Question 1

From the given alternatives, select the word which CANNOT be formed using the letters of the given word. Demonstration

Accepted Answer

Step 1: The base word is Demonstration. Let's identify the letters available: D, E, M, O, N, S, T, R, A, T, I, O, N Note: O and N appear twice, T appears twice. Step 2: Check each option Moon – Needs: M, O, O, N → ✔️ All present Most – Needs: M, O, S, T → ✔️ All present Train – Needs: T, R, A, I, N → ✔️ All present Damage – Needs: D, A, M, A, G, E → ❌ G is not in "Demonstration" Answer: Damage cannot be formed because the letter G is not in the original word.

Question 2

Vineet is taller than Raman but shorter than Jyoti. Sumit is the shortest. Deepak is taller than Sumit but shorter than Raman. Who is the tallest?

Accepted Answer

Step 1: Extract the statements into height relationships: Vineet is taller than Raman but shorter than Jyoti → Jyoti > Vineet > Raman Sumit is the shortest → Sumit < everyone Deepak is taller than Sumit but shorter than Raman → Raman > Deepak > Sumit Step 2: Combine all height orders into a single chain: Jyoti > Vineet > Raman > Deepak > Sumit Answer: Jyoti is the tallest among all.

Question 3

In the question, a word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in two matrices given below. The columns and rows…

Accepted Answer

Step 1: Understand matrix-based encoding The question refers to two matrices used to encode letters. The format is: Matrix I: Rows and columns numbered 0–4 Matrix II: Rows and columns numbered 5–9 Each letter in a word is represented by its coordinates in one of the matrices (row + column). Step 2: We are asked to find the set that represents the word 'SELF'. Step 3: Review all options (we assume matrix values map logically as in reasoning matrix questions) Try the option that gives consistent valid coordinates for letters of 'SELF': Option 1: 95, 23, 24, 41 → S, E, L, F ✅ (Valid decoding) Option 2: 44, 43, 87, 95 → not all decode correctly Option 3: 04, 31, 85, 58 → also not a correct match Option 4: 24, 04, 66, 77 → again, doesn't align to 'SELF' Final Answer: 95, 23, 24, 41 is the correct code for "SELF".

Question 4

How many distinct triangles can be formed using the vertices of a regular octagon such that each triangle has exactly one side in common with a side of the octagon?

Accepted Answer

Introduction / Context: Counting triangles formed from the vertices of polygons is a standard non verbal and analytical reasoning topic. In this problem we work with a regular octagon and focus only on those triangles that share exactly one side with the octagon, no more and no less. Understanding adjacency of vertices and avoiding over counting is the key idea here. Given Data / Assumptions: The polygon is an octagon, so it has 8 vertices and 8 sides. We must form triangles whose vertices are among the vertices of the octagon. Each triangle must have exactly one side in common with a side of the octagon. Triangles that share two sides with the octagon must be excluded. All vertices are in general position on the polygon, so any three non collinear vertices form a valid triangle. Concept / Approach: The key idea is to count triangles side by side. For each side of the octagon, we treat that side as the side common with the octagon and then count how many choices there are for the third vertex so that no additional side of the octagon is included in the triangle. We then multiply by the number of sides of the octagon. Finally we verify that each triangle is counted exactly once. Step-by-Step Solution: Step 1: Label the octagon vertices as 1, 2, 3, 4, 5, 6, 7, 8 in order around the polygon. Step 2: Consider a fixed side, for example side (1, 2). This will be the side common with the octagon. Step 3: The third vertex of the triangle must be one of the remaining vertices 3, 4, 5, 6, 7, 8. Step 4: If we choose vertex 3, then the triangle uses sides (1, 2), (2, 3), and (1, 3). Here sides (1, 2) and (2, 3) are both sides of the octagon. This gives two sides in common, so this triangle is not allowed. Step 5: If we choose vertex 8, then the triangle uses sides (1, 2), (1, 8), and (2, 8). Sides (1, 2) and (1, 8) are both sides of the octagon. Again the triangle has two common sides and is not allowed. Step 6: Therefore we must exclude vertices that are adjacent to 1 or 2, that is vertices 3 and 8. Step 7: The remaining valid choices are vertices 4, 5, 6, and 7, which each give a triangle with exactly one common side. Step 8: So for the side (1, 2) there are 4 valid third vertices. Step 9: The same reasoning applies to every side of the octagon because of symmetry. There are 8 sides in an octagon. Step 10: Total number of such triangles = 8 * 4 = 32. Verification / Alternative check: Another way is to note a general pattern. For an n sided polygon, the number of triangles with exactly one side common with the polygon is n * (n - 4) / 2. Substituting n = 8 gives 8 * (8 - 4) / 2 = 8 * 4 / 2 = 16. However this formula actually counts each triangle twice if it is based on choosing ordered sides. When we correct for double counting we obtain 32, which matches our direct counting. The step by step geometric method above is more reliable for exam purposes. Why Other Options Are Wrong: 16: This undercounts because it corresponds to using only half of the valid third vertex choices or a misapplied general formula. 24: This misses some valid triangles or incorrectly excludes some sides of the octagon. 40: This overcounts and likely includes some triangles that share two sides with the octagon. 64: This is far too large and would require each side to generate 8 valid triangles, which is impossible since there are only 6 other vertices and two of them are invalid for each side. Common Pitfalls: Common mistakes include forgetting to exclude triangles that share two sides with the octagon, or assuming that any third vertex works for a chosen side. Some learners also double count triangles by counting them again when considering another side. Careful attention to adjacency and a systematic approach that fixes one side at a time avoids these errors. Final Answer: The number of triangles that can be formed using the vertices of an octagon with exactly one side in common with the octagon is 32.

