Reasoning Analysis

Understanding the pattern First figure: Second figure: Third figure (finding the missing number): Answer: The missing number is 16.

Clearly, by observation we get the answer as C.

A. While playing chess with Geeta and Meena, Bipin often loses: There is no direct information about Bipin's performance in chess, so we can't conclude that Bipin often loses based on the given information. (Doesn't logically follow). B. Geeta is the oldest among the three: According to the information, Bipin is older than Geeta, so this is incorrect. (Doesn't logically follow). C. Geeta hates to lose the game: There is no information provided about Geeta's emotional response to losing the game. This statement is an assumption. (Doesn't logically follow). D. Meena is the youngest of the three: The information explicitly tells us that Geeta is older than Meena, and Bipin is older than Geeta, which means Meena is the youngest. (Logically follows).

Step 1: Interpreting the positions The queue consists of seven men in the order: A, B, C, D, E, F, G. Each wears a different-colored cap: Violet, Indigo, Blue, Green, Yellow, Orange, and Red. Step 2: Analyzing the clues Clue 1: D can see Green and Blue, but not Violet. Therefore, D is not wearing Violet, and D must be in a position such that Green and Blue are ahead of him (possibly at positions C and B). D cannot see Violet, so Violet is likely at a position behind D. Clue 2: E can see Violet and Yellow, but not Red. Therefore, E is in a position where Violet and Yellow are ahead of him, and Red is behind him. Clue 3: G can see all caps except Orange. So, G must be wearing Orange, and the remaining six caps are in front of him (since Orange is not visible to him). Step 3: Determining F’s cap Given that E is wearing an Indigo-colored cap (from the condition), we can use this fact to deduce the position of F. Since E can see Violet and Yellow but not Red, and G must be wearing Orange, F must be wearing the Red cap to satisfy the given constraints. Final Answer: The color of the cap worn by F is Red. Thus, the correct answer is: C. Red.

The key here is that the person is starting from P and visiting all cities, returning to P. From P, the person can go to Q (by boat or rail). From Q, the person can go to T (by air only). From T, the person can go to R (by rail or bus). From R, the person can go to S (by bus or boat). Finally, to return to P from S, the person must travel to R first (by bus or boat), and then travel from R to P (by boat). Thus, the person must visit R twice: once when traveling from T to R, and once when returning to P from R. The correct answer is B. R.

Step 1: Calculate the LCM of 2, 3, 4, 5, and 6. Prime factorizations: LCM is obtained by taking the highest powers of all prime factors: Highest power of 2: Highest power of 3: Highest power of 5: Therefore, LCM = Step 2: Determine how many times they meet within 180 days. Divide 180 days by the LCM: Conclusion: All five groups meet on the same day 3 times within 180 days. Therefore, the correct answer is: A. 3

Option A: Rohit, Shobha, Kunal, and Kaushal Rohit and Tanya are not together, so condition 1 is satisfied. Kunal and Shobha are together, which violates condition 2. Hence, Option A is not acceptable. Option B: Tanya, Kaushal, Shobha, and Rohit Rohit and Tanya are together, violating condition 1. Hence, Option B is not acceptable. Option C: Tanya, Mukesh, Kunal, and Jaswant Rohit and Tanya are not together (condition 1 satisfied). Kunal and Shobha are not together (condition 2 satisfied). Mukesh and Kunal are together (condition 3 satisfied). Hence, Option C is acceptable. Option D: Shobha, Tanya, Rohit, and Mukesh Rohit and Tanya are together, violating condition 1. Hence, Option D is not acceptable.

Statement 1 is incorrect. While many families function as primary groups due to their intimate and enduring relationships, not all families exhibit these characteristics. Some families may lack close bonds or regular interaction, which are essential features of a primary group. Statement 2 is incorrect. Because primary groups encompass more than just families. They include any group where members share close, personal, and enduring relationships, such as circles of friends or small community groups. Statement 3 is incorrect. The size of a group alone does not determine its classification as a primary group. While primary groups are typically small to facilitate intimate interactions, not all small groups possess the deep emotional bonds and enduring relationships characteristic of primary groups. Statement 4 is correct. This statement accurately reflects a defining characteristic of primary groups. The intimate knowledge and close relationships among members are central to the concept of a primary group.

