Question 1

The weights of four boxes are 100 kg, 70 kg, 50 kg and 90 kg. For these box weights, which of the following values cannot be obtained as the total weight, in kilograms, of any combination if in each combination a box can be used at most once?

Accepted Answer

Introduction / Context: This arithmetic reasoning question deals with combinations of given weights. You are provided with four box weights and several candidate total weights. The task is to identify which total cannot be obtained by selecting some or all of the boxes, with the important restriction that each box can be used at most once in any combination. This type of problem checks your ability to think systematically and to handle simple but careful arithmetic operations. Given Data / Assumptions: - Box weights: 100 kg, 70 kg, 50 kg and 90 kg. - Each box can either be included or excluded in a combination, but cannot be repeated. - We can form totals using one, two, three or all four boxes. - Candidate totals (in kg): 310, 260, 230, 210 and 240. - We must find the total weight that is impossible to obtain from any valid combination. Concept / Approach: The safest strategy is to list all possible distinct sums that can be obtained from the four weights. Since only four boxes are involved, the number of subsets is small enough to enumerate directly. After obtaining all achievable totals, we simply compare them with the options. Any option that does not appear in this list of sums is the required answer. This exhaustive but short approach avoids guesswork and ensures that no valid combination is overlooked. Step-by-Step Solution: Step 1: Single box totals are: 50, 70, 90 and 100 kilograms. Step 2: Two box combinations and their sums: - 100 + 70 = 170 - 100 + 50 = 150 - 100 + 90 = 190 - 70 + 50 = 120 - 70 + 90 = 160 - 50 + 90 = 140 Step 3: Three box sums: - 100 + 70 + 50 = 220 - 100 + 70 + 90 = 260 - 100 + 50 + 90 = 240 - 70 + 50 + 90 = 210 Step 4: Four box sum: 100 + 70 + 50 + 90 = 310. Step 5: Collect all distinct achievable totals: 50, 70, 90, 100, 120, 140, 150, 160, 170, 190, 210, 220, 240, 260 and 310. Step 6: Compare these with the options. We see that 310, 260, 210 and 240 are achievable, but 230 does not appear in the list. Verification / Alternative check: An additional check is to try to construct 230 kilograms directly. To obtain 230, one might attempt sums like 100 + 70 + 50 (which is 220) or 100 + 90 + 50 (which is 240). Any pair such as 100 + 70 gives 170, and adding 50 or 90 overshoots 230. Similarly, 90 + 70 = 160, and adding 50 gives 210, still not equal to 230. There is no way to select these four weights without repetition to sum exactly to 230 kilograms, which confirms our earlier conclusion. Why Other Options Are Wrong: - 310 kilograms is achieved by using all four boxes together. - 260 kilograms is obtained from 100 + 70 + 90. - 210 kilograms is obtained from 70 + 50 + 90. - 240 kilograms is obtained from 100 + 50 + 90. Because these totals can be formed by appropriate selections, they are not correct answers to the question that asks for an impossible total. Common Pitfalls: Many candidates attempt to rely on quick mental arithmetic without listing all combinations, and in the process they may miss a valid sum or incorrectly conclude that a total is impossible. Another common error is to accidentally count a box more than once, violating the condition that a box can be used only once. Systematic listing of single, double, triple and full combinations helps avoid these issues and leads to an accurate answer. Final Answer: The total weight that cannot be obtained from any combination of the four boxes is 230 kilograms.

Question 2

The weights of four boxes are 20 kg, 40 kg, 50 kg and 30 kg. For these box weights, which of the following values cannot be obtained as the total weight, in kilograms, of any combination if in each combination a box can be used at most once?