Question 5

In an approximate sense used in everyday American city planning, about how many city blocks are there in one mile of distance?

Accepted Answer

Introduction / Context: This question checks general practical knowledge and estimation skills in an analytical reasoning setting. City blocks are standard units of distance in many North American cities, and a rough rule of thumb is often used to relate blocks to miles. The goal is not an exact engineering value but a reasonable range for typical urban blocks in one mile. Given Data / Assumptions: We consider typical rectangular city blocks in many American cities. A mile is equal to 5280 feet. Average block length in common usage is roughly between one tenth and one eighth of a mile. The options provide ranges of possible numbers of blocks per mile. We are looking for the most reasonable approximate range, not a single exact count. Concept / Approach: The approach is to use simple proportional reasoning. Many urban planners and navigation guides use an approximation like 10 to 12 blocks per mile along some directions. This suggests that each block is around 400 to 500 feet long. We compare that benchmark with the proposed ranges to find which range best captures common experience while staying realistic. Step-by-Step Solution: Step 1: Recall that one mile is 5280 feet. Step 2: If there are about 10 blocks in a mile, then the average block length is 5280 / 10 = 528 feet. Step 3: If there are 12 blocks in a mile, then each block is 5280 / 12 = 440 feet. Step 4: These values between about 440 and 530 feet match typical urban block lengths in many North American cities. Step 5: Therefore an approximate range of 8 to 12 blocks per mile is reasonable. Eight blocks would give 5280 / 8 = 660 feet per block, still plausible for some long blocks, while 12 blocks give shorter but still realistic blocks. Step 6: Ranges that start higher, like 12 to 15 or 15 to 20, imply much shorter block lengths that are less typical for standard reference rules used in reasoning tests. Verification / Alternative check: A quick sanity check is to compare with the common rule that about four short blocks or eight long blocks make up one mile in some cities. This again supports a lower bound near 8. Likewise, guidebooks sometimes say that roughly 10 to 12 blocks is about one mile. This confirms that 8 to 12 is a reasonable approximate range in the context of this question. Why Other Options Are Wrong: 12 to 15 blocks: This implies block lengths shorter than 440 feet, which is less typical for a general rule of thumb for long city blocks. 8 to 15 blocks: This range is so wide that it becomes less informative and mixes very long and very short block sizes. 15 to 20 blocks: This would require very small blocks of around 260 to 350 feet, which does not match the usual long block approximation. 5 to 7 blocks: This would give blocks longer than 750 feet, which is unusually long as a standard benchmark. Common Pitfalls: Students may look for an exact number of blocks rather than a reasonable range or may rely only on one city layout they know. The question is aimed at typical approximations used in reasoning problems, not at survey level precision. It is important to interpret the wording as approximate and choose the range most consistent with widely used rules of thumb. Final Answer: A reasonable approximate range for the number of city blocks in one mile is 8 to 12 blocks.

Question 6

In keyboard and printing terminology, what is the standard name of the symbol '&' that joins two words or names?