Let's analyze the direct connections between the cities based on the provided information: P and Q are connected by boat and rail. S and R are connected by bus and boat. Q and T are connected by air only. P and R are connected by boat only. T and R are connected by rail and bus. Now, checking the options: P and T: There is no direct connection mentioned between P and T. T and S: There is no direct connection mentioned between T and S. Q and R: There is no direct connection between Q and R mentioned either. Thus, none of the pairs are directly connected without going through another city. The correct answer is D. None of these.

Given the constraints: At least 2 males must be in the team. B cannot play with W. C cannot play with Z. W cannot play with Y. B is selected, and Y is rejected. Step 1: Analyze the constraint that B is selected and Y is rejected. B is included in the team, so we need to select 3 more players. Y is excluded from the team, so Y's pairing with others does not matter. Step 2: Consider the combinations of male and female players: Since at least 2 males are required, and B is already selected, the other males available are A and C. Since Y is rejected, the available females are W, X, and Z. Step 3: Analyze the pairing restrictions: B cannot play with W — This means W cannot be on the team if B is included. C cannot play with Z — This means if C is selected, Z cannot be on the team. W cannot play with Y — This restriction does not matter since Y is already rejected. Step 4: Eliminate invalid options based on restrictions: Option A (A, B, C, and W): B cannot play with W, so this option is invalid. Option B (A, B, C, and Z): C cannot play with Z, so this option is invalid. Option C (A, B, C, and X): There are no restrictions between these players. This is a valid combination. Option D (A, W, Y, and Z): Y is rejected, so this option is invalid. Conclusion: The only valid option is Option C: A, B, C, and X.

We need to find X by identifying a pattern in each row of the matrix. Step-by-Step Analysis: Consider each row and examine how the numbers are related: Row 1: 3, 370, 7 Row 2: 2, 224, 6 Row 3: 1, 730, X Look at how the middle column is related to the first and third columns: In Row 1, , but 370 is much larger. We observe that . In Row 2, , and 224 follows . In Row 3, . Solving for X: , .

B and C do not belong to Q: This means Q cannot be assigned to B or C. So, Q must be assigned to either A or D. B and E do not belong to P and R: This means B and E cannot be assigned to P or R. So, B and E must be assigned to S or T. A and C do not belong to R, S, and T: This means A and C must be assigned to P or Q. Since B and C do not belong to Q (from statement 1), C must go to P, and A must go to Q. D and E do not belong to Q and T: Since A is already assigned to Q, D cannot go to Q. Therefore, D must go to R (the only available city left for D). Since E cannot go to T (from statement 4), E must go to S. Final assignments: A → Q B → T C → P D → R E → S Evaluating the statements: A. C belongs to P: This is correct, as C is assigned to P. B. D belongs to R: This is correct, as D is assigned to R. C. A belongs to Q: This is correct, as A is assigned to Q. D. B belongs to S: This is incorrect, as B is assigned to T, not S. Conclusion: The incorrect statement is D. B belongs to S.

B and C play cricket and hockey. C and D play hockey and basketball. Now, let's determine which game all three—B, C, and D—play together: B plays cricket and hockey. C plays cricket, hockey, and basketball. D plays basketball and football (but not cricket). The common game between B, C, and D is hockey because all three play it. Thus, the correct answer is B. Hockey.

A and B play football and cricket. B and C play cricket and hockey. A and D play basketball and football. C and D play hockey and basketball. From these, we see: A plays football and cricket, not hockey. B plays football, cricket, and hockey. C plays cricket, hockey, and basketball. D plays basketball and football, not hockey. Thus, the person who does not play hockey is A. The correct answer is D. A.

Clearly, by observation we get the answer as B.

Arrangement: Seat 1: A Seat 2: C Seat 3: D Seat 4: B Seat 5: E This satisfies all conditions: C is next to A. A is two seats from D. B is not next to A

Let's examine the available travel options between each pair of cities based on the provided information: P and Q: Connected by boat and rail. So, there are travel options. P and R: Connected by boat only. So, there is travel option. P and T: There is no direct connection mentioned between P and T. Q and R: There is no direct connection between Q and R mentioned. The pair with the maximum number of travel options is P and Q, which have travel options. Thus, the correct answer is A. Q and S.

