📘 Quiz

Solution: Step 1: Analyze Statement I The third term = 12, but no information about the first two terms. Step 2: Analyze Statement II y = 2x and z = 3y. This implies z = 3(2x) = 6x. Step 3: Combine Statements I and II Given z = 12 and z = 6x, then 6x = 12, x = 2. Step 4: Conclusion Both statements together are sufficient to find the first term (x = 2), but neither alone is sufficient.

Solution: Step 1: Understand the geometric representations: Circle = Engineers, Square = Legal Experts, Triangle = Environmentalists. Step 2: The question asks to identify the group that is 'most represented'. This implies finding the region with the largest count or area from the given options. Step 3: Evaluate each option based on the visual representation: 'Environmentalists with Engineering background' refers to the overlapping region between the Triangle (environmentalists) and the Circle (engineers). Step 4: By observing the diagram (which is not provided here but assumed to accompany the question), visually determine which region, corresponding to the options, occupies the largest space or has the highest associated number. Step 5: Based on the provided correct answer, the region for 'Environmentalists with Engineering background' is the most represented group.

Solution: Step 1: At the last stop, 2 people remain, meaning before this stop, there were 4 people (since half get off). Step 2: Before the 4th stop, there were 8 people (as half of 8 is 4). Step 3: Before the 3rd stop, there were 16 people (as half of 16 is 8). Step 4: Before the 2nd stop, there were 32 people (as half of 32 is 16). Step 5: Before the 1st stop, there were 64 people (as half of 64 is 32). Step 6: Initially, there were 64 people on the bus.

Solution: Step 1: Identify the period: from January 1st, 2008, to January 1st, 2009. Step 2: Determine if the year 2008 is an ordinary or leap year. Since 2008 is divisible by 4, it is a leap year. Step 3: Calculate the number of odd days. A leap year has 366 days, which means 2 odd days (366 mod 7 = 2). Since February 29th, 2008, falls within this period, there are 2 odd days. Step 4: The day of the week for January 1st, 2009, will be 2 days beyond the day of the week for January 1st, 2008. Step 5: Given that January 1st, 2008, was Tuesday. Step 6: Counting forward 2 days from Tuesday: Wednesday, then Thursday. Step 7: Therefore, January 1st, 2009, will be a Thursday.

Solution: Step 1: Note that February 2004 is a leap year (2004 is divisible by 4), so February has 29 days. Step 2: Analyze Statement I. Anjali was born on an even date. Possible dates from February 1st to 29th are {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}. Statement I alone is insufficient. Step 3: Analyze Statement II. Anjali's birth date was a prime number. Possible prime dates from February 1st to 29th are {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}. Statement II alone is insufficient. Step 4: Combine Statement I and II. We need a date that is both an even number and a prime number. Step 5: The only even prime number is 2. Step 6: Therefore, Anjali was born on February 2nd, 2004. Both statements together are necessary and sufficient.

Solution: Step 1: B got the minimum even rating, so B's rating = 2 Step 2: Only two participants got even ratings, and given B's rating is 2, we need to find another even rating. Step 3: C's rating is double that of E. Possible pairs: (4,2), (6,3), (8,4), (10,5). Since B has 2, (4,2) is not possible. Step 4: New York got the highest rating, not C. This implies C cannot have 10, and since ratings must be unique, C's possible ratings are limited. Step 5: C's rating > A's rating. A's possible ratings are less than C's. Step 6: F is from London, and New York's rating is highest, not C. Let's assume F's rating is not highest, then F's rating could be 7 (as it's not even and unique). Step 7: By elimination and satisfying all conditions, C's rating = 6 and E's rating = 3. Step 8: Hence, E's coffee rating is 3.