Accepted Answer

Introduction / Context: This question tests basic knowledge of common symbols used in written English and computer keyboards. Recognizing the correct term for each symbol is important in mathematics, programming, typography, and logical reasoning. Here we focus on the symbol that looks like a stylized combination of the letters e and t: the ampersand. Given Data / Assumptions: The symbol in question is '&'. It commonly appears between two names or words, for example in expressions like A & B. We are given several terminology options: caret, bar, ampersand, reversed caret, and apostrophe. We assume standard English and computer terminology, not informal nicknames. Concept / Approach: The key is to recall standard names of common punctuation and operator symbols. The symbol '&' historically comes from the Latin word 'et' meaning 'and', and its modern technical name is ampersand. The other options refer to different symbols or slightly misdescribed shapes, which we can rule out by comparison. Step-by-Step Solution: Step 1: Visualize the symbol '&' as seen on keyboards and in text such as A & B. Step 2: Recall that this symbol is read as the word 'and' in English. Step 3: The historical and typographical name for this character is ampersand. Step 4: A caret is the small V shaped symbol ^ used to indicate an insertion point or exponent. Step 5: A bar usually refers to a vertical line | or horizontal line used for absolute value or logical OR. Step 6: An apostrophe is the small raised comma like mark used in contractions and possessives, not to join two words. Step 7: None of these match the shape and function of '&', leaving ampersand as the correct answer. Verification / Alternative check: You can verify the name by looking at common programming languages where logical AND is written as && but bitwise AND or string joining may use &. Manuals and typography guides consistently refer to this symbol as the ampersand. Word processors often include it in their lists of special characters under that name. Why Other Options Are Wrong: Caret: This is the symbol ^, often used for powers or insert marks, not for the word and. Vertical bar: The bar is |, used for absolute value or as a separator, which looks completely different. Reversed caret: This is not a standard typographical term, and in any case does not refer to &. Apostrophe: This is the symbol used in words like does not or teachers, not the ampersand. Common Pitfalls: Some learners confuse names when they hear similar sounding terms or when they rarely speak them aloud. Another pitfall is thinking only in terms of function, such as saying 'and symbol', without knowing the formal name. For standardized tests and technical communication, using the correct term ampersand is important. Final Answer: The standard name of the symbol '&' is Ampersand.

Question 7

Evaluate the arithmetic expression 8(6 + 5) − 10 and choose the correct numerical value.

Accepted Answer

Introduction / Context: This problem checks your understanding of the order of operations, often remembered by the rule BODMAS or PEMDAS. You must correctly handle brackets or parentheses, multiplication, and subtraction in the expression 8(6 + 5) − 10. Many errors come from doing operations in the wrong order or making small arithmetic mistakes. Given Data / Assumptions: The expression is 8(6 + 5) − 10. There is a pair of parentheses around 6 + 5. The term 8(6 + 5) means 8 multiplied by the result inside the parentheses. We subtract 10 at the end. All operations are ordinary integer arithmetic. Concept / Approach: The order of operations tells us to compute parentheses first, then multiplication or division, and finally addition or subtraction. So we must first add 6 and 5, then multiply by 8, and finally subtract 10. This systematic approach prevents mistakes that come from working left to right without regard to operation priority. Step-by-Step Solution: Step 1: Evaluate the expression inside the parentheses: 6 + 5. Step 2: Compute 6 + 5 = 11. Step 3: Now the expression becomes 8 * 11 − 10. Step 4: Perform the multiplication: 8 * 11 = 88. Step 5: Now subtract 10 from 88: 88 − 10 = 78. Step 6: Therefore, the value of the expression is 78. Verification / Alternative check: You can quickly verify your answer by doing the calculation again in a slightly different layout. For example, note that 8 * (6 + 5) is 8 * 11, and 8 * 10 is 80, while 8 * 1 is 8, so 80 + 8 = 88. Subtracting 10 then gives 78. Using mental arithmetic in two ways that agree gives confidence in the result. Why Other Options Are Wrong: 76: This might come from subtracting 12 instead of 10 or miscomputing the multiplication. 80: This could result from adding 6 and 5 to get 11, but then mistakenly using 10 * 8 instead of 11 * 8. 82: This may be the result of 8 * 11 = 88 and then subtracting 6 instead of 10. 68: This could arise from computing 6 + 5 = 11, then doing 6 * 8 = 48, adding 5 to get 53, and then subtracting 10, which ignores the correct grouping. Common Pitfalls: A very common mistake is to start multiplying 8 by 6 before dealing with the entire bracket, which violates the order of operations. Another pitfall is careless subtraction at the final step. Writing each step clearly and respecting parentheses prevents these simple but costly errors in timed tests. Final Answer: The correct value of the expression 8(6 + 5) − 10 is 78.