Accepted Answer

Introduction / Context: This question is another example of a weight combination puzzle. You are given four box weights and asked which of several candidate totals cannot be formed by taking some or all of the boxes, with the rule that each box can be used at most once. Problems like this appear frequently in aptitude tests because they combine basic arithmetic with systematic reasoning about combinations and totals. Given Data / Assumptions: - Box weights: 20 kg, 40 kg, 50 kg and 30 kg. - Each box may be chosen or not chosen, but cannot be repeated. - Combinations can include one, two, three or all four boxes. - Candidate totals (in kg): 140, 130, 90 and 120, plus one more option. - We must find the total weight that cannot be formed from any valid combination of the four weights. Concept / Approach: As in other combination questions, the most reliable method is to enumerate all possible distinct sums from the available weights. With only four numbers, this enumeration is quite manageable. After listing all achievable totals, we compare them with the given options. Any option that does not appear in the list must be the impossible total. This method guarantees that no valid sum is missed and makes the answer clear. Step-by-Step Solution: Step 1: List single box totals: 20, 30, 40 and 50 kilograms. Step 2: Compute two box sums: - 20 + 40 = 60 - 20 + 50 = 70 - 20 + 30 = 50 - 40 + 50 = 90 - 40 + 30 = 70 - 50 + 30 = 80 Step 3: Compute three box sums: - 20 + 40 + 50 = 110 - 20 + 40 + 30 = 90 - 20 + 50 + 30 = 100 - 40 + 50 + 30 = 120 Step 4: Sum of all four boxes: 20 + 40 + 50 + 30 = 140. Step 5: Collect distinct achievable totals: 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120 and 140. Step 6: Compare with options: 140, 130, 90, 120 and 100. We see that 140, 90, 120 and 100 are present in the achievable list, but 130 does not appear. Verification / Alternative check: To double check, we can specifically look for ways to form 130 kilograms. Try combinations involving the larger weights. The sum 50 + 40 + 30 = 120. Adding 20 to any triple would exceed 130 and actually give 140. Pair sums such as 50 + 40 = 90 and 50 + 30 = 80 cannot reach 130 even if a third weight is added because only one remaining weight is left. There is therefore no subset of the four weights that yields exactly 130 kilograms, confirming that it is impossible. Why Other Options Are Wrong: - 140 kilograms is achieved by combining all four boxes. - 90 kilograms is obtained from 40 + 50 or from 20 + 40 + 30. - 120 kilograms is obtained from 40 + 50 + 30. - 100 kilograms is obtained from 20 + 50 + 30. Since these totals can all be formed from the given weights, they do not satisfy the requirement of being impossible totals. Common Pitfalls: A frequent mistake is to assume that a certain option looks unusual and must be impossible without performing a full combination check. Another pitfall is accidentally reusing a weight, which violates the condition that each box can appear only once in any combination. By listing single, double, triple and full combinations carefully, you ensure that all sums are considered and that the final answer is accurate. Final Answer: The total weight that cannot be obtained from any combination of the four boxes is 130 kilograms.

Question 3

The speed of the Duronto Express is greater than the speed of the Rajdhani Express. The Shatabdi Express moves faster than the Garib Rath Express but slower than the Rajdhani Express. Based on these comparisons of train speeds, which one of the four…

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Introduction / Context: This verbal reasoning problem involves comparing relative speeds of four trains. Instead of giving exact numerical speeds, the question presents inequality relations such as faster than and slower than. The goal is to use these comparisons to determine which train is the slowest overall. Questions of this type test your ability to translate verbal relations into a logical order and to reason about extremal values like the fastest or the slowest. Given Data / Assumptions: - Trains: Duronto, Rajdhani, Shatabdi and Garib Rath. - The speed of Duronto is more than the speed of Rajdhani. - The Shatabdi moves faster than Garib Rath. - The Shatabdi moves slower than Rajdhani. - All trains are considered on the same route or under comparable conditions. - We must identify the train with the lowest speed among the four. Concept / Approach: The idea is to express speed comparisons using inequalities. Let higher speed mean greater in an ordering. From the statements, Duronto is faster than Rajdhani, so Duronto is above Rajdhani in the speed order. Shatabdi is slower than Rajdhani but faster than Garib Rath, which gives a chain involving three trains. By combining both pieces of information into a single consistent order, we can see clearly which train lies at the lowest position. No exact speed values are needed; only relative ordering matters. Step-by-Step Solution: Step 1: From the statement that Duronto is faster than Rajdhani, write Duronto > Rajdhani in terms of speed. Step 2: From the second statement, Shatabdi moves faster than Garib Rath but slower than Rajdhani. This means Rajdhani > Shatabdi > Garib Rath. Step 3: Combine the inequalities from both steps. We already know Duronto > Rajdhani, and now we have Rajdhani > Shatabdi > Garib Rath. Step 4: The single chain of speeds from highest to lowest is: Duronto, then Rajdhani, then Shatabdi, then Garib Rath. Step 5: The train at the bottom of this chain, with the lowest speed, is Garib Rath. Verification / Alternative check: To verify, imagine assigning sample speeds consistent with the inequalities. For example, let Garib Rath have speed 80 units, Shatabdi 90 units, Rajdhani 100 units and Duronto 110 units. These assumed values satisfy all conditions: Shatabdi (90) is faster than Garib Rath (80) and slower than Rajdhani (100), and Duronto (110) is faster than Rajdhani (100). In this example, Garib Rath clearly remains the slowest, confirming the conclusion. Any other set of values that respects the inequalities will also place Garib Rath at the lowest position. Why Other Options Are Wrong: - Shatabdi cannot be the slowest because it is explicitly said to be faster than Garib Rath. - Rajdhani cannot be the slowest because Shatabdi is slower than Rajdhani but still faster than Garib Rath. - Duronto cannot be the slowest because it is faster than Rajdhani, which itself is faster than Shatabdi and Garib Rath. - Therefore, only Garib Rath consistently appears at the minimum speed. Common Pitfalls: A common error is to misread phrases like slower than and faster than, especially when two comparisons are combined in one sentence. Students may also prematurely assume that Rajdhani or Shatabdi is the slowest without building the full chain of inequalities. Another pitfall is to overlook the impact of the first statement about Duronto and Rajdhani, even though it does not directly mention Garib Rath. Systematically writing a single ordered sequence of speeds avoids these mistakes. Final Answer: The train with the lowest speed among the four is Garib Rath.