Let's denote the number of red balls as , yellow balls as , and green balls as . From the given conditions: 1. There are as many red balls as yellow balls 2. There are twice as many yellow balls as there are green ones: Now, let's analyze each option: Option A: "The number of red balls is equal to the sum of yellow and green balls." - The sum of yellow and green balls is . - From and , we have . Therefore, the sum of yellow and green balls is . - But , so . This option is incorrect. Option B: "The number of red balls is double the number of green balls." - We know from the earlier reasoning. This option is correct. Option C: "The number of red balls is equal to yellow balls minus green balls." - Yellow balls minus green balls is . - But , so . This option is incorrect. Option D: "The number of red balls cannot be ascertained." - We have already established , so the number of red balls can indeed be ascertained. This option is incorrect. Final Answer: The correct answer is: **B. is double the number of green balls.**

P and Q are connected by boat and rail. S and R are connected by bus and boat. Q and T are connected by air only. P and R are connected by boat only. T and R are connected by rail and bus. Now, starting from Q: Q to T is by air only (so we cannot continue by air to R). Q to P is by boat or rail. From P, P to R is by boat only. Hence, starting from Q, we would need to travel via boat to reach P, and from P, we can travel by boat to R. Thus, the mode of transport would be Boat. The correct answer is A. Boat.

By rotating the 3rd dice, we'll get the required faces. By observating the 3rd dice, we know B is . And by 2nd dic, we can determine that the number corresponding to must be . Therefore, A is and B is .

Initially, the boy was ranked 20th in a class of 45 students. After two boys joined, his rank dropped to 21st. So, the total number of students becomes 47. To find his new rank from the end: The total number of students is 47. His rank from the beginning is 21st. Rank from the end = Total students - Rank from the beginning + 1 = th. Thus, his new rank from the end is 27th. The correct answer is C. 27th.

Given the constraints: At least 2 males must be in the team. B cannot play with W. C cannot play with Z. W cannot play with Y. Y is selected, and B is rejected. Step 1: Analyze the constraint that Y is selected and B is rejected. Y is included in the team, so we need to select 3 more players. B is excluded from the team, so B's pairing with others does not matter. Step 2: Consider the combinations of male and female players: Since at least 2 males are needed, and B is rejected, the remaining males available are A and C. Y is already included, and there are 2 females left to choose from: W and Z. Step 3: Analyze the pairing restrictions: B cannot play with W — Since B is excluded, this restriction does not affect us. C cannot play with Z — This means if C is selected, Z cannot be on the team. W cannot play with Y — Since Y is selected, W cannot be on the team. Step 4: Eliminate invalid options based on restrictions: Option A (A, C, W, Y): W cannot play with Y, so this option is invalid. Option B (A, C, X, Y): There are no restrictions between these players. So, this is a valid combination. Option C (A, C, Y, Z): C cannot play with Z, so this option is invalid. Option D (A, W, Y, Z): W cannot play with Y, so this option is invalid. Conclusion: The only valid option is Option B: A, C, X, and Y. Correct Answer: B. A, C, X, and Y.

Four friends, A, B, C, and D, distribute some money among themselves in such a manner that: 1. A gets one less than B → If B receives units, then A gets units. 2. C gets 5 more than D → Since D receives , C gets units. 3. D gets 3 more than B → D receives units. Now, comparing the amounts each person receives: - C: - D: - B: - A: The order of amounts is: . Therefore, A gets the smallest amount. Correct answer: A

Clearly, by observation we get the answer as D.

So the answer is D. Becomes: A and B play football and cricket. B and C play cricket and hockey. A and D play cricket and football. C and D play hockey and basketball. Now, let's check each friend's sports: A plays cricket, football, and cricket. B plays football, cricket, and hockey. C plays cricket, hockey, and basketball. D plays basketball, football, and hockey. Now, we need someone who plays football, basketball, and hockey. A plays football and basketball, but not hockey. B plays football and hockey, but not basketball. C plays basketball and hockey, but not football. D plays football, basketball, and hockey. Correct answer: A. D So the answer is D.

Clearly, by observation we get the answer as B.

