Question 1

A student’s marks in five subjects are 25, 26, 27, 28, and 29. In this data set, which measure(s) of central tendency is 27?

Accepted Answer

Introduction / Context:We compare the mean, median, and mode for a small, ordered data set.Given Data / Assumptions:Data: 25, 26, 27, 28, 29 (distinct values).All observations have equal weight.Concept / Approach:Median is the middle value in ordered data; mean is the arithmetic average; mode is the most frequent value.Step-by-Step Solution:Median = middle of five numbers = 27.Mean = (25 + 26 + 27 + 28 + 29) / 5 = 135 / 5 = 27.Mode: none (all values occur once), so 27 is not the mode.Verification / Alternative check:Symmetry around 27 makes it both mean and median.Why Other Options Are Wrong:“Mode” or “Median and Mode” are incorrect because the distribution has no mode; “Median” alone omits the mean; “Mean” alone omits the median.Common Pitfalls:Assuming a mode exists just because a central number looks typical.Final Answer:Mean and Median

Question 2

Find the median of the data set: 2, 4, 6, 8, 10, 12, 14.

Accepted Answer

Introduction / Context:The median is the middle value in an ordered data set. For odd-sized samples, it is the central observation.Given Data / Assumptions:Ordered data (n = 7): 2, 4, 6, 8, 10, 12, 14.Concept / Approach:With 7 values, the 4th value is the median.Step-by-Step Solution:Indexing from 1: the 4th value is 8.Verification / Alternative check:Equal number of observations on either side (three below and three above).Why Other Options Are Wrong:6 and 10 are adjacent but not central; 9.5 would be the median for an even-sized data set between 9 and 10, not applicable here.Common Pitfalls:Confusing mean and median; the mean here is also 8 but that is coincidental due to symmetry.Final Answer:8

Question 3

Directions: Study the following table carefully and answer the questions given below: Number (N) of Candidates (In lakhs) Appearing For An Entrance Examination From Six Different States And The Percentage (P) of Candidates Clearing the Same Over the…

Accepted Answer

Concept & Strategy: To determine the highest absolute number of successful candidates for a given state over several years, we must calculate the product of the appearing candidates (N) and the passing percentage (P) for State D for the years listed in the options. Step-by-Step Solution: We need to evaluate the number of candidates clearing for State D in the given options (2006, 2007, 2008, 2009). The actual number is N × P%. We can just compare N × P directly without dividing by 100. 1. 2006: 1.96 × 35 \approx 2 × 35 = 70 (Exact: 68.6) 2. 2007: 1.88 × 46 \approx 1.9 × 46 \approx 87 (Exact: 86.48) 3. 2008: 1.83 × 60 = 109.8 4. 2009: 2.01 × 56 \approx 2 × 56 = 112 (Exact: 112.56) Comparing the values: 112.56 > 109.8 > 86.48 > 68.6. The highest value occurs in the year 2009. Exam Strategy & Shortcut: Do not perform precise decimal multiplications for every year unless two values are exceptionally close. Use rounding to quickly estimate. For instance, in 2008, 1.8 × 60 \approx 108. In 2009, 2 × 56 \approx 112. Since 112 is clearly larger than 108, and the exact values confirm this trend, 2009 is definitively the answer without wasting time on perfect arithmetic. Common Pitfall: A frequent mistake is simply looking at the highest "N" value or the highest "P" value independently and guessing the answer. The highest "N" or "P" does not guarantee the highest product. Both variables must be evaluated together. Final Answer: Therefore, the correct answer is 2009.

Question 4

Directions: Study the following table carefully and answer the questions given below: Number (N) of Candidates (In lakhs) Appearing For An Entrance Examination From Six Different States And The Percentage (P) of Candidates Clearing the Same Over the…

Accepted Answer

Concept & Logic: To find the average number of appearing candidates, sum the actual numerical values for State D in the specified years and divide by the total number of years (3). Step-by-Step Solution: 1. Extract the N Values for State D: - 2007: 1.88 lakhs - 2008: 1.83 lakhs - 2009: 2.01 lakhs 2. Sum the Values: - Total appearing = 1.88 + 1.83 + 2.01 = 5.72 lakhs. 3. Convert to Actual Integers: - 5.72 lakhs = 5.72 × 100,000 = 572,000. 4. Calculate the Average: - Average = (572,000/3). - Performing the division: 572,000 \div 3 = 190,666 with a remainder of 2. - Expressed as a mixed fraction: 190666 (2/3). Exam Strategy & Shortcut: Once you have the total 5.72 lakhs, recognize that 5.72 divided by 3 is slightly less than 2 (1.9 something). 5.72 / 3 = 1.9066... in lakhs. Therefore, the answer must be in the range of 190,000. Looking at the options, 190666 (2/3) is the only sensible choice. You don't need to carry out the division to the very last decimal point if you check the magnitude. Common Pitfall: A standard trap here is failing to convert the decimal value in lakhs (5.72/3 = 1.9066) into the full numerical value. This oversight leads to choosing distractor options like (a) 1907 (2/3) due to missing the zeroes multiplier. Final Answer: Therefore, the correct answer is 190666 (2/3).