Question 4

In a row of girls, Aruna is the first girl from one end. There are 8 girls between Aruna and Bimla. There are 5 girls between Bimla and Chetna. If there are 14 girls standing after Chetna in the row, then what is the minimum possible total number of…

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Introduction / Context: This problem is a classic example of position and distance reasoning in a row arrangement. You are given the relative positions of three girls, Aruna, Bimla and Chetna, as well as information about how many girls stand between them and after one of them. The goal is to determine the minimum possible number of girls in the entire row. Such questions are common in verbal and arithmetic reasoning and test your ability to convert verbal descriptions into a positional model. Given Data / Assumptions: - Aruna is the first girl in the row, so she stands at position 1 from the left. - There are 8 girls between Aruna and Bimla. - There are 5 girls between Bimla and Chetna. - There are 14 girls standing after Chetna in the same row. - We are asked for the minimum possible total number of girls in the row. Concept / Approach: The key idea is to convert between the number of girls between two positions and their numeric positions in the row. If there are k girls between two persons, their positions differ by k + 1. Aruna is fixed at position 1, so Bimla has a fixed position relative to her. Chetna can be placed either to the right or to the left of Bimla with 5 girls between them. Each scenario implies a different total length of the row, once we also account for the 14 girls after Chetna. Among these scenarios, we must select the one that yields the smallest possible total number of girls. Step-by-Step Solution: Step 1: Since Aruna is first, assign her position as 1. Step 2: There are 8 girls between Aruna and Bimla, so the distance between Aruna and Bimla is 8 + 1 = 9 positions. Thus, Bimla stands at position 1 + 9 = 10 from the left. Step 3: There are 5 girls between Bimla and Chetna. This means the distance between their positions is 5 + 1 = 6 positions. Step 4: Case 1: Chetna is to the right of Bimla. Then her position is 10 + 6 = 16. If 14 girls stand after Chetna, they occupy positions 17 to 30, giving a total of 30 girls in this configuration. Step 5: Case 2: Chetna is to the left of Bimla. Then her position is 10 - 6 = 4. If 14 girls stand after Chetna, they occupy positions 5 to 18, so the last position in the row is 18, and there are 18 girls in total. Step 6: Both configurations satisfy the given conditions, but the question explicitly asks for the minimum possible number of girls, which is 18 from Case 2. Verification / Alternative check: Verify that Case 2 really satisfies all statements. With Aruna at position 1 and Bimla at position 10, there are indeed 8 girls between them at positions 2 through 9. Chetna is at position 4, so between Bimla at 10 and Chetna at 4 there are girls at positions 5, 6, 7, 8 and 9, a total of 5 girls. From Chetna at 4 to the end of the row at position 18, there are girls at positions 5 through 18, giving 14 girls after Chetna. All conditions are met, and the row length is 18. Why Other Options Are Wrong: - Totals such as 13, 15 or 16 are too small to accommodate the distances and counts specified, especially the requirement of 14 girls after Chetna. - Any total less than 18 would fail to provide enough positions beyond Chetna to place 14 girls after her. - Although a larger total such as 20 is possible in some alternative arrangements, the question asks for the minimum possible, so such larger numbers are not correct answers. Common Pitfalls: Students often forget that when two persons have k people between them, their positions differ by k + 1, not just k. Another frequent error is to assume that the second person must always be to the right, whereas here Chetna can be on either side of Bimla. Ignoring one of the possible directions can lead to missing the minimum configuration. Carefully considering both cases and then comparing their totals avoids these mistakes. Final Answer: The minimum possible total number of girls in the row is 18.

Question 5

Sanjeev scored the highest marks in the class. Rahul scored more marks than Nirbhay but fewer marks than Sameer. Arpit scored more marks than Rahul. If there are exactly five students Sanjeev, Rahul, Nirbhay, Sameer and Arpit, who obtained the 4th r…