George attends Music classes on Monday. So, Monday is for Music. He attends Mathematics classes on Wednesdays. So, Wednesday is for Mathematics. His Literature classes are not on Friday. So, Literature is not on Friday. He attends History classes on the day following the day of his Mathematics classes. Since he attends Mathematics on Wednesday, his History classes must be on Thursday. On Tuesday, he attends his Sports classes. So, Tuesday is for Sports. We can now deduce his schedule: Monday: Music Tuesday: Sports Wednesday: Mathematics Thursday: History Friday: The only day left for Literature, as Literature is not on Friday (statement 3 is negated), so Friday is free. Thus, Friday is the free day.

The letters L, M, N, O, P, Q, R, S, and T are substituted with integers from 1 to 9, but not in the order given. 4 is assigned to P. The difference between P and T is 5, so . Since P is 4, . The difference between N and T is 3, so . Since T is 9, . Therefore, the integer assigned to N is 6.

Given: Total children = 630 Let x = number of children in the first row Each subsequent row has 3 fewer children than the previous row Number of rows = n Formula for sum of an arithmetic series: Checking possible values of n: For n = 3: For n = 4: For n = 5: For n = 6: (not an integer) Conclusion: 6 rows are not possible.

Given conditions: 1. A is taller than B 2. C is taller than A 3. D is taller than C 4. E is the tallest Arranging in order from tallest to shortest: Since there are 5 people, the **middle position** is the 3rd one. The 3rd person in the order is **C**.

The pattern follows a sequential flipping of arrows: In the first column, the first arrow remains pointing upward, while the second arrow rotate 90 degrees clockwise. In the second column, the second arrow rotates 90 degrees while the first arrow stays the same. In the third column, the first arrow remains pointing downwards, while the second arrow rotate 90 degrees clockwise. Following this pattern, the correct figure can be will be where both arrows are point upwards, hence B is the answer.

Sum of numbers in the 1st row: Sum of numbers in the 3rd row: For the 2nd row: NOTE: UPSC answer key considered both options B and D as correct.

Given: Total money = Rs. 100. Alok + Bhupesh = Chander + Dinesh. Alok has Rs. 5 more than Dinesh. Chander has half the money of Dinesh. We assign variables: A = Alok's money, B = Bhupesh's money, C = Chander's money, D = Dinesh's money. From the relations: , , and . Solving the equations, we find: , , , . Thus, Alok has the maximum amount of money: Rs. 38.33.

Since modern poets appear in alternate years, and last year’s question was on a medieval poet (A), this year should have a modern poet in the question paper. The modern poets available for selection are E, F, G, and H. F is unlikely to be chosen because the paper-setter avoids asking about F. Those who like F also like E, which suggests E is a strong candidate. While H and G are linked, nothing strongly suggests that H must be chosen over E. Since this year a modern poet should be chosen, and F is ruled out, the most likely option is E. Thus, the correct answer is: (B) E

Given conditions: 1. A is above E but below C → 2. B is in the middle → 4th position 3. G is between A and B → 4. E is between B and F → 5. F is between E and D → Arranging in order from top to bottom based on the conditions: The person on the **bottom step** is **D**

The pattern shows squares increasing and circles decreasing consistently across the rightward columns. Simply extend the sequence logically to determine the missing element.

We are given the following information: Books labeled: A, B, C, D, E, F. Cover colors: Books B, C, E, F have green covers; Books A, D have yellow covers. New and old books: Books A, B, D are new; Books C, E, F are old. Types of books: A, B, C are law reports. D, E, F are medical extracts. We need to identify which two books are old medical extracts and have green covers. Old books are C, E, F. Medical extracts are D, E, F. The green-covered books are B, C, E, F. Now, we want to find the books that are both old medical extracts and have green covers. From the above information: Books E and F are both old and are medical extracts. Both E and F also have green covers.

Statement A is incorrect. The passage does not focus solely on the ability to bring the government to book in a court of law but emphasizes the broader concept of government accountability in preserving liberty. Statement B is incorrect. Identifying a man as a political unit distinct from others does not directly relate to the justification of government accountability in safeguarding liberty. Statement C is incorrect. While a decentralized society may ensure basic needs, it does not address the relationship between liberty and government accountability as discussed in the passage. Statement D is correct. The passage implies that liberty can only be meaningful when balanced with restraints, ensuring that the government remains accountable for any actions that infringe upon individual rights.