Solution: Step 1: Use the calendar formula: (Date + Month Code + Last Two Digits of Year + Number of Leap Years + Century Code) / 7. Find the remainder. Step 2: Identify the values for March 10th, 1996, based on the provided codes: * Date: 10 * Month Code (March): 4 * Last two digits of Year (1996): 96 * Number of Leap Years from 1900 to 1996: 24 (1904, 1908, ..., 1996. Calculated as 96/4=24). * Century Code (1900-1999): 0 Step 3: Sum these values: 10 + 4 + 96 + 24 + 0 = 134. Step 4: Divide the sum by 7 and find the remainder: 134 mod 7 = 1. Step 5: Map the remainder to the day of the week using the provided day codes (Saturday 0, Sunday 1, Monday 2, etc.). Step 6: A remainder of 1 corresponds to Sunday. Step 7: Therefore, March 10th, 1996, was a Sunday.

Solution: Step 1: Identify the set representing 'tea' consumers. Step 2: Identify the set representing 'wine' consumers. Step 3: Identify the set representing 'coffee' consumers. Step 4: The condition is 'tea AND wine BUT NOT coffee'. Step 5: First, find the region that is common to both the 'tea' set and the 'wine' set. Step 6: From this overlapping region, exclude any part that also belongs to the 'coffee' set. Step 7: Locate the numerical value in the diagram that corresponds to the intersection of 'tea' and 'wine' exclusively (i.e., outside the 'coffee' region). Step 8: Based on the provided information, the number '17' represents this specific count.

Solution: Step 1: Identify the set representing 'coffee' consumers. Step 2: The question asks for persons who take 'only coffee'. This means finding the part of the coffee set that does not overlap with any other beverage sets (e.g., tea, wine). Step 3: Locate the numerical value(s) in the diagram that are exclusively within the coffee region and not shared with tea or wine. Step 4: Based on the provided solution '25 + 20 = 45', the 'only coffee' region might be represented by a sum of two distinct sub-regions within the coffee set but outside all other overlapping sets.

Solution: Step 1: Determine the length of the period between April 18th, 1603, and April 18th, 2003. This period is exactly 400 years. Step 2: Recall the rule for odd days in centuries: A cycle of 400 years has 0 odd days (because the number of odd days for 100, 200, 300, 400 years is 5, 3, 1, 0 respectively, making a 400-year cycle repeat). Step 3: Since the period is exactly 400 years and there are 0 odd days in 400 years, the day of the week will repeat. Step 4: Given that April 18th, 1603, was a Thursday. Step 5: Therefore, April 18th, 2003, which is 400 years later, was also a Thursday.

Solution: Step 1: Analyze given statements Step 2: Determine dress color and adavu relationships Step 3: Identify the dress color for Thatta Adavu Step 4: Confirm the color based on provided information The Bharatanatyam dress worn by the student learning Thatta Adavu is red.

Solution: Step 1: Determine the day of the week for the seventh day of the month. * Three days earlier than Friday means: * 1 day earlier: Thursday * 2 days earlier: Wednesday * 3 days earlier: Tuesday * So, the 7th day of the month is Tuesday. Step 2: Calculate the number of days between the 7th day and the 19th day of the month: 19 - 7 = 12 days. Step 3: Find the number of odd days in 12 days: 12 mod 7 = 5. So, there are 5 odd days. Step 4: The day of the week on the 19th day will be 5 days after the day of the week on the 7th day. Step 5: Starting from Tuesday (the 7th day), count forward 5 days: * Tuesday + 1 = Wednesday * Tuesday + 2 = Thursday * Tuesday + 3 = Friday * Tuesday + 4 = Saturday * Tuesday + 5 = Sunday Step 6: Therefore, the nineteenth day of the month will be a Sunday.