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Introduction / Context: This ranking question is based on comparative statements about examination marks. Instead of providing exact scores, the problem gives relative information such as higher marks and lower marks among the five students. You are asked to find who occupies the 4th rank when the students are arranged in order of decreasing marks. Such questions test logical ordering skills and the ability to work with inequalities involving several individuals. Given Data / Assumptions: - Students: Sanjeev, Rahul, Nirbhay, Sameer and Arpit. - Sanjeev scored the highest marks in the class. - Rahul scored more than Nirbhay but fewer than Sameer, giving Sameer > Rahul > Nirbhay. - Arpit scored more marks than Rahul, so Arpit > Rahul. - No contradictions are implied, and all five students have distinct scores. - We must find who stands at the 4th position when ordered from highest marks to lowest marks. Concept / Approach: The core idea is to build an order from the given inequalities. Sanjeev is known to be the topper, so he occupies rank 1. Among the remaining four students, we know that Sameer is above Rahul, and Rahul is above Nirbhay. We also know that Arpit is above Rahul, but we do not initially know whether Arpit is above or below Sameer. However, regardless of this detail, the relative positions of Rahul and Nirbhay are fixed, and that is enough to identify the student at 4th place. Step-by-Step Solution: Step 1: Place Sanjeev first, since he has the highest marks overall. Step 2: From the relation Sameer > Rahul > Nirbhay, we know that among these three, Nirbhay must be below Rahul, and Rahul must be below Sameer. Step 3: From Arpit > Rahul, we know Arpit is above Rahul. There are two possibilities: - Possibility 1: Arpit is above Sameer, so the order (top to bottom) is Sanjeev, Arpit, Sameer, Rahul, Nirbhay. - Possibility 2: Arpit is between Sameer and Rahul, so the order is Sanjeev, Sameer, Arpit, Rahul, Nirbhay. Step 4: In both possibilities, the student at the 4th position from the top is Rahul. Thus his rank is 4th regardless of the exact position of Arpit relative to Sameer. Verification / Alternative check: To further verify, you can assign sample marks that respect all inequalities. For example, in the first possibility, let Sanjeev have 95, Arpit 90, Sameer 88, Rahul 80 and Nirbhay 70. All given relations hold, and Rahul is 4th. In the second possibility, let Sanjeev have 95, Sameer 92, Arpit 88, Rahul 80 and Nirbhay 70. Again, all relations hold and Rahul is 4th. The fact that different consistent assignments still place Rahul at rank 4 confirms that his position is fixed by the data. Why Other Options Are Wrong: - Sameer is always ranked above Rahul and cannot be 4th. - Nirbhay is always below Rahul and therefore has rank 5 in every consistent ordering. - Arpit is above Rahul and therefore must be ranked either 2nd or 3rd, not 4th. - The conclusion is fully determined, so the option stating that it cannot be determined is incorrect. Common Pitfalls: Many students attempt to force a single linear order too early or assume that the position of Arpit relative to Sameer must be specified. They may also misread the phrase scored more than and reverse the inequality. Another frequent mistake is to assume that because one comparison is not completely specified, the entire ranking cannot be determined, which is not true here. Focusing on the relative position of Rahul and Nirbhay within all possible orders leads to the correct answer. Final Answer: The student who obtained the 4th rank in the class is Rahul.

Question 6

In a row of professors, Akash is the first professor from one end. There are 12 professors between Akash and Bhumi. There are 6 professors between Bhumi and Charu. If there are 15 professors standing after Charu in the row, then what is the minimum …

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Introduction / Context: This reasoning question is closely related to other position based row problems. You have three named professors Akash, Bhumi and Charu, and you know how many professors stand between each pair and how many stand after Charu. The task is to determine the minimum possible total number of professors in the row. These problems test your understanding of positions, distances, and how counts of people between two individuals translate into numeric positions. Given Data / Assumptions: - Akash is the first professor in the row, so Akash stands at position 1 from the left. - There are 12 professors between Akash and Bhumi. - There are 6 professors between Bhumi and Charu. - There are 15 professors after Charu in the row. - We are asked for the minimum possible total number of professors in the row. Concept / Approach: We convert the description into position numbers. If there are k professors between two people, then their positions differ by k + 1. Akash has a fixed position, so Bhumi gets a fixed position relative to him. Charu can be placed either to the right or to the left of Bhumi while maintaining 6 professors between them. Each choice leads to a different total row length once we account for the 15 professors after Charu. We then choose the configuration with the smallest valid total. Step-by-Step Solution: Step 1: Akash is first, so assign Akash position 1. Step 2: There are 12 professors between Akash and Bhumi, so the distance between their positions is 12 + 1 = 13 positions. Thus, Bhumi stands at position 1 + 13 = 14 from the left. Step 3: There are 6 professors between Bhumi and Charu, so their positions differ by 6 + 1 = 7. Step 4: Case 1: Charu is to the right of Bhumi. Then Charu is at position 14 + 7 = 21. If there are 15 professors after Charu, they occupy positions 22 through 36, giving a total of 36 professors in this arrangement. Step 5: Case 2: Charu is to the left of Bhumi. Then Charu is at position 14 - 7 = 7. With 15 professors after Charu, they occupy positions 8 through 22. Thus, the last position in the row is 22, so there are 22 professors in total. Step 6: Both cases satisfy all relative position conditions. The question asks for the minimum possible total, so we select 22 professors from Case 2. Verification / Alternative check: Check Case 2 carefully. With Akash at position 1 and Bhumi at position 14, professors at positions 2 through 13 count to 12, which matches the number between Akash and Bhumi. Charu at position 7 leaves positions 8, 9, 10, 11, 12 and 13 between Bhumi at 14 and Charu at 7, a total of 6 professors, as required. From Charu at 7 to the end at position 22, positions 8 through 22 inclusive represent 15 professors, confirming the statement about professors after Charu. Therefore, all conditions hold for a row of length 22. Why Other Options Are Wrong: - Totals such as 20 or 21 are too small to allow 15 professors after Charu along with the given distances between Akash, Bhumi and Charu. - A total of 24 or higher is possible but not minimal. The question specifically asks for the minimum number, so larger consistent totals are not correct answers. - Among the listed choices, 22 is the smallest value that fits all positional constraints. Common Pitfalls: Learners sometimes assume that the person described first must always be on the left and the others to the right, ignoring the possibility of someone standing to the left of another intermediate person. Another common mistake is miscalculating the relation between the number of people between two positions and the difference in their positions. Remember that if there are k people between two individuals, their positions differ by k + 1. Considering both left and right possibilities and applying this rule correctly ensures a correct solution. Final Answer: The minimum possible total number of professors in the row is 22.