Statement A is incorrect. The statement does not mention the number of buses and trucks on the road, only that buses cause more accidents than cars and trucks cause fewer accidents than buses. Statement B is incorrect. The statement does not provide any information about the relative care taken by car drivers compared to bus drivers. Statement C is incorrect. The statement does not imply that truck drivers are more skilled than car or bus drivers; it only compares the number of accidents caused by buses and trucks. Therefore, the correct conclusion is D. None of the above.

Let's calculate the total number of people in the row. Initially, 'A' is in the 11th position from the left, and 'B' is in the 10th position from the right. After interchanging, 'A' becomes 18th from the left. This means 'B' must now occupy the 18th position from the left. Let the total number of people in the row be denoted by "N". Since 'B' is in the 10th position from the right, the total number of people in the row is: position of 'B' from left position of 'B' from right From the given information, we know that after the interchange, 'A' becomes 18th from the left. This means the number of people in the row is: Now, subtract the 2 persons (A and B) from the total count to find how many persons are there other than 'A' and 'B'. Persons other than 'A' and 'B' The total number of persons in the row, other than 'A' and 'B', is 25.

Given positions: 1. F is 1 km west of D → F , D 2. B is 1 km east of E → E , B 3. A is 2 km north of E → A 4. C is 1 km east of A → C 5. D is 1 km south of A → D Arranging positions: - A - D - E Since A, D, and E lie on the same vertical line, they are collinear. Answer: **Option B (A, D, E)**

There are six women: Girija, Vanaja, Jalaja, Shailaja, Tanuja, and Pooja. Four dancers: Tanuja, Shailaja, and two others (yet to be determined). Four vocal musicians: Jalaja, Vanaja, Shailaja, and Tanuja. One actress: Pooja. Three violinists: Girija, Vanaja, and one other (yet to be determined). Girija and Vanaja are violinists. Jalaja and Shailaja do not play the violin. Shailaja and Tanuja are dancers. Jalaja, Vanaja, Shailaja, and Tanuja are vocal musicians, and two of them are also violinists. Given these conditions, we know: Jalaja is a vocal musician but does not play the violin, so she cannot be a violinist. Shailaja is a dancer and a vocal musician, but she does not play the violin. Tanuja is a dancer, vocal musician, and must also be a violinist since there are only three violinists and Vanaja and Girija are already violinists. Vanaja is a violinist and a vocal musician. Pooja is the actress and does not fit into the dancer or violinist categories. From the above reasoning, Tanuja is the only person who is certainly both a dancer and a violinist.

The given sequence follows a specific cyclic pattern for the movement of beads in four different directions: Left (L), Right (R), Top (T), and Bottom (B). Each bead follows a set order of movement across the figures. Observing the pattern for each bead: Top-left bead: Moves in the sequence L → R → B → T across the figures. Bottom-left bead: Moves in the sequence R → L → T → B, which is a mirror image of the top-left bead’s movement. Top-right bead: Moves in the sequence T → B → R → L, which is the exact reverse of the top-left bead’s pattern. Bottom-right bead: Moves in the sequence B → T → L → R, which is a mirror image of the top-right bead’s movement. By repeating this cycle for each bead, we can predict the next position in the sequence. Following this logical pattern, the correct answer can be determined.

Clearly, by observing the given graph we get the answer C.

Statement A is incorrect. The passage does not suggest that the values of all things would remain constant; instead, it highlights that the value of money would change. Statement B is incorrect. The passage does not imply that the values of things sold would be doubled, only that their prices would increase. Statement C is incorrect. The passage does not discuss halving the value of things bought, but rather focuses on the value of money being halved. Statement D is correct. The passage indicates that if the prices of all things doubled, the value of money would be halved. This is because money would have less purchasing power, meaning that the same amount of money would buy fewer goods and services.

2. The judge is married to the lawyer. Since C is the lawyer, the judge must be B. 3. F is the draughtsman, son of B and brother of E. 4. C is the lawyer and daughter-in-law of D, meaning D is married to the judge (B). Thus: - and are a couple (A is the engineer and D is the grandmother of F). - and are a couple (B is the judge and C is the lawyer). So, both and are couples.