Question 5

Directions: Study the following table carefully and answer the questions that follow: Number of Candidates (in lakhs) Appearing In an Entrance Examination From Six Different Cities  | City | A | B | C | D | E | F | | :--- | :--- | :--- | :--- | :---…

Accepted Answer

Concept & Strategy: To find the number of candidates failing from a specific city, multiply the total number of candidates appearing from that city by the fraction of students who failed. The failing fraction is \frac{Failing Ratio}{Total Ratio}. Both values are in lakhs, so we can ignore the unit when computing their ratio. Step-by-Step Solution: 1. Candidates failing from City D: - Total candidates = 2.27 lakhs - Passing to Failing Ratio = 1 : 3 - Failing fraction = (3/1 + 3) = (3/4) - Number of failing candidates = 2.27 × (3/4) 2. Candidates failing from City A: - Total candidates = 1.25 lakhs - Passing to Failing Ratio = 7 : 3 - Failing fraction = (3/7 + 3) = (3/10) - Number of failing candidates = 1.25 × (3/10) 3. Calculate the Ratio: - Ratio = (2.27 × \frac{3/4)}{1.25 × (3/10)} - The 3 in the numerators cancels out: Ratio = (\frac{2.27/4)}{(1.25/10)} - Simplify the denominator: (1.25/10) = (1/8) - Rewrite the expression: (2.27/4) × 8 - Simplify: 2.27 × 2 = 4.54 4. Convert to Ratio Format: - 4.54 can be written as (454/100). - Divide both by 2 to simplify: (227/50). - The ratio is 227 : 50. Exam Strategy & Shortcut: When computing the ratio (2.27 × \frac{3/4)}{1.25 × (3/10)}, immediately cancel the common factor of 3. You are left with (2.27/4) × (10/1.25). Notice that (10/1.25) is exactly 8. Then, 2.27 × (8/4) = 2.27 × 2 = 4.54. Expressing 4.54 as a ratio gives 454:100, which reduces instantly to 227:50. Common Pitfall: A common error is confusing the failing ratio for the passing ratio or dividing by just the failing part instead of the total ratio parts (e.g., using (3/1) instead of (3/4) for City D). Final Answer: Therefore, the correct answer is 227 : 50.

Question 6

Directions: Study the following table carefully and answer the questions that follow: Number of Candidates (in lakhs) Appearing In an Entrance Examination From Six Different Cities  | City | A | B | C | D | E | F | | :--- | :--- | :--- | :--- | :---…

Accepted Answer

Concept & Strategy: To determine which city has the highest absolute number of failing students, we must calculate the failing candidates for each city by multiplying the total appearing candidates by the failing fraction for that city. The failing fraction is \frac{Failing Ratio}{Total Ratio}. Step-by-Step Solution: Let's compute the failing candidates (in lakhs) for the cities provided in the options and potentially others to be safe: 1. City A: 1.25 × (3/10) = 0.375 2. City B: 3.14 × (3/8) = 1.1775 3. City C: 1.08 × (5/9) = 0.60 4. City D: 2.27 × (3/4) = 1.7025 5. City E: 1.85 × (2/5) = 0.74 6. City F: 2.73 × (5/12) \approx 2.73 × 0.416 \approx 1.1375 Comparing all values: - A: 0.375 - B: 1.1775 - C: 0.60 - D: 1.7025 - E: 0.74 - F: 1.1375 The highest value is 1.7025 lakhs, which belongs to City D. Exam Strategy & Shortcut: You can often identify the highest without exact calculations by looking for a combination of a high total population and a high failing fraction. City D has a huge failing ratio of 3 out of 4 (75%). 75% of 2.27 is obviously quite large. City B has a high population (3.14) but its failing fraction is only 3/8 (37.5%). 37.5% of 3.14 is slightly more than 1. City D (75% of 2.27) is clearly closer to 1.7. Visual inspection quickly narrows the race down to B and D, and a rough estimation proves D is the winner. Common Pitfall: A typical trap is assuming that the city with the largest total population (City B) will naturally have the most failing students. You must always account for the specific passing/failing ratio of that city. Final Answer: Therefore, the correct answer is D.

Question 7

Directions: Study the table given below carefully and answer the questions that follow : Number of Athletes (In Hundred) Who Participated In a Sports Event From 5 Different Countries Over The Years M → Male & F → Female | Countries →
Years ↓ …

Accepted Answer

Concept & Table Analysis: To find the total number of participants from a specific country in a given year, you must add the number of male (M) and female (F) athletes for that year. We need to calculate this for Country C across all years and identify the year with the second-highest total. Step-by-Step Solution: • Total participants in 2005: 4.5 + 3.1 = 7.6 (in hundreds) • Total participants in 2006: 6.9 + 3.3 = 10.2 (in hundreds) • Total participants in 2007: 4.8 + 2.8 = 7.6 (in hundreds) • Total participants in 2008: 6.6 + 4.2 = 10.8 (in hundreds) • Total participants in 2009: 7.9 + 6.3 = 14.2 (in hundreds) • Total participants in 2010: 10.8 + 6.9 = 17.7 (in hundreds) Comparing the totals: 1st Highest: 2010 (17.7) 2nd Highest: 2009 (14.2) Looking at the given options, the year 2009 is not listed among (a), (b), (c), or (d). Exam Strategy & Shortcut: Instead of doing precise decimal addition for every row, quickly scan the columns for Country C (M and F). Notice that 2009 and 2010 have significantly larger digits. Compute only those two: 7+6 = 13 (2009) and 10+6 = 16 (2010). Since 2009 is clearly the second highest and is absent from the options, mark "None of these" immediately. Common Pitfall: A common mistake is finding the highest instead of the *second highest*, or assuming that because the true answer is not among the specific years listed, there must be a calculation error. Always trust your math and confidently choose "None of these" if required. Final Answer: Therefore, the correct answer is None of these.

Question 8

Directions: Study the table carefully and answer the given questions. Total exports of six countries over five years (in ₹ crore) | Years $\rightarrow$
Country $\downarrow$ | 1998 | 1999 | 2000 | 2001 | 2002 | | :--- | :--- | :--- | :--- | :-…

Accepted Answer

Concept & Averages: Calculate the average of a dataset by dividing the total sum by the number of observations. Then, find the percentage difference between two averages. Percentage Difference = \frac{Difference}{Base Value} × 100 Step-by-Step Solution: 1. Calculate average export for T: - Total = 60 + 50 + 55 + 100 + 110 = 375. - Average = (375/5) = 75. 2. Calculate average export for R: - Total = 50 + 55 + 70 + 90 + 65 = 330. - Average = (330/5) = 66. 3. Find the percentage difference: We need how much T is *more than* R, so R is the base. - Difference = 75 - 66 = 9. - Percentage = ((9/66)) × 100 = (3/22) × 100 = (150/11)%. 4. Convert to mixed fraction: (150/11) = 13(7/11)%. Exam Strategy & Shortcut: Instead of finding averages first, find the difference in the sums: 375 - 330 = 45. Divide by 5 to find the average difference: 9. Then calculate (9/66) × 100. This saves an extra division step. Common Pitfall: Using the wrong base for the percentage calculation. Since the question asks "more than the average export of R", R's average (66) must be the denominator. Final Answer: Therefore, the correct answer is 13(7/11)%.

Question 9

Directions: Study the table carefully and answer the given questions. Total exports of six countries over five years (in ₹ crore) | Years $\rightarrow$
Country $\downarrow$ | 1998 | 1999 | 2000 | 2001 | 2002 | | :--- | :--- | :--- | :--- | :-…

Accepted Answer

Concept & Percentage Increase: The percentage increase formula compares the growth in value to the initial (base) year value. Percentage Increase = \frac{New Value - Old Value}{Old Value} × 100 Step-by-Step Solution: 1. Calculate total exports in 1999: - Total = 40 + 25 + 55 + 60 + 50 + 40 = 270 crore. 2. Calculate total exports in 2001: - Total = 45 + 50 + 90 + 15 + 100 + 75 = 375 crore. 3. Calculate the increase: - Increase = 375 - 270 = 105 crore. 4. Calculate percentage increase: - % Increase = ((105/270)) × 100 = ((1050/27))% \approx 38.888...% 5. Round off: Rounding to two digits gives 38.89%. Exam Strategy & Shortcut: Simplify the fraction before dividing: (105/270) = (105 \div 15/270 \div 15) = (7/18). The fraction (1/18) \approx 5.55%, so 7 × 5.55% \approx 38.89%. Common Pitfall: Including wrong columns (e.g., using 2000 data instead of 2001 data) or performing a simple difference without dividing by the base year value. Final Answer: Therefore, the correct answer is 38.89%.

Question 10

Directions: Study the table carefully and answer the given questions. Number of pages printed by 5 printers during 5 days | Printers $\rightarrow$
Days $\downarrow$ | A | B | C | D | E | | :--- | :--- | :--- | :--- | :--- | :--- | | Monday | …

Accepted Answer

Concept & Averages: The average