Question 7

Vishu, Pooja, Vishakha, Rani and Ram are sitting in a straight line. Pooja is third from the extreme right end. Vishu is second to the left of Pooja. Vishakha is to the right of Pooja. Rani is third to the right of Ram, and Ram is the immediate neig…

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Introduction / Context: This is a linear seating arrangement question involving five persons in a row. Several positional clues are provided, including phrases like third from the extreme right, second to the left, immediate neighbour and third to the right. The objective is to determine who occupies the central, or middle, seat in the row. Such problems are very common in reasoning sections of competitive exams and require careful stepwise placement of individuals. Given Data / Assumptions: - Persons: Vishu, Pooja, Vishakha, Rani and Ram. - Pooja is third from the extreme right end. - Vishu is second to the left of Pooja. - Vishakha is to the right of Pooja. - Rani is third to the right of Ram. - Ram is the immediate neighbour of Vishu. - We assume there are exactly five seats in a straight row. Concept / Approach: The approach is to fix positions using absolute clues first, then fill in remaining positions using relative clues. Since we know that Pooja is third from the extreme right in a row of five seats, Pooja must be in the middle seat. Once Pooja is placed, we can locate Vishu, Ram, Rani and Vishakha step by step using the given left, right and neighbour relationships. After filling all five positions, we simply identify who occupies the central seat, which we already know from the first step, but verifying the whole arrangement confirms our answer. Step-by-Step Solution: Step 1: Label the seats from left to right as positions 1, 2, 3, 4 and 5. Step 2: Pooja is third from the extreme right. In a five seat row, the seat positions from the right are 5 (first), 4 (second) and 3 (third). Therefore, Pooja must sit at position 3, which is the middle. Step 3: Vishu is second to the left of Pooja. Moving two seats left from position 3 lands at position 1. So Vishu sits at position 1. Step 4: Ram is the immediate neighbour of Vishu. Since Vishu is at position 1, his only neighbour is at position 2. Therefore, Ram sits at position 2. Step 5: Rani is third to the right of Ram. Starting from Ram at position 2, the seats to his right are positions 3 (first), 4 (second) and 5 (third). Thus, Rani sits at position 5. Step 6: Vishakha is to the right of Pooja, meaning her seat has a position greater than 3. The only remaining unoccupied seat is position 4, so Vishakha must sit at position 4. Step 7: The final arrangement from left to right is Vishu (1), Ram (2), Pooja (3), Vishakha (4) and Rani (5). The middle position is seat 3, which is occupied by Pooja. Verification / Alternative check: Check that all conditions are satisfied by the final arrangement. Pooja is indeed third from the right, as seats from the right are Rani (1st), Vishakha (2nd) and Pooja (3rd). Vishu is at position 1, which is two seats to the left of Pooja at position 3. Ram at position 2 is the immediate neighbour of Vishu at position 1. Rani at position 5 is three seats to the right of Ram at position 2. Lastly, Vishakha at position 4 is to the right of Pooja at position 3. Since all clues match, the arrangement is correct. Why Other Options Are Wrong: - Ram is at position 2, not in the middle. - Vishakha is at position 4, which is right of the middle seat. - Rani is at position 5, at the extreme right, not in the centre. - Vishu is at the extreme left at position 1, also not in the middle. Only Pooja occupies the central seat, so the other options cannot be correct. Common Pitfalls: Learners sometimes misinterpret phrases like third from the extreme right and mistakenly place that person at the second or fourth position. Another typical mistake is to forget to number the seats and mentally juggle positions, which makes errors in left and right moves more likely. Also, some candidates assume more than five seats or leave gaps, which breaks the structure of the puzzle. Drawing a simple row, labelling positions and placing persons step by step is a robust method to avoid these errors. Final Answer: The person sitting in the middle position of the line is Pooja.