D is the grandmother of F, so D is an older member of the family. C, the lawyer, is the daughter-in-law of D, so D is married to the judge (B). E is the unmarried doctor, so D is not the doctor. F is the draughtsman, son of B and brother of E. A is the engineer and married to the stenographer (so A is married to E, and B is the stenographer). The remaining profession that has not been explicitly assigned is Stenographer, and since A is married to the stenographer, it makes sense that D must be the Stenographer.

We know the following facts from the passage: 1. A is the engineer and married to the lady stenographer. 2. The judge is married to the lawyer. 3. F is the draughtsman, son of B and brother of E. 4. C, the lawyer, is the daughter-in-law of D. 5. E is the unmarried doctor. 6. D is the grandmother of F. 7. There are two married couples in the family. Let's analyze: - A is married to the stenographer (so the stenographer is not B). - The judge is married to the lawyer, so B cannot be the lawyer because C is the lawyer. - F is the draughtsman, and since B is F's parent, B cannot be the draughtsman either. - B must therefore be the judge, as the only remaining option. Thus, the profession of B is **Judge**.

Given conditions: 1. A is next to B but not next to C. 2. C is not sitting next to D. Possible arrangement satisfying these conditions: - If A is next to B but not C , , , , , , , . - Since C is not next to D, D must be placed at one end. Valid arrangement: , Therefore, A is occupying seats adjacent to D.

Given the following relationships: A and B are enemies. C and D are friends. E and F are indifferent to each other. A and E are not enemies. B and F are enemies. We can deduce the following: Since A and B are enemies, one must be a fighter and the other a coward. C and D are friends, so both are cowards. E and F are indifferent to each other, indicating both are fighters. A and E are not enemies, so both are fighters. B and F are enemies, so B is a coward and F is a fighter. Based on these deductions, the correct statement is: B. A, E, and F are fighters.

Let and be real numbers such that and . Then is equal to (a) (b) (c) (d) Solution: We are given that and . We know that . Substituting the given values, we have . . Therefore, . The value of is . Final Answer: The final answer is

A is the tallest among the four. This implies A is male. Both the women are shorter than their respective husbands. This indicates that B and C are the women, and they are married to A and D, respectively. C is taller than B. This means C is taller than B. D is B’s brother. This confirms that D is male and B's brother. Now, let's evaluate each statement: A. All four have family ties. This is correct. A and B are married, and C and D are married. Additionally, D is B's brother. B. B is the shortest among the four. This is correct. Since C is taller than B, and A is the tallest, B is the shortest. C. C is taller than D. This is incorrect. Since C is taller than B, and B is shorter than D (because both women are shorter than their husbands), it follows that D is taller than C. D. A is B’s husband. This is correct. Therefore, the incorrect statement is C. C is taller than D.

Conclusion I is not valid. This conclusion suggests that all men are either great or wise, which cannot be derived from the statements. The statements only imply that "some" men are great and "some" men are wise. Conclusion II is also not valid. The statements do not provide any information about men who are neither great nor wise. It is possible that all other men could fall into this category, or they might not.

Case 1: Task-2 is assigned to Person-3 Task-1 Assignment: Since Task-1 cannot be assigned to Person-1 or Person-2, it must be assigned to one of the remaining persons: Person-4 or Person-5. This gives us 2 choices. Remaining Tasks: After assigning Tasks-1 and -2, we have 3 tasks left (Tasks-3, -4, and -5) and 3 persons left (Persons-1, -2, and -5). These remaining tasks can be assigned to the remaining persons in any order, which can be done in (3 factorial) ways. Therefore, the total number of assignments for Case 1 is: 2 (choices for Task-1) × (ways to assign remaining tasks) = 2 × 6 = 12 ways. Case 2: Task-2 is assigned to Person-4 Task-1 Assignment: Similarly, Task-1 must be assigned to one of the remaining persons: Person-3 or Person-5. This gives us 2 choices. Remaining Tasks: After assigning Tasks-1 and -2, we have 3 tasks left (Tasks-3, -4, and -5) and 3 persons left (Persons-1, -2, and -3). These remaining tasks can be assigned to the remaining persons in any order, which can be done in ways. Therefore, the total number of assignments for Case 2 is: 2 (choices for Task-1) × (ways to assign remaining tasks) = 2 × 6 = 12 ways. Total Number of Assignments: Adding the results from both cases, we get: 12 (from Case 1) + 12 (from Case 2) = 24 ways. Therefore, the assignment can be done in 24 ways. The correct answer is C. 24.