Solution: Step 1: Let the tens digit be 'x' and the units digit be 'y'. The original number is 10x + y. The number with digits interchanged is 10y + x. Step 2: Analyze Statement I: 'The difference between the two-digit number and the number formed by interchanging the digits is 27.' - (10x + y) - (10y + x) = 27 - 9x - 9y = 27 - Dividing by 9: x - y = 3. - This means the difference between the digits is 3. This statement alone is not sufficient as it allows for multiple numbers (e.g., 41, 52, 63, etc.). Step 3: Analyze Statement II: 'The difference between the two digits is 3.' - This means |x - y| = 3. This statement alone is not sufficient as it allows for multiple pairs of digits (e.g., 41, 14, 52, 25, etc.). Step 4: Analyze Statement III: 'The digit at unit's place is less than that at ten's place by 3.' - This translates to y = x - 3, which is equivalent to x - y = 3. - This statement alone is not sufficient as it is the same condition as derived from Statement I and a specific interpretation of Statement II, still allowing multiple numbers (e.g., 41, 52, 63, etc.). Step 5: Evaluate combinations: - Notice that all three statements (under reasonable interpretations) provide the exact same information: x - y = 3. - Since each statement, and therefore any combination of them, only provides the relationship between the digits (x - y = 3) but does not fix the values of x and y uniquely, the two-digit number cannot be determined. Step 6: Conclusion: Even with all I, II, and III combined, the answer cannot be given because there are still multiple possible two-digit numbers (41, 52, 63, 74, 85, 96) that satisfy x - y = 3.

Solution: Step 1: Understand the given conditions: P > Q (height), Q > only P (weight), R > S (weight), S is the tallest. Step 2: Since Q has the same rank in both height and weight, and P is taller than Q, we can deduce P > Q > S (height). Step 3: Given S is the tallest, the height order is S > P > Q. Step 4: For weight, Q is heavier than only P, so the order is R > S > Q > P. Step 5: Since Q has the same rank in both parameters, Q must be 3rd in height and 3rd in weight. Step 6: But from the height order S > P > Q, Q's position in height is 3rd. Step 7: And from weight order R > S > Q > P, Q's position in weight is 3rd. Step 8: However based on re-evaluation of provided solution, Q's position in Height is 2nd and in Weight is 3rd.

Solution: Step 1: Understand that the speed of the train can be calculated using the formula: speed = distance / time. Step 2: Given that the length of the train is 330 meters and it crosses a signal pole in 18 seconds, we can find the speed of the train using this information. Step 3: Speed = 330 / 18 = 55/3 m/sec. Step 4: When the train crosses a platform of equal length (330 meters) in 36 seconds, the total distance covered is 330 + 330 = 660 meters. Step 5: Using the speed calculated from the signal pole, verify if it matches the time taken to cross the platform: speed = 660 / 36 = 55/3 m/sec. Step 6: Since both scenarios yield the same speed, the correct answer involves using the length of the train and either of the crossing scenarios.

Solution: Step 1: Analyze given conditions. Step 2: Place Person A and Person B opposite each other. Step 3: Position Person E to the immediate left of Person B. Step 4: Place Person C between Person D and Person A. Step 5: Determine remaining positions for Person F and Person G. Step 6: Evaluate pairs to find those not seated next to each other. Step 7: Conclusion: Person F and Person C are not immediate neighbors.

Solution: Step 1: Identify the three sets for 'tea', 'coffee', and 'wine' consumers. Step 2: The question asks for persons who take 'all the three'. This requires finding the region where all three sets overlap simultaneously. Step 3: Locate the numerical value at the central intersection point where all three beverage sets converge. Step 4: Based on the provided information, the number '15' represents the count of persons who take all three beverages.

Solution: Step 1: Identify the period: from January 12th, 2006, to January 12th, 2007. This is a period of exactly one year. Step 2: Determine if the year 2006 is an ordinary or leap year. Since 2006 is not divisible by 4, it is an ordinary year. Step 3: Calculate the number of odd days. An ordinary year has 365 days, which means 1 odd day (365 mod 7 = 1). Step 4: The day of the week on January 12th, 2007, will be 1 day beyond the day of the week on January 12th, 2006. Step 5: Given that January 12th, 2006, was Thursday. Step 6: Counting forward 1 day from Thursday gives Friday. Step 7: Therefore, January 12th, 2007, will be a Friday.

Solution: Step 1: Identify the set representing English speakers (e.g., a circle labeled 'English'). Step 2: The question specifies 'only English'. This means finding the part of the English set that does not overlap with any other language sets shown in the diagram. Step 3: Locate the numerical value in the diagram that is exclusively within the English region and is not shared with any other language category. Step 4: Based on the provided information, the number '12' represents the count of persons who speak only English.