Question 8

There are five friends I, J, K, L and M. The income of K is more than the income of L but less than the income of M. The income of J is the least among all. The income of I is less than the income of K. Based on this information, whose income is the…

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Introduction / Context: This is a typical comparison question based on the incomes of five friends. Rather than giving actual income figures, the problem describes who earns more or less compared to others. You must use these comparative statements to identify the friend who has the highest income. Questions like this test basic logical ordering skills without needing any numerical calculations. Given Data / Assumptions: - Friends: I, J, K, L and M. - Income of K is more than income of L. - Income of K is less than income of M, so M earns more than K. - Income of J is the least among all five friends. - Income of I is less than income of K. - All incomes are distinct and comparable. Concept / Approach: The goal is to translate the verbal relationships into an ordered list from highest to lowest income. We look for the person who does not have anyone above them in this ordering. K is known to be above L and I but below M. J is at the bottom because J has the least income. Without knowing the exact positions of L and I relative to each other, we can still see that M is above K, and therefore above everyone else who is below K. That observation is enough to identify the maximum income holder. Step-by-Step Solution: Step 1: From K is more than L and I is less than K, both L and I lie below K in the income order. Step 2: From J is the least, we know J is at the very bottom, below everyone including L and I. Step 3: From K is less than M, we know M lies above K in the income order. Step 4: Combining these relations, we obtain a partial ordering: M above K, and K above I and L, and all four above J. Step 5: Even if we do not know whether I is above L or L is above I, both of them are below K, and K is below M. Therefore, no one can be above M in the income order. Step 6: Hence, M has the highest income among the five friends. Verification / Alternative check: To verify, you can assign sample incomes consistent with the conditions. For example, suppose M earns 50 units, K earns 40 units, I earns 30 units, L earns 25 units and J earns 10 units. All statements are satisfied: K (40) is more than L (25) but less than M (50), J (10) is the least, and I (30) earns less than K (40). In this sample, M is clearly the highest earner. No matter how you adjust the exact values while respecting the inequalities, M will always remain on top because the relation K less than M puts M above K, and K is already above I, L and far above J. Why Other Options Are Wrong: - L earns less than K, so L cannot have maximum income. - I earns less than K, so I cannot be at the top either. - K is explicitly stated to earn less than M, so K is not the maximum. - The information is sufficient and unambiguous, so the answer cannot be that it cannot be determined. Common Pitfalls: A common error is to focus on the lower end of the ranking and get confused about the relative positions of I and L, even though the question only asks for the maximum. Some students also misread K is less than M as the opposite, leading to incorrect placements. Carefully reading comparative phrases and maintaining a mental or written order diagram prevents these mistakes and makes the solution straightforward. Final Answer: The friend with the maximum income is M.

Question 9

Mohan, Ritika, Janvi, Priya and Riya are friends who participate in a running race. Janvi runs faster than Ritika but slower than Priya. Mohan is the slowest runner. Riya runs faster than Priya. Who runs the fastest among the five friends?

Accepted Answer

Introduction / Context: This question is about comparing the running speeds of five friends. The problem uses relative terms such as faster than and slower than rather than giving specific times. You must interpret these comparisons and determine who is the fastest runner among Mohan, Ritika, Janvi, Priya and Riya. This type of ordering puzzle is common in reasoning tests and helps evaluate your ability to handle inequalities involving several individuals. Given Data / Assumptions: - Participants: Mohan, Ritika, Janvi, Priya and Riya. - Janvi runs faster than Ritika but slower than Priya, so Priya > Janvi > Ritika in speed. - Mohan is the slowest runner of all. - Riya runs faster than Priya, so Riya > Priya. - Each person has a distinct speed, and no ties are considered. Concept / Approach: We translate each statement into a speed inequality and then combine them into a single order from fastest to slowest. The information Priya > Janvi > Ritika immediately orders three runners. Mohan being slowest places him at the very bottom. Riya running faster than Priya places Riya at the top of this chain. After combining all these relations, the highest position in the order corresponds to the fastest runner, which is what the question asks us to find. Step-by-Step Solution: Step 1: From Janvi runs faster than Ritika but slower than Priya, write Priya > Janvi > Ritika in terms of speed. Step 2: Mohan is the slowest, so Mohan is below all others in the speed list. Step 3: Riya runs faster than Priya, so Riya > Priya. Step 4: Combine these relations. We already have Priya > Janvi > Ritika, and now Riya > Priya. Therefore, the full order from fastest to slowest is Riya, Priya, Janvi, Ritika and Mohan. Step 5: The fastest runner is the one at the top of this chain, which is Riya. Verification / Alternative check: As a check, you can assign sample running times. For example, suppose Riya completes the race in 10 seconds, Priya in 11 seconds, Janvi in 12 seconds, Ritika in 13 seconds and Mohan in 15 seconds. Smaller time means faster speed. These times satisfy all conditions: Janvi (12) is faster than Ritika (13) but slower than Priya (11), Mohan (15) is slowest, and Riya (10) is faster than Priya (11). With these values, Riya is clearly the fastest runner. Any other consistent assignment that respects the inequalities will also place Riya at the top. Why Other Options Are Wrong: - Priya cannot be the fastest because Riya is explicitly stated to run faster than Priya. - Ritika is below Janvi and Priya in speed, so she cannot be fastest. - Mohan is slowest among all, so he is at the bottom of the list, not at the top. - The information given is sufficient and clear, so the situation is fully determined, and it is incorrect to claim that it cannot be determined. Common Pitfalls: Some students confuse faster with slower and accidentally reverse inequalities. Others try to place Riya somewhere in the middle rather than at the top, forgetting the transitive nature of the comparisons. If Riya is faster than Priya, and Priya is faster than Janvi, then Riya is also faster than Janvi and so on. Writing down the order explicitly from fastest to slowest or slowest to fastest helps avoid such errors and makes the hierarchy clear. Final Answer: The friend who runs the fastest among the five is Riya.