Let: = number of persons who read magazine X only, = number of persons who read magazine Y only, = number of persons who read both magazines. Step 1: Given Relationships 1. (number of persons who read X only is thrice those who read Y only). 2. (number of persons who read Y only is thrice those who read X only). Step 2: Contradiction in Relationships The two conditions, and , cannot hold simultaneously unless and . Thus, we assume the problem compares relationships involving . Step 3: Check the Conclusions Conclusion 1: "The number of persons who read both magazines is twice the number of persons who read only magazine X." This implies: Conclusion 2: "The total number of persons who read either one magazine or both magazines is twice the number of persons who read both magazines." This implies: Step 4: Simplify and Verify From , substitute into : Check Conclusion 1: If and , then: (True) Conclusion 2: (True) Final Answer: Both conclusions are correct. Correct Option: C (Both 1 and 2).

By drawing the diagram, using the instructions:  Clearly, Y, V, and W are parallel.

Cousins' Ages: (oldest) Youngest = 17 Relative Age Relationships: Deduce Ages: Possible ages: 17, 18, 19, 20, 21, 22 (fixed as oldest) The youngest is 17. Conditions to satisfy: A is older than B C is older than D F's age is between B and D A is one year older than C Possible Combinations: 2 Order 1 17: B 18: C 19: A 20: D 21: F 22: E Order 2: 17: D 18: C 19: A 20: B 21: F 22: E

The given equation is: We are told that ABCABC can be written as , where ABC is a 3-digit number, and DEED represents a 4-digit number. The hint given is that ABCABC is divisible by 1001, as 1001 is the product of 13, 11, and 7. So, we can rewrite the equation as: Now, we know that the number ABCABC is essentially the number ABC repeated twice. Let’s analyze the multiplication: Since , we have: The number 1001 is written as DEED, so and . Thus, the correct values are: , So, the correct answer is C. , .

Let the number of red marbles be r, the number of green marbles be g, and the number of white marbles be w. From the given information, we have the following relationships: 1. (3 fewer white marbles than red ones) 2. (5 more white marbles than green ones) 3. (there are 10 white marbles) Now, solve for r and g. From : From : The total number of marbles is: Total marbles =

Let be the number of students who only attended music class, be the number of students who only attended art class, and be the number of students who attended both music and art classes. We are given the following information: Total number of students = 400 Percentage of students who attended music class = 75% Number of students who attended music class = Percentage of students who attended art class = 50% Number of students who attended art class = We have three equations: 1. 2. 3. From equation (1) and (2), we have: From equation (3), we have: From equation (2), we have: The number of students who attended both music and art classes is . Therefore, the number of students who attended both classes is 100. Final Answer: The final answer is

To determine the missing number 'X' in the series 7, X, 21, 31, 43, let's analyze the differences between consecutive terms: - 21 - 31 = - 31 - 43 = The differences between 31 and 21, and between 43 and 31, are increasing by 2 (10 and 12). Following this pattern, the difference between X and 21 should be 8. Therefore, X = 21 - 8 = . Thus, the missing number 'X' is 13. The correct option is C.

Option A: Only the man’s wife was left at home — This option assumes certainty, but the problem only suggests the likelihood that she stayed home. Option B: It is likely that the man’s wife was left at home — This option matches the reasoning. There is no explicit confirmation that she went anywhere. Option C: None was left at home — This option is unlikely because there is no direct information stating everyone was away. Option D: More than one person was left at home — This option is incorrect because the information does not support the presence of anyone else at home besides the wife.

Now, let's evaluate the options: A. Both Tamil speakers can drive. False. Only one Tamil speaker, Anil, cannot drive. B. Both Marathi speakers can drive. False. Only one Marathi speaker, Shabnam, cannot drive. C. Both drivers speak Marathi. False. Rekha speaks Tamil, and David speaks Marathi. D. Only one driver speaks Tamil. True. Rekha speaks Tamil, and David speaks Marathi. Therefore, the correct answer is D. Only one driver speaks Tamil.

Usha runs faster than Kamala. This implies: Swati runs slower than Kamala. This implies: Priti runs slower than Swati. This implies: Combining these relationships, we get: Therefore, Priti is the slowest runner among them. Answer: B. Priti