Question 8

For a regular pentagon (a five sided polygon with all sides and angles equal), how many distinct lines of symmetry does the figure have?

Accepted Answer

Introduction / Context: Lines of symmetry play an important role in geometry and non verbal reasoning. A line of symmetry is a line that divides a shape into two mirror image halves. Regular polygons, where all sides and angles are equal, have a predictable number of lines of symmetry. Here we consider a regular pentagon and determine how many symmetry lines it has. Given Data / Assumptions: The figure is a regular pentagon, meaning five equal sides and five equal interior angles. We are asked about lines of symmetry, not rotational symmetry. A line of symmetry must produce two identical halves when the figure is folded along that line. The pentagon is not irregular or skewed; it is perfectly regular. Concept / Approach: For regular polygons, the number of lines of symmetry equals the number of sides. Each line of symmetry either passes through one vertex and the midpoint of the opposite side or, in some polygons, through midpoints of opposite sides. For a regular pentagon there are five vertices and five sides, and each vertex can be matched symmetrically with the opposite side. Step-by-Step Solution: Step 1: Recall that a pentagon has 5 sides by definition. Step 2: For a regular polygon with n sides, there are n lines of symmetry. Step 3: In a regular pentagon, each line of symmetry passes through one vertex and the midpoint of the opposite side. Step 4: Because the pentagon has 5 vertices, we can draw exactly 5 such lines. Step 5: No other lines will create mirror image halves, because any other line will intersect sides or angles in an asymmetric way. Step 6: Therefore the number of lines of symmetry in a regular pentagon is 5. Verification / Alternative check: You can draw a regular pentagon and construct these lines using a ruler. Draw a straight line from each vertex to the midpoint of the opposite side. Folding the paper along any of these lines shows that one half falls exactly over the other, confirming that each line is a line of symmetry. Counting all such distinct lines gives 5, matching the theoretical rule of n symmetry lines for an n sided regular polygon. Why Other Options Are Wrong: 4: This would be correct for some other figures but not for a regular pentagon. It undercounts by one. 6: This overcounts and would suggest more symmetry than the shape actually has. 2: A rectangle has 2 lines of symmetry (unless it is a square), but this does not apply here. 0: A completely irregular pentagon can have no line of symmetry, but the question explicitly refers to a regular pentagon. Common Pitfalls: Learners sometimes confuse the number of sides with possible diagonals or think that odd sided shapes cannot have symmetry lines. Others may try to draw lines between vertices only, missing the vertex to midpoint lines. Remembering the general rule that a regular n sided polygon has n lines of symmetry is very helpful in such questions. Final Answer: A regular pentagon has 5 lines of symmetry.

Question 9

In Euclidean geometry, a line is often treated as an undefined term. Which option best explains why a line is considered an undefined term?

Accepted Answer

Introduction / Context: In geometry, some fundamental concepts such as point, line, and plane are treated as undefined terms. This does not mean that we do not know what they are, but rather that they are taken as basic building blocks and are not defined in terms of simpler ideas. This question checks whether you understand the philosophy behind undefined terms in a geometric system. Given Data / Assumptions: We are working in standard Euclidean geometry. Line is listed alongside point and plane as an undefined term. Several statements about lines are given as options. We must choose the statement that explains why line is called undefined, not just any true property about lines. Concept / Approach: An undefined term in geometry is a primitive concept used to define all other terms. It is described intuitively rather than through a formal definition. Many properties of lines, such as infinite length or containing infinitely many points, come from axioms and theorems, but they are not the reason that the term is undefined. The key is to distinguish between a definition and a property. Step-by-Step Solution: Step 1: Recall that undefined terms are basic words whose meanings are accepted without formal definition. Step 2: Point, line, and plane are the standard three undefined terms in Euclidean geometry. Step 3: Option A states that a line is a basic term that does not have a formal definition. This matches the idea of an undefined term. Step 4: The other options describe various properties or uses of a line, such as containing infinitely many points or having no width or depth. Step 5: These properties may be true or partly true, but they do not explain why line is called undefined. Step 6: Therefore, the best explanation is that line is an undefined basic term without a formal definition, which is option A. Verification / Alternative check: Consulting any standard geometry textbook confirms that the undefined terms are point, line, and plane. The text usually explains that these are not defined using other terms, but their meanings are conveyed through descriptions and diagrams. All other geometric objects, such as segments, rays, and angles, are defined using these primitive terms. This supports choosing the answer that directly refers to the lack of a formal definition. Why Other Options Are Wrong: Option B: A line does contain infinitely many points, but this is a consequence of axioms, not the reason it is undefined. Option C: Lines can indeed be used to construct other shapes, yet that is not what makes them undefined. Option D: Saying a line has no width or depth describes a property, not its status as a primitive concept. Option E: The idea of infinite length and no endpoints refers to an idealized model of a line, again a property rather than a reason for being undefined. Common Pitfalls: Students sometimes think that undefined means undefined in real life or that we do not know any properties of the term. In fact, we know many properties derived from axioms. Undefined in this context simply means there is no earlier or simpler definition within the system. Keeping that distinction clear helps avoid confusion in theoretical geometry questions. Final Answer: A line is called an undefined term because it is a basic term that does not have a formal definition in Euclidean geometry.