Question 10

Five people A, B, C, D and E are compared by weight. The weight of A is more than the weight of C, and A has the second highest weight among all five. The weight of E is more than the weight of A. The weight of B is more than the weight of D. Based …

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Introduction / Context: This reasoning question is about comparing the weights of five individuals, labelled A, B, C, D and E. Instead of exact numerical weights, you are given relative information such as second highest and more than. The problem asks you to identify which person is the heaviest. Such questions help develop skills in working with partial orders and ranking based on comparative statements. Given Data / Assumptions: - People: A, B, C, D and E. - A is heavier than C. - A has the second highest weight among all five people. - E is heavier than A. - B is heavier than D. - All weights are distinct, and the term second highest refers to the rank when ordered from heaviest to lightest. Concept / Approach: The crucial statement is that A has the second highest weight. That means exactly one person is heavier than A, and the remaining three are lighter. We are also told that E is heavier than A, which immediately indicates that E must be the one person above A in the ranking. Therefore, E must be heaviest. The information about B being heavier than D and A being heavier than C helps to position B, C and D below A, but does not affect the identity of the heaviest individual once we know that someone is heavier than the person in second place. Step-by-Step Solution: Step 1: Since A has the second highest weight, exactly one person is heavier than A and three people are lighter than A. Step 2: The statement that E is heavier than A means E is above A in the weight ranking. Step 3: Because only one person can be heavier than A, E must be that single person. Therefore, E is heaviest among all five. Step 4: The statements that A is heavier than C and that B is heavier than D position C and D somewhere below A. They also indicate that B is above D, but all of these persons remain below A and therefore below E as well. Step 5: No other person can be heavier than A, so no one can be heavier than E either. Hence, E is the heaviest. Verification / Alternative check: You can assign sample weights consistent with the description to check the logic. For instance, suppose E weighs 80 units, A weighs 75 units, B weighs 70 units, D weighs 65 units and C weighs 60 units. Here, A is heavier than C, A is second heaviest, E is heavier than A, and B is heavier than D. In this arrangement, E is clearly the heaviest. Any other assignment that respects the same inequalities will still have E above A, and A in second place, so E must always remain the top ranked by weight. Why Other Options Are Wrong: - A cannot be the heaviest, because the question explicitly states that A is second heaviest and that E is heavier than A. - B and D are only compared to each other, and both are not given any relation that places them above A. Since A is second heaviest, B and D must be below A and thus below E. - C is lighter than A, which means C also cannot be the heaviest. Only E can occupy the highest position in the weight order. Common Pitfalls: Some students misinterpret second highest as second in some arbitrary order rather than second in the descending list of weights. Another common mistake is to ignore the strong implication of A having the second highest weight and to focus instead on weaker comparisons like B heavier than D. Remember that once you know someone is second, anyone strictly heavier than that person must be first. Recognising this makes the solution straightforward. Final Answer: The heaviest person among the five is E.

Question 11

A is taller than B. B is shorter than C but taller than D. Based on these comparisons of heights, who is the shortest among A, B, C and D?

