so there is no missing information. Not applicable: The question is directly about classification in basic geometry, so it is fully applicable. Common Pitfalls: A frequent misunderstanding is to think that if a solid has polygonal faces, then the solid itself might also be called a polygon. This confusion arises from not keeping the distinction between dimensions clear. In exams, such questions are designed to check whether you know that polygons are strictly two dimensional while solids like cubes, cuboids and prisms are three dimensional polyhedra. Always ask yourself how many dimensions a shape has before assigning it to a category. Final Answer: The statement that a cube is a polygon is incorrect; a cube is a three dimensional polyhedron, not a two dimensional polygon.

Question 5

In English grammar and punctuation, which of the following sentences is punctuated correctly when introducing the question “Am I pleased with the results?” as part of a longer sentence?

Accepted Answer

Introduction / Context: This verbal reasoning question tests your understanding of correct English punctuation when a sentence introduces a direct question in quotation marks. Many competitive exams include items like this because punctuation around colons, verbs such as ask, and closing quotation marks is a common source of error for learners and even fluent speakers. Identifying the correctly punctuated sentence requires you to recall standard rules for colons and quoted questions inside a larger statement. Given Data / Assumptions: Each option contains some version of the embedded question “Am I pleased with the results?”. The task is to find the sentence that is grammatically and punctuationally correct in standard written English. We assume modern, neutral English style, where colons follow complete clauses and quotation marks enclose the entire question. Concept / Approach: When you introduce a direct question with a clause like “One question you should always ask yourself is”, that introductory clause must be a complete sentence. A colon can be used after such a complete clause to introduce the question. The quoted question must have a capital letter at the beginning and a question mark at the end, placed inside the closing quotation mark. Any sentence where the colon follows an incomplete clause, where the closing quotation mark is missing, or where the punctuation falls outside the quotes will be considered incorrect for this exam context. Step-by-Step Solution: Check option A: “One question you should always ask yourself: ‘Am I pleased with the results?’”. The part before the colon lacks the verb is, so it is not a fully complete clause. This use of the colon is therefore awkward and considered incorrect. Check option B: “Always ask yourself this question: ‘Am I pleased with the results?”. Here the closing quotation mark and the closing question mark do not both appear at the end of the quoted question, so punctuation is incomplete. Check option C: “Always ask yourself a question like: ‘Am I pleased with the results?’”. Placing a colon after a question like, which is not a full clause, is stylistically weak and normally avoided in exam style answers. Check option D: “One question you should always ask yourself is: ‘Am I pleased with the results?’”. The introductory clause is complete, the colon correctly introduces the quoted question, and the question mark appears inside the closing quotation mark. This matches standard rules. Check option E: “Always ask yourself this: ‘Am I pleased with the results?’”. This is also quite good, but exam keys almost always favour the option that explicitly keeps question parallel to question, so D is preferred. Verification / Alternative check: You can verify by removing the quoted part and asking whether the remaining clause stands alone as a correct sentence. In option D, “One question you should always ask yourself is” is a full clause that naturally leads into an explanation, so a colon is acceptable. Also, if we look at punctuation at the end, the question mark correctly belongs to the quoted question and stays inside the quotation marks. No other option meets both of these conditions simultaneously in as clear a manner. Why Other Options Are Wrong: Option A omits the linking verb is before the colon, so the clause feels grammatically incomplete. Option B leaves out the closing quotation mark and the correct internal question mark. Option C uses a colon after a phrase that is not an independent clause, which is considered improper in careful writing. Option E is serviceable English, but exam patterns usually designate the clearest textbook structure as correct, which is option D in this case. Common Pitfalls: Students often think that any pause can take a colon and forget that the part before a colon should normally be a full clause. It is also easy to misplace the question mark outside the quotation marks or forget it entirely. Another common error is to focus only on the quoted question and ignore whether the introductory wording is grammatically sound. Always check both the structure of the lead in and the punctuation around the quotation. Final Answer: The correctly punctuated sentence that follows standard English rules is “One question you should always ask yourself is: ‘Am I pleased with the results?’”, which corresponds to option D.

Question 6

In the context of statistics and research, which of the following activities is an example of actually gathering or collecting raw data, rather than organizing or analysing it?

Accepted Answer

Introduction / Context: This verbal reasoning and basic statistics question asks you to distinguish between data gathering and data processing. In any research or decision making process, information passes through stages: collection, organisation, analysis and interpretation. Examinations often test whether you can recognise which activities correspond to each stage. Here you must pick the option that shows the act of collecting raw data from the real world. Given Data / Assumptions: Option A describes counting votes in an election to find the next governor. Option B describes making a pie chart based on information about television sets. Option C involves computing the mean weight of cancer patients. Option D uses results of a mathematical model to predict weather. Option E involves calculating the median of test scores. We assume that data gathering means physically or directly obtaining original values from observations, people or instruments. Concept / Approach: Data gathering, also called data collection, is the stage at which you obtain primary values. For example, asking questions in a survey, measuring a person's weight, or counting votes are all data gathering activities. Once you already have the numbers, drawing graphs, computing averages and making predictions are later stages. The key is to see whether the activity described is capturing new values or simply using existing values for analysis or presentation. Step-by-Step Solution: Analyse option A: Counting the votes in an election means reading each ballot or electronic record and tallying it. Each individual vote is a primary data point coming directly from voters. This is a classic example of data collection. Analyse option B: Making a pie chart using a sample of 1,000 people does not gather new data. The data about types of television sets must already be collected. Creating the chart is an example of data organisation and visualisation, not collection. Analyse option C: Finding the mean weight of cancer patients requires weight data that has already been measured. The calculation of the mean is a form of data analysis, not gathering. Analyse option D: Using a mathematical model to predict weather relies on previously collected data and formulas. Prediction is a form of interpretation and forecasting, not data collection. Analyse option E: Calculating the median of test scores again assumes that test scores are available. This is statistical analysis rather than gathering. Verification / Alternative check: A quick way to verify is to ask: in which option is someone directly interacting with the real world to produce new primary values? Counting votes clearly involves reading each vote and recording it. All other options begin with a dataset already present, because one cannot make a pie chart, compute a mean or median, or run a predictive model without prior numbers. Therefore only option A qualifies as primary data gathering in a strict sense. Why Other Options Are Wrong: Option B is a method of presenting data visually but does not create the data. Option C performs an arithmetic operation on collected numbers. Option D uses existing data to forecast future conditions. Option E again performs an operation on given scores. These are important statistical activities, but they represent analysis or presentation rather than the initial act of data collection that the question is asking about. Common Pitfalls: Students sometimes label any activity involving numbers as data gathering, even when no new information is collected. Another mistake is to ignore the phrase example of data gathering and instead focus on which activity seems more complex or technical. Remember that data gathering is about the source stage where the values first enter the system. If the data must already exist for the described action to take place, then that action is not gathering but processing. Final Answer: The activity that best represents the direct collection of raw data is counting the votes in an election to determine the next governor, which is option A.

Question 7

Consider the statement: “Primary care physicians are responsible for diagnosis and treatment of common health problems.” How should this statement be evaluated in terms of its correctness in the context of modern health care systems?

Accepted Answer

Introduction / Context: This question checks basic general knowledge about the role of primary care physicians in a health care system. Many aptitude and reasoning tests include simple factual statements and ask you to judge whether the statement is correct. Here the focus is on understanding what primary care physicians actually do in everyday practice and whether diagnosis and treatment are central parts of their job. Given Data / Assumptions: The statement to evaluate is that primary care physicians are responsible for diagnosis and treatment of common health problems. We are talking about typical modern health care systems where patients initially approach a general practitioner, family doctor or similar primary care professional. Primary care is contrasted with specialist care such as cardiology or neurosurgery. We assume routine conditions such as fever, cough, hypertension, diabetes and minor injuries, not highly specialised surgical procedures. Concept / Approach: Primary care is usually the first point of contact for patients. Doctors in these roles are trained to take histories, perform examinations, order basic tests, make diagnoses and provide suitable treatment or management plans. When a condition is beyond their scope, they refer patients to specialists. Therefore, a correct understanding of primary care should include both diagnosis and treatment at a general level. To answer the question, we simply need to compare this real world role with the given statement and see if they match. Step-by-Step Solution: Identify key functions of a primary care physician: listening to patient complaints, taking medical history, performing physical examination, requesting basic investigations and making initial diagnoses. Recognise that after diagnosing common conditions, primary care physicians prescribe medicines, give lifestyle advice and monitor response. This clearly shows a responsibility for treatment. Acknowledge that for complex or rare disorders, primary care physicians may refer patients to specialists, but this does not remove their responsibility for basic diagnosis and initial management. Compare this with the statement in the question, which directly says that primary care physicians are responsible for diagnosis and treatment. This matches our understanding of their role. Therefore, the statement is correct, and any option claiming they only do paperwork, only refer, or work only in laboratories must be considered incorrect. Verification / Alternative check: You can verify by recalling common experiences. When people have fever, sore throat or minor injuries, they usually visit a local doctor or clinic. That doctor interacts with the patient, arrives at a probable diagnosis such as viral fever or throat infection and prescribes medicines. This shows that primary level doctors both diagnose and treat. Even government and insurance definitions of primary care emphasise comprehensive, continuous first contact care, which again includes diagnosis and treatment of general conditions. Why Other Options Are Wrong: Option B claims primary care physicians only refer and do not diagnose or treat, which is clearly false because referrals generally follow an initial assessment and provisional diagnosis. Option C says they only handle administrative tasks, which ignores their clinical training. Option D restricts them to emergencies only, which is wrong because routine and preventive care are major parts of their work. Option E suggests they work only in laboratories without seeing patients, which actually describes some specialists like pathologists but not the typical primary care physician. Common Pitfalls: A common mistake is to confuse primary care with paramedical or purely administrative roles. Some candidates also assume that only specialists diagnose and treat, while primary care doctors merely act as gatekeepers. In reality, primary care physicians manage a very large share of everyday illnesses and are trained to diagnose and treat within their scope. Reading the statement carefully and relating it to real world practice helps avoid such confusion. Final Answer: The statement is correct; primary care physicians are indeed responsible for diagnosis and treatment of common health problems, so option A is the right choice.

Question 8

Each of the following options presents a pair of premises followed by a conclusion. Three arguments are logically valid if you ignore factual absurdity and focus only on logical structure. One argument is logically wrong or doubtful. Which argument …

Accepted Answer

Introduction / Context: This question belongs to the area of syllogisms and logical validity. You are given arguments that may sound absurd in everyday life, but you are explicitly asked to ignore factual absurdity and examine only the logical form. Three of the arguments follow valid patterns of deduction, while one argument has an invalid conclusion that does not follow from its premises. Your task is to identify the logically wrong or doubtful argument. Given Data / Assumptions: We treat sentences like “Birds fly in the air” or “Trees are birds” as premises, whether or not they are true in real life. We focus only on whether the conclusion necessarily follows from the premises if those premises are assumed to be true. Standard set notation can be used in the background: All A are B, Some A are B, etc. We ignore emotional or factual judgement and examine pure structure. Concept / Approach: In syllogistic reasoning, an argument is valid if, whenever the premises are true, the conclusion must also be true. The actual truth of the premises does not affect validity. So even if a premise says something factually impossible, the argument can still be valid as long as the conclusion obeys the logical rules. To solve this question, translate each option into a simple logical form and then check whether the conclusion logically follows. Exactly one will fail this test. Step-by-Step Solution: Option A: “Birds fly in the air. Trees are birds. Therefore, trees fly in the air.” Formally: All birds fly. All trees are birds. Therefore, all trees fly. This follows the valid pattern: All B are F; All T are B; therefore, All T are F. The logic is valid, even though the premises are factually wrong. Option B: “Some boys steal. All who steal are naughty. All naughty are honest. Therefore, some boys are honest.” The form is: Some boys are thieves; All thieves are naughty; All naughty are honest. Therefore, Some boys are honest. Since the same subset of boys moves through thief to naughty to honest, this is logically valid. Option C: “All girls like dance. Some girls are Indian. All Indians are artists. Therefore, some artists like dance.” Here, some girls are both girls and Indian and all girls like dance. All Indians are artists. So some individuals are both artists and people who like dance. Therefore, some artists like dance. The structure is valid. Option D: “All liars are not thieves. All thieves are criminals. Therefore, all liars are criminals.” Interpreting “All liars are not thieves” as “No liars are thieves”, we get: All L are non thieves. All thieves are criminals. From this it does not follow that all liars are criminals, because liars could be outside the set of thieves and criminals entirely. No link is established from liars to criminals. Verification / Alternative check: To verify option D, construct a simple counterexample. Suppose there are liars who are not thieves and not criminals at all. The premise “All liars are not thieves” is satisfied. The premise “All thieves are criminals” is also satisfied, because any thief that exists is a criminal. Yet in this situation, not all liars are criminals, which shows the conclusion fails even when both premises are true. Therefore the argument in option D is invalid, while the others can be shown to hold for all interpretations that respect their premises. Why Other Options Are Wrong: Options A, B and C are logically correct even though they may contain absurd premises. In A, the structure All B are F and All T are B gives All T are F. In B, the chain Some boys are thieves, all thieves are naughty and all naughty are honest forces some boys to be honest. In C, the overlap between girls and Indians ensures that some artists are among those who like dance. None of these arguments admit a counterexample where the premises are true and the conclusion false. Common Pitfalls: A frequent mistake is to reject arguments because the real world content seems silly, such as trees being birds. The instructions specifically warn you to ignore factual absurdity and focus on logical form. Another pitfall is misreading “All liars are not thieves” as if it somehow means liars are criminals, which it does not. Always translate such statements carefully and check whether there is a clear link from the subject of the conclusion back through the premises. Final Answer: The only argument that is logically wrong or doubtful is “All liars are not thieves. All thieves are criminals. Therefore, all liars are criminals.”, which is option D.

Question 9

Each of the following options presents a small argument with premises and a conclusion. Three arguments are logically correct if you ignore factual absurdity. One argument is logically wrong or doubtful. Which argument is logically incorrect?

Accepted Answer

Introduction / Context: This question again tests your understanding of logical validity in syllogisms. You are asked to identify which argument is logically wrong or doubtful when you focus only on the structure of the reasoning and not on whether the premises sound realistic. Some arguments may have absurd sounding premises but still be valid, while another has a faulty generalisation that does not follow from the given information. Given Data / Assumptions: We must treat premises as temporarily true and judge whether the conclusion necessarily follows if the premises hold. We ignore real world knowledge about houses, trees or physical laws and rely on pure logical form. In each option, two or more sentences lead to a conclusion about a broader group or category. Exactly one argument fails to be logically valid; our task is to find that argument. Concept / Approach: An argument is valid if there is no possible situation in which all premises are true but the conclusion is false. If such a situation exists, the argument is invalid or doubtful. In these options we often move from statements about specific individuals or subsets to broader general statements. A classic error is hasty generalisation: assuming that what is true for one example is true for all members of a group. We check each option for such errors. Step-by-Step Solution: Option A: “Ramesh is tall. Ramesh is a boy. Therefore, boys are tall.” Here the premises only tell us about Ramesh. The conclusion talks about all boys. There could be many boys who are not tall. So it is quite possible for the premises to be true and the conclusion false. This is an invalid argument. Option B: “All who can fly are animals. Some birds can fly. Therefore, some birds are animals.” If all flyers are animals and some birds are flyers, then those particular birds are both birds and animals. So it must be true that some birds are animals. This argument is valid. Option C: “Men live in houses. Houses grow on trees. Trees float in water. Therefore, men float in water.” Although factually absurd, the logic is: All men live in houses; all houses are on trees; all trees float. If each link is treated as true, then everything that is a man belongs to the class that floats in water. The conclusion that men float in water logically follows. Option D: “All living things are mobile. Some non-living things are mobile. Therefore, some mobile things are living and some are non-living.” If every living thing is mobile, then living things form a subset of mobile things. If some non-living things are mobile, then mobile things include at least one living and at least one non-living example. Hence the conclusion correctly summarises the situation and is valid. Verification / Alternative check: To verify option A is invalid, imagine a world with two boys: Ramesh and Suresh. Let Ramesh be tall and Suresh be short. Both premises “Ramesh is tall” and “Ramesh is a boy” are true. Yet the conclusion “boys are tall” is false because Suresh is not tall. This shows that the premises do not guarantee the conclusion. For options B, C and D, any interpretation that satisfies all premises will also satisfy the conclusion, which means those arguments are logically valid despite any factual absurdity in their content. Why Other Options Are Wrong: Options B, C and D are not wrong in the logical sense. In B, some birds inherit the property of being animals through flying. In C, men inherit the property of floating in water via the chain of houses and trees. In D, the set of mobile things contains examples from both living and non-living categories. Each of these conclusions faithfully reflects what must be true if the premises are taken as true. Common Pitfalls: Many test takers are distracted by the obvious factual nonsense in option C and conclude that it must be the incorrect argument. However, the instructions clearly tell you to ignore factual absurdity and concentrate on logical connections. Another common mistake is not noticing that option A tries to generalise from a single individual to an entire class without sufficient information. In logic questions, always ask whether the conclusion talks about more instances than the premises actually cover. Final Answer: The only logically wrong or doubtful argument is “Ramesh is tall. Ramesh is a boy. Therefore, boys are tall.”, which is option A.

Question 10

If P = 9695 × 97, Q = 9796 × 98 and R = 197, then which of the following order relations between P, Q and R is correct?

Accepted Answer

Introduction / Context: This question tests your ability to compare large numbers without necessarily computing them in full detail. You are given two large products, P and Q, and a smaller number R, and you must decide which inequality correctly describes their order from smallest to largest. Such questions are common in quantitative and verbal reasoning because they check both number sense and careful reading of symbolic expressions. Given Data / Assumptions: P is defined as 9695 × 97. Q is defined as 9796 × 98. R is defined as 197. All three quantities are positive integers. We must determine which inequality among the options correctly orders R, P and Q. Concept / Approach: The first observation is that P and Q are products of numbers close to 10,000 and 100, so they will be much larger than the two digit number 197. Therefore R will obviously be the smallest. The main comparison that matters is between P and Q. Because 9796 and 98 are each slightly larger than 9695 and 97 respectively, we expect Q to be greater than P. We can support this intuition by either computing the products exactly or by using a careful approximate difference argument to confirm that Q exceeds P. Step-by-Step Solution: First compare R with P and Q. R = 197. The product 9695 × 97 is almost 9700 × 100, which is close to 970,000, so P is in the hundreds of thousands. Similarly, 9796 × 98 is also in the hundreds of thousands. Therefore, R is far smaller than both P and Q. So R must come first in any correct inequality. Now compare P and Q numerically. Compute P exactly: P = 9695 × 97 = 9695 × (100 - 3) = 9695 × 100 - 9695 × 3 = 969,500 - 29,085 = 940,415. Compute Q exactly: Q = 9796 × 98 = 9796 × (100 - 2) = 9796 × 100 - 9796 × 2 = 979,600 - 19,592 = 960,008. Compare P and Q: 960,008 is clearly greater than 940,415. Therefore Q > P. Combining these facts, we have R < P and P < Q, which together give the final order R < P < Q. Verification / Alternative check: If you prefer an approximate check without full multiplication, note that both products are of the form (about 9700) × (about 100). The pair for Q is slightly larger in both factors: 9796 > 9695 and 98 > 97. When two positive factors increase, their product increases. This guarantees that Q is larger than P. Because 197 is much smaller than 900,000, it cannot compete with these products. Any inequality that places R above P or Q must be wrong. Only the pattern R < P < Q is consistent with both intuition and the exact calculations given above. Why Other Options Are Wrong: Option A, P < Q < R, incorrectly places R as the largest number, which is impossible since R is only 197. Option B, R < Q < P, correctly puts R first but wrongly claims Q < P despite Q being computed as 960,008 and P as 940,415. Option C, Q < P < R, is wrong in both directions, claiming Q is smallest and R largest. Only option D matches the computed order R < P < Q. Common Pitfalls: A common mistake is to be intimidated by the large numbers and to guess based purely on the fact that 9695 is slightly smaller than 9796 without checking both factors carefully. Another typical error is forgetting that the tiny number R must be the smallest and carelessly choosing an inequality where R appears at the end. When working with large products, comparing relative sizes of factors and using simple algebraic rearrangements can help avoid full, time consuming calculations. Final Answer: The correct ordering of the three numbers is R < P < Q, so option D is the correct choice.

Question 11

Which of the following statements about the ordering of three digit numbers is true? I. 235 < 325 < 543 II. 325 < 233 < 745

Accepted Answer

Introduction / Context: This question checks basic understanding of inequalities involving three digit numbers. You are given two compound inequalities and asked which one or ones are true. Such questions appear in reasoning sections to confirm that candidates can read inequality chains correctly and compare whole numbers accurately without overthinking. Given Data / Assumptions: Statement I claims: 235 < 325 < 543. Statement II claims: 325 < 233 < 745. Each statement uses standard ordering on the number line. We must identify whether I is true, II is true, both are true, or neither is true. Concept / Approach: To compare three digit numbers, we first compare hundreds digits. If the hundreds digits differ, the number with the larger hundreds digit is larger. Only when hundreds are equal do we move on to tens and then units. A chain like A < B < C means both A < B and B < C must be true. One false part makes the whole chain false. We will check each inequality piece by piece using place value logic. Step-by-Step Solution: Examine statement I: 235 < 325 < 543. Compare 235 and 325. The hundreds digits are 2 and 3. Since 2 < 3, we have 235 < 325, so the first part is true. Compare 325 and 543. The hundreds digits are 3 and 5. Since 3 < 5, we have 325 < 543, so the second part is also true. Therefore, both parts in statement I are correct, and the chain 235 < 325 < 543 holds true. Now examine statement II: 325 < 233 < 745. Compare 325 and 233. The hundreds digits are 3 and 2. Since 3 > 2, in reality 325 > 233, not 325 < 233. The very first part of the chain is false. Because 325 < 233 is false, the whole chain in statement II is false, even though 233 < 745 by itself is true. Verification / Alternative check: A quick way to check is to place the numbers in ascending order. The set {235, 325, 543} naturally orders as 235, 325, 543, which matches statement I exactly. For the set {325, 233, 745}, ordering them from smallest to largest gives 233, 325, 745. This clearly shows that the correct chain would be 233 < 325 < 745, not 325 < 233 < 745. Since statement II conflicts with this ordering, it must be false. Thus only statement I is true. Why Other Options Are Wrong: Option B, which claims only II is true, is wrong because we have shown statement II fails at its first comparison. Option C, which claims both statements are true, is wrong because a false statement cannot be labelled true. Option D, which claims neither is true, is wrong because statement I is clearly correct. Only option A accurately reflects that I is true and II is false. Common Pitfalls: A common mistake is to rush through and not carefully check each inequality in the chain, sometimes assuming that the examiner will make both look symmetrical. Another pitfall is to focus only on tens or units digits and forget that the hundreds digit dominates in three digit comparisons. Always compare from left to right and remember that even one wrong comparison in an inequality chain makes the whole statement false. Final Answer: Only the first inequality chain is correct, so the right choice is Only I, which is option A.

Question 12

Which of the following statements about numbers is/are true? I. The total number of positive factors of 72 is 12. II. The sum of the first 20 odd numbers is 400. III. The largest two digit prime number is 97.

Accepted Answer

Introduction / Context: This question checks elementary number theory and arithmetic facts. You are given three independent statements about factors, sums of odd numbers and a prime number, and asked which statements are true. Such questions are popular in reasoning tests because they combine simple formulas with basic knowledge of prime numbers and divisors. Given Data / Assumptions: Statement I: The total number of positive factors of 72 is 12. Statement II: The sum of the first 20 odd numbers is 400. Statement III: The largest two digit prime number is 97. We work with standard definitions of factors, odd numbers, primes and basic arithmetic formulas. Concept / Approach: To evaluate Statement I, we use prime factorisation and the standard formula for counting divisors. For Statement II, we recall that the sum of the first n odd numbers is n^2, a classic result which can also be checked directly. For Statement III, we examine the few two digit numbers above 90 to see which are prime and identify the largest. Once each statement has been tested, we select the option that correctly summarises which ones are true. Step-by-Step Solution: Check Statement I: Factorise 72 into primes. We have 72 = 2^3 × 3^2. If a number has the prime factorisation p^a × q^b, the total number of positive divisors is (a + 1)(b + 1). Here a = 3 and b = 2, so the divisor count is (3 + 1)(2 + 1) = 4 × 3 = 12. Therefore, Statement I is true. Check Statement II: The first 20 odd numbers are 1, 3, 5, ..., up to 39. It is a known result that the sum of the first n odd numbers is n^2. For n = 20, the sum is 20^2 = 400. So Statement II is true. If desired, you can verify by pairing numbers or by computing the arithmetic progression sum. Check Statement III: Two digit numbers run from 10 to 99. We need the largest prime less than 100. Numbers 98 and 96 are even, 99 is divisible by 3 (since 9 + 9 = 18 is a multiple of 3). The number 97 is not divisible by 2, 3, 5 or 7, and its square root is less than 10, so no higher small prime can divide it. Hence 97 is prime and 99, 98, 96, etc. are not. Therefore, 97 is indeed the largest two digit prime, and Statement III is true. Verification / Alternative check: You can quickly verify Statement II by partial sums. The sum of the first two odd numbers, 1 + 3, is 4 which is 2^2. The sum of the first three odd numbers is 1 + 3 + 5 = 9, which is 3^2. This pattern continues, supporting the formula n^2. For Statement I, you can list the factors of 72 explicitly: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72, counting 12 in total. For Statement III, checking the small set {91, 93, 95, 97, 99} confirms only 97 is prime. All three verifications support the truth of each statement. Why Other Options Are Wrong: Option A claims that only I and II are true, ignoring the fact that III is also true. Option B claims that only II and III are true and incorrectly discards the correct divisor count in I. Option C claims only I and III are true, incorrectly rejecting the correct formula based sum in II. Since none of these options acknowledge that all three statements hold, they are incorrect. Option D correctly recognises that I, II and III are all true. Common Pitfalls: Some candidates misremember the sum of first n odd numbers or mistakenly think it is n(n + 1). Others may make factorisation mistakes, for example writing 72 as 2^4 × 3 instead of 2^3 × 3^2, which leads to a wrong divisor count. In prime questions, it is common to overlook 97 and incorrectly think 99 or 95 might be prime. Carefully applying known formulas and checking divisibility by small primes avoids these errors. Final Answer: All three statements are correct, so the right choice is “All are true.”, which is option D.

Question 13

Which of the following statements involving square roots is/are true? I. √11 + √7 < √10 + √8 II. √17 + √11 > √15 + √13

Accepted Answer

Introduction / Context: This question tests your ability to compare expressions containing square roots without a calculator. Instead of exact decimal values, you are expected to use estimation and inequality reasoning to decide which of two sums of square roots is larger. Such questions are common in aptitude tests because they strengthen number sense and the ability to compare approximate magnitudes. Given Data / Assumptions: Statement I claims: √11 + √7 < √10 + √8. Statement II claims: √17 + √11 > √15 + √13. All square roots are positive principal square roots. We must decide which statements are true. Concept / Approach: Direct squaring of sums like (√a + √b)^2 expands into a + b + 2√(ab), which can be compared, but often a simpler approach is to estimate approximate decimal values of each root. For small integers, square roots are easy to estimate using nearby perfect squares. After getting reasonable approximations, we compare the two sums in each statement. If the difference is consistent and not extremely tiny, we can confidently label the inequality as true or false. Step-by-Step Solution: Consider Statement I: √11 + √7 versus √10 + √8. Use nearby perfect squares. 9 and 16 are squares of 3 and 4. So √10 is a little more than 3.16 and √11 a little more than 3.31. Similarly, 4 and 9 are squares of 2 and 3, so √7 is around 2.64 and √8 around 2.83. Approximate sums: √11 + √7 ≈ 3.32 + 2.65 ≈ 5.97. √10 + √8 ≈ 3.16 + 2.83 ≈ 5.99. So √10 + √8 is slightly larger. Therefore √11 + √7 < √10 + √8 appears to be true. Now consider Statement II: √17 + √11 versus √15 + √13. Estimate values: √17 is just above 4.12, √11 about 3.32, giving √17 + √11 ≈ 4.12 + 3.32 = 7.44. √15 is about 3.87 and √13 about 3.61, so √15 + √13 ≈ 3.87 + 3.61 = 7.48. Comparing 7.44 and 7.48, the second sum is slightly larger. So √17 + √11 is actually less than √15 + √13, not greater. Hence Statement II is false. Verification / Alternative check: For a more algebraic check, you could compare the squares of each sum. However, the approximate calculations already show a clear consistent difference in both cases. For Statement I, even if the approximations are slightly off, the values on the right side remain a bit larger than those on the left, confirming the inequality √11 + √7 < √10 + √8. For Statement II, the left side sum is consistently a little smaller than the right side sum, making the claimed inequality √17 + √11 > √15 + √13 incorrect. Why Other Options Are Wrong: Option B claiming that only II is true is wrong because we have shown II is false. Option C claiming both statements are true is wrong because II fails. Option D claiming neither is true is wrong because Statement I is supported by our estimates. Only option A correctly recognises that exactly Statement I is true and Statement II is false. Common Pitfalls: A common mistake is to assume that because 11 + 7 equals 10 + 8, the sums of square roots must also be equal or hard to compare, leading to confusion. Another error is to compare each pair separately, such as deciding whether √11 is greater than √10, without considering the effect of the entire sum. Candidates also sometimes reverse inequalities when working too quickly. Carefully estimating each root using nearby perfect squares and then adding them helps avoid these issues. Final Answer: Only the first inequality, √11 + √7 < √10 + √8, is true, so the correct choice is Only I, which corresponds to option A.

Question 14

Which of the following statements is/are true? I. 333 > 333 II. 333 > (33)³

Accepted Answer

Introduction / Context: This question tests the ability to interpret inequalities and exponential notation correctly. You are given two comparisons, one between a number and itself, and another between a number and an expression involving a power. You must decide whether each statement is true or false, and then choose the option that best summarises your findings. Such items verify basic comfort with greater than symbols and simple exponent computations. Given Data / Assumptions: Statement I: 333 > 333. Statement II: 333 > (33)³, meaning 333 is greater than 33 cubed. The greater than sign > means strictly larger, not equal to or larger. We assume (33)³ means 33 × 33 × 33. Concept / Approach: For Statement I, we compare a number with itself. A number can be equal to itself but cannot be strictly greater than itself. Therefore, any statement of the form x > x is false. For Statement II, we must compute or estimate 33³ and then compare it with 333. Since 33³ involves multiplying 33 by itself three times, we expect a result that is much larger than 333. After confirming this, we decide whether the inequality direction in the statement is correct. Step-by-Step Solution: Check Statement I: 333 > 333. The left side and right side are exactly the same number. For a strict inequality x > y to be true, x must be larger than y. Here x equals y, so the statement is false. At best we could write 333 ≥ 333, but not 333 > 333. Check Statement II: 333 > (33)³. Compute 33³ by stages. First, 33² = 33 × 33 = 1089. Next, 33³ = 1089 × 33. Multiply 1089 by 33. 1089 × 30 = 32,670 and 1089 × 3 = 3,267. Adding gives 32,670 + 3,267 = 35,937. So (33)³ = 35,937. Compare 333 with 35,937. Clearly 35,937 is much larger than 333. Therefore 333 is not greater than 35,937. The true relation is 333 < 35,937, so Statement II is also false. Verification / Alternative check: Even without full multiplication, you can observe that 33² is already 1,089, which is greater than 333. Multiplying by 33 again must produce a number in the tens of thousands. Thus 33³ must exceed 1,089 and is certainly greater than 333. Since the statement claims 333 > 33³, which contradicts this reasoning, we know Statement II is false. Combined with the obvious falsity of Statement I, we conclude that neither statement is true. Why Other Options Are Wrong: Option A, claiming only I is true, is wrong because I is false: no number can be strictly greater than itself. Option B, claiming only II is true, is wrong because II is also false, as 33³ is far larger than 333. Option C, claiming both statements are true, is clearly incorrect since both involve reversed inequalities. Only option D correctly states that neither I nor II is true. Common Pitfalls: Some candidates misread 333 > 333 as 333 ≥ 333 and mistakenly accept it as true, ignoring the difference between strict and non strict inequalities. Others may see (33)³ and assume it is only slightly bigger than 333, without realising that cube growth is rapid. Confusing 33³ with 3³ or 33² also leads to errors. Always read the inequality symbol carefully and, when powers appear, compute or estimate their magnitude before deciding which side is larger. Final Answer: Both statements are false, so the correct choice is “Neither I nor II”, which is option D.

Verification of Truth Questions