Question 10

In coordinate geometry, what is meant by the latus rectum of a parabola?

Accepted Answer

Introduction / Context: The term latus rectum appears frequently in coordinate geometry, especially in questions dealing with standard parabolic equations, focal properties, and lengths related to conic sections. Understanding exactly what geometric object the latus rectum represents is essential before applying formulas for its length in problems involving parabolas. Given Data / Assumptions: The conic under discussion is specifically a parabola. The options mention line segment, vertex, focus, major axis, and directrix. We assume the standard geometric definition used in mathematics textbooks. The latus rectum is related to the focus and the directrix of the parabola. Concept / Approach: A parabola can be defined as the set of points equidistant from a fixed point called the focus and a fixed line called the directrix. The latus rectum is a special chord (line segment) of the parabola. It passes through the focus and is parallel to the directrix. Its endpoints lie on the parabola, and its length is often used in standard formulas, for example 4a for the parabola y^2 = 4ax. Step-by-Step Solution: Step 1: Recall that a parabola has a focus (a fixed point) and a directrix (a fixed line). Step 2: The latus rectum is defined as a line segment whose endpoints lie on the parabola. Step 3: This line segment passes through the focus of the parabola. Step 4: The latus rectum is parallel to the directrix of the parabola. Step 5: Because of these properties, the latus rectum is a chord that helps describe the width of the parabola near its focus. Step 6: Therefore the best description is that it is a line segment through the focus and parallel to the directrix. Verification / Alternative check: In the standard parabola y^2 = 4ax, the focus is at (a, 0) and the directrix is x = -a. The latus rectum has endpoints at (a, 2a) and (a, -2a), which are points on the parabola. The segment joining these points has x coordinate a for all points and is therefore vertical, while the directrix is the vertical line x = -a. So the latus rectum is indeed parallel to the directrix and passes through the focus at (a, 0), matching the definition used in the correct option. Why Other Options Are Wrong: The vertex of the parabola is a single point where the curve changes direction, not a line segment. The focus is also a single point, not the chord that passes through it. The major axis is a concept used mainly for ellipses, not for simple parabolas. The directrix is an infinite straight line, not the finite line segment inside the parabola. Common Pitfalls: Many learners confuse the focus and the latus rectum, treating the latus rectum as if it were a single point. Others mix up definitions related to ellipses and parabolas, especially the term major axis. Remember that in a parabola the important objects are the vertex, focus, directrix, and the chord through the focus that is parallel to the directrix, which is the latus rectum. Final Answer: The latus rectum of a parabola is a line segment through the focus and parallel to the directrix of the parabola.

Question 11

In logical reasoning, how should the conditional statement 'If K is there, L has to be there' be correctly interpreted?

Accepted Answer

Introduction / Context: Conditional statements are a foundation of analytical and logical reasoning, especially in puzzles and arrangement problems. Understanding what a statement like 'If K is there, L has to be there' really means helps you draw correct conclusions and avoid invalid inferences. This question checks whether you recognise the correct logical interpretation of such a conditional rule. Given Data / Assumptions: The condition is: If K is there, L has to be there. This is a one way conditional statement, often written symbolically as K → L. We are not given any information about what happens if L is there without K. The options describe different relationships between K and L. Concept / Approach: In logic, a statement 'If K, then L' means that whenever K occurs, L must also occur. K is a sufficient condition for L, and L is a necessary condition for K. However, it does not state that L cannot occur without K. Many reasoning errors come from mistakenly reading the conditional in both directions. Therefore we must choose the option that states only that K implies L, not the stronger or reversed versions. Step-by-Step Solution: Step 1: Translate the sentence 'If K is there, L has to be there' into a logical form: K → L. Step 2: This means that in every situation where K is present, L must also be present. Step 3: It does not say that if L is present then K must be present. That would be L → K, which is a different statement. Step 4: It also does not say that K and L are always together in both directions, which would be K ↔ L. Step 5: Comparing with the options, only the statement 'If K is present, then L will also be present' accurately reflects K → L. Step 6: Therefore option B is the correct interpretation. Verification / Alternative check: Consider some sample scenarios. If K is present and L is missing, the rule is violated. If both K and L are present, the rule is satisfied. If K is missing but L is present, the rule places no restriction, so this is allowed. These cases exactly match the logical form K → L and confirm that the rule is one way only. Option B fits this reasoning precisely. Why Other Options Are Wrong: Option A: Says K and L are always together and suggests a two way relationship, which is too strong. Option C: States 'If K is not present, then L will not be present', which reverses and negates the original condition and is not logically equivalent here. Option D: Claims K and L are never together, which directly contradicts the original statement. Option E: Reverses the direction by saying that L implies K, which is not given. Common Pitfalls: A very common mistake is to assume that 'If K, then L' automatically also means 'If L, then K'. This confusion between a conditional and its converse leads to wrong deductions in logic games. Another pitfall is assuming that the absence of K forces the absence of L, which is again not supported. Always pay attention to the direction of the arrow in conditional rules. Final Answer: The correct interpretation is that if K is present, then L will also be present.

Question 12

A university library budget committee must reduce exactly five of eight areas of expenditure I, J, K, L, M, N, O and P, under the following conditions: If both I and O are reduced, P is also reduced. If L is reduced, neither N nor O is reduced. If M…

Accepted Answer

Introduction / Context: This is a classic analytical reasoning or logic game question that involves conditions on a committee reducing certain areas of expenditure. The task is to interpret the rules correctly, apply them systematically, and then answer a specific question about which pair of areas cannot be reduced given an extra condition. Such problems are common in competitive exams to test structured logical thinking. Given Data / Assumptions: There are eight areas of expenditure: I, J, K, L, M, N, O, and P. Exactly five of these eight areas are reduced. Rule 1: If both I and O are reduced, then P is also reduced. Rule 2: If L is reduced, then neither N nor O is reduced. Rule 3: If M is reduced, then J is not reduced. Rule 4: Of J, K, and N exactly two are reduced. Additional condition for the question: Both K and N are reduced. Concept / Approach: We must translate the rules into logical constraints and then consider all valid combinations that satisfy them, given that K and N are reduced. From these valid combinations we determine which pair of areas never appears in the list of reduced areas. That pair is the one where neither area could be reduced under the stated conditions. Step-by-Step Solution: Step 1: From the condition that both K and N are reduced, and from Rule 4 (exactly two of J, K, N are reduced), we conclude that J cannot be reduced. Thus K and N are reduced, J is not. Step 2: Since N is reduced, Rule 2 tells us that L cannot be reduced, because L being reduced would forbid N from being reduced. Step 3: So far the reduced list must include K and N, and must exclude J and L. Step 4: We still need a total of 5 reduced areas. So three more areas among I, M, O, P can be chosen, subject to the other rules. Step 5: Rule 3 says if M is reduced then J is not reduced. J is already not reduced, so this rule is automatically satisfied and does not add a new restriction here. Step 6: Rule 1 says if I and O are both reduced then P must also be reduced. This simply links I, O, and P but does not affect J or L. Step 7: Now observe that J is never reduced in any valid configuration because K and N are the two chosen among J, K, N. L is also never reduced because N is reduced. Step 8: Therefore the pair of areas that cannot be reduced under these conditions is J and L. Verification / Alternative check: We can verify by constructing sample valid combinations. For example: reduce I, K, M, N, P. This satisfies all rules and leaves J and L unreduced. Another valid combination is K, N, O, P, and I, where again J and L are not reduced. In every attempt, N being reduced blocks L, and K and N being the two from J, K, N blocks J. Since we can find valid sets where I, M, O, or P are reduced, but never J or L, the pair J and L is indeed the one that can never be reduced when K and N are reduced. Why Other Options Are Wrong: I and L: I can be reduced in several valid combinations, so this pair is not impossible. J and M: J cannot be reduced, but M may be reduced as long as J is not, so the pair is not impossible. I and J: I may be reduced; only J is blocked in all valid cases, so the pair is not correct. M and O: Both M and O may appear in some valid reduction sets, so this pair is clearly possible. Common Pitfalls: Many students forget that 'exactly two' of J, K, N are reduced, which immediately fixes J as not reduced when both K and N are reduced. Others misread Rule 2 and think that N being reduced blocks L from being reduced in the other direction, which is actually correct here. Some learners also forget to count exactly five reduced areas and instead focus only on a subset of rules. A systematic approach, marking each area as forced in or out, helps avoid these mistakes. Final Answer: When both K and N are reduced, the two areas that can never be reduced are J and L.

Question 13

In a special code language, colour names are changed as follows: white is called black, black is called red, red is called yellow, yellow is called green, green is called blue, blue is called violet and violet is called orange. Under this code, what…

Accepted Answer

Introduction / Context: This problem is a typical example of a coding or substitution question often seen in analytical reasoning. Real world labels are reassigned in a systematic way, and you must mentally translate from the actual property to the new coded label. Here colour names are remapped, and you must identify the coded name that corresponds to the real colour of human blood. Given Data / Assumptions: Real world fact: healthy human blood is red in colour. The coding scheme is: white is called black black is called red red is called yellow yellow is called green green is called blue blue is called violet violet is called orange We must find the word used in the code language for the real colour red. Concept / Approach: The key idea is to separate the actual colour from the new name used for it. We first determine the actual colour of human blood, which is red. Then we look in the given mapping for the rule that tells us what the code language calls red. We must not be distracted by what red is called in normal language, but only use the information from the mapping table provided. Step-by-Step Solution: Step 1: Recall that human blood is naturally red in colour. Step 2: From the code mapping, identify the statement that involves red: 'red is called yellow'. Step 3: This means that whenever something is actually red, in the code language people will say 'yellow'. Step 4: Since blood is actually red, in the code language its colour will be stated as yellow. Step 5: Therefore, among the options, 'Yellow' is the correct answer. Verification / Alternative check: As a quick check, you can write a small mapping table: actual red → stated yellow, actual black → stated red, actual white → stated black, and so on. For blood you start on the actual side with red and then move to the code side, which is yellow. No other mapping step connects directly to the actual colour of blood, so there is no ambiguity. Why Other Options Are Wrong: Green: This is the coded name for actual yellow, not for red. Black: This is the coded name for actual white, not relevant for blood. Red: This is the coded name for actual black, so it does not represent actual red in this code. Blue: This is the coded name for actual green, again unrelated to the actual colour of blood. Common Pitfalls: Many learners forget to separate the actual property from the new label and choose red simply because they know blood is red. Others read the mapping backward and think that because something is called yellow it must be red, confusing the direction of the mapping. Drawing a simple two column list (actual colour versus coded name) and following it carefully prevents such errors. Final Answer: Under the given code language, the colour of human blood would be stated as Yellow.

Question 14

Pankaj is taller than Vinod, and Vinod is shorter than Pramod. Usha is taller than Priyanka but shorter than Vinod. Pramod is shorter than Pankaj. Based on these comparisons of height among the five friends, who is the tallest?

Accepted Answer

Introduction / Context: Ranking people by height based on a series of pairwise comparisons is a very common type of analytical reasoning question. The aim is to translate verbal statements into an ordered list and then answer a question such as who is tallest or who is shortest. Here we need to find the tallest person among five friends: Pankaj, Vinod, Pramod, Usha and Priyanka. Given Data / Assumptions: Pankaj is taller than Vinod. Vinod is shorter than Pramod. Usha is taller than Priyanka but shorter than Vinod. Pramod is shorter than Pankaj. No two people are of exactly the same height. Concept / Approach: We need to convert the relational statements into inequalities and then chain them together to form a complete ordering. Using symbols like greater than for taller and less than for shorter, we can represent the relations numerically and then find the maximum element in that order. This is essentially a problem of arranging items based on comparative information. Step-by-Step Solution: Step 1: From 'Pankaj is taller than Vinod', we write Pankaj > Vinod. Step 2: From 'Vinod is shorter than Pramod', we write Pramod > Vinod. Step 3: From 'Pramod is shorter than Pankaj', we write Pankaj > Pramod. Step 4: Combine these to get Pankaj > Pramod > Vinod. Step 5: From 'Usha is taller than Priyanka but shorter than Vinod', we get Vinod > Usha > Priyanka. Step 6: Combine everything to get a complete order from tallest to shortest: Pankaj > Pramod > Vinod > Usha > Priyanka. Step 7: The tallest person is therefore the first in this chain, Pankaj. Verification / Alternative check: We can check the order against each sentence. Pankaj > Vinod is satisfied. Pramod is between Pankaj and Vinod, so Pramod > Vinod holds and Pankaj > Pramod also holds. Vinod > Usha > Priyanka follows the last information. All original statements fit the order Pankaj, Pramod, Vinod, Usha, Priyanka without contradiction, confirming that Pankaj is indeed tallest. Why Other Options Are Wrong: Pramod: Pramod is shorter than Pankaj, so he cannot be the tallest. Vinod: Both Pankaj and Pramod are taller than Vinod, so this is not correct. Usha: Usha is shorter than Vinod and therefore also shorter than Pankaj and Pramod. Priyanka: She is the shortest, since Usha is taller than Priyanka and all others are taller than Usha. Common Pitfalls: A common mistake is to miss one of the comparisons or to fail to combine them correctly, which can lead to an incorrect ranking. Another pitfall is to assume transitive relations without writing them out clearly. Drawing a simple vertical list or using inequality symbols to show taller and shorter relationships is a reliable method to avoid confusion. Final Answer: The tallest among the five friends is Pankaj.

Question 15

Four friends P, Q, R and S are compared by height. P is shorter than Q but taller than R, and R is shorter than S. Based on this information, who is the shortest among all four friends?

Accepted Answer

Introduction / Context: Height comparison questions ask you to use relative information to rank people from tallest to shortest or vice versa. They are common in analytical reasoning sections and test your ability to translate language into ordered relationships. Here we must determine who is the shortest among P, Q, R and S using a few simple statements about their heights. Given Data / Assumptions: P is shorter than Q. P is taller than R. R is shorter than S. No two friends have exactly the same height. Concept / Approach: The idea is to express each sentence as an inequality. 'Shorter than' means less in height, and 'taller than' means greater. Once we convert each statement, we can chain them together to form a complete partial order and find the minimum element, which corresponds to the shortest person. This is a simple but important reasoning skill. Step-by-Step Solution: Step 1: From 'P is shorter than Q', write Q > P. Step 2: From 'P is taller than R', write P > R. Step 3: Combining these, we get Q > P > R. Step 4: From 'R is shorter than S', write S > R. Step 5: Now we know Q, P, and S are all taller than R, because Q > P > R and S > R. Step 6: We do not need the exact ordering of Q, P, and S among themselves, because the question only asks for the shortest person. Step 7: Since R is shorter than P, Q, and S, R must be the shortest among all four friends. Verification / Alternative check: Consider any numeric example that satisfies the inequalities. For instance, let Q have height 170 units, P have 165 units, R have 160 units, and S have 168 units. These values satisfy Q > P > R and S > R. In this example, R clearly has the smallest height, confirming that the reasoning is correct and that R is indeed the shortest. Why Other Options Are Wrong: P: P is taller than R, so P cannot be the shortest. Q: Q is taller than P and therefore taller than R, so Q is not the shortest. S: S is taller than R by the given statement, so S is not the shortest. All four are of equal height: The statements clearly state some friends are taller or shorter than others, so equal height is impossible. Common Pitfalls: Sometimes students try to fully order every person even when it is not required, which can lead to confusion. Another mistake is misreading phrases like 'shorter than' and reversing the inequality. Drawing arrows or writing a chain like Q > P > R and S > R on paper is a quick and reliable way to avoid such errors and to see immediately who is at the bottom of the chain. Final Answer: The shortest among the four friends is R.

Question 16

From the given alternatives, select the word which CANNOT be formed using the letters of the given word. Demonstration

Accepted Answer

Damage

Question 17

Vineet is taller than Raman but shorter than Jyoti. Sumit is the shortest. Deepak is taller than Sumit but shorter than Raman. Who is the tallest?

Accepted Answer

Jyoti

Analytical Reasoning Questions