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Introduction / Context: This question is a straightforward height comparison puzzle. You are given relative height information for four people A, B, C and D, and must determine who is the shortest. These types of questions test your ability to interpret inequalities and arrange individuals in increasing or decreasing order based on given statements, without needing any actual numerical heights. Given Data / Assumptions: - A is taller than B. - B is shorter than C. - B is taller than D. - All four individuals have distinct heights. - We are asked to identify the shortest person among A, B, C and D. Concept / Approach: The statements can be translated into inequalities that express a strict order. A taller than B means A is above B in height. B shorter than C means C is above B. B taller than D means B is above D. Combining these relations allows us to rank all four people. The shortest person is the one who does not have anyone below them in this ordering. It is helpful to visualise this by placing the names on a vertical line in order of increasing or decreasing height. Step-by-Step Solution: Step 1: From A is taller than B, write A > B in terms of height. Step 2: From B is shorter than C, write C > B. Step 3: From B is taller than D, write B > D. Step 4: Combine the inequalities to form a consistent order. We know both A and C are taller than B, and B is taller than D. Therefore, at least we have A > B > D and C > B > D. Step 5: Although we do not know whether A or C is taller than the other, this uncertainty only affects the top of the order, not the bottom. Step 6: D is below B, and B is below both A and C. Hence D has no one shorter than them, making D the shortest person. Verification / Alternative check: To verify, assign sample heights that satisfy the inequalities. For example, let D be 150 cm, B be 160 cm, A be 170 cm and C be 175 cm. Then A is indeed taller than B, B is shorter than C, and B is taller than D. In this example, D is clearly the shortest. Even if we swap the heights of A and C while keeping both above B, D will always remain the smallest because D is still below B, and B is below both A and C. This consistency shows that the conclusion about D is reliable. Why Other Options Are Wrong: - B is taller than D, so B cannot be the shortest. - C is taller than B, which is itself taller than D, so C is certainly not the shortest. - A is taller than B and thus taller than D as well, so A also cannot be the shortest. - The relationships are sufficient to determine the ordering, so claiming that it cannot be determined is incorrect. Common Pitfalls: Learners sometimes attempt to create a full tallest to shortest order before answering, and may get confused by the unknown order between A and C. However, the question only asks for the shortest, so the unresolved comparison between A and C does not matter. Another pitfall is misreading taller and shorter and accidentally reversing the inequalities, which leads to wrong conclusions. Carefully writing each relation in inequality form greatly reduces these errors. Final Answer: The shortest person among A, B, C and D is D.

Question 12

The birth rates in five countries India, Nepal, Sri Lanka, Bangladesh and Pakistan were compared. The birth rate in Nepal is the lowest among the five. The birth rate in Pakistan is higher than that in Sri Lanka but lower than that in India. The bir…

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Introduction / Context: This question concerns comparative birth rates in five countries. You are not given exact numerical birth rates, but only relative information such as higher than and lower than. The task is to determine which country has the highest birth rate among India, Nepal, Sri Lanka, Bangladesh and Pakistan. This type of conceptual ordering problem is common in reasoning tests and helps assess how well you can work with chains of inequalities. Given Data / Assumptions: - Countries considered: India, Nepal, Sri Lanka, Bangladesh and Pakistan. - Birth rate in Nepal is the lowest among all five countries. - Birth rate in Pakistan is higher than that in Sri Lanka but lower than that in India. - Birth rate in Bangladesh is higher than that in Nepal but lower than that in Sri Lanka. - All birth rates are distinct and comparable. Concept / Approach: To solve this, we convert each statement into an inequality, using greater than to mean higher birth rate. The information about Pakistan places it between Sri Lanka and India. The information about Bangladesh places it between Nepal and Sri Lanka. Knowing that Nepal is lowest sets the baseline. Combining all inequalities in a consistent order allows us to see which country must be at the top with the highest birth rate. We do not need exact values; only the relative chain matters. Step-by-Step Solution: Step 1: From Nepal has the lowest birth rate, we know every other country has a higher birth rate than Nepal. Step 2: From Pakistan is higher than Sri Lanka but lower than India, we write India > Pakistan > Sri Lanka. Step 3: From Bangladesh is higher than Nepal but lower than Sri Lanka, we get Sri Lanka > Bangladesh > Nepal. Step 4: Combine these chains. We now have India at the top of the partial order, since India is above Pakistan, and Pakistan is above Sri Lanka. Also, Sri Lanka is above Bangladesh, and Bangladesh is above Nepal. Step 5: The fully consistent order from highest to lowest birth rate is India, Pakistan, Sri Lanka, Bangladesh and Nepal. Step 6: From this order, India is clearly at the top and therefore has the highest birth rate among the five countries. Verification / Alternative check: As a check, you can imagine sample numerical birth rates that satisfy all the inequalities. For example, let India have a birth rate of 30 units, Pakistan 26 units, Sri Lanka 22 units, Bangladesh 18 units and Nepal 12 units. Pakistan (26) is higher than Sri Lanka (22) but lower than India (30), and Bangladesh (18) is higher than Nepal (12) but lower than Sri Lanka (22). Nepal is lowest. In this assignment, India clearly has the highest birth rate. Any other set of numbers that satisfies the same relationships will still position India above all others, confirming our conclusion. Why Other Options Are Wrong: - Pakistan cannot have the highest birth rate because it is explicitly stated to be lower than India. - Sri Lanka is below Pakistan in birth rate, so it also cannot be the highest. - Bangladesh is lower than Sri Lanka and certainly lower than Pakistan and India, so it is not the highest. - Nepal is given as the lowest of all five countries, so it definitely cannot be the highest. Common Pitfalls: A common mistake is to overlook the statement about Nepal being the lowest and to treat all comparisons as isolated pieces instead of integrating them. Another error is to misread higher than and lower than, inverting the intended order. Some students may be tempted to choose Pakistan because it is mentioned as higher than Sri Lanka, but they forget that it is still lower than India. Writing down the full chain of inequalities in a clear order helps avoid these mistakes. Final Answer: The country with the highest birth rate among the five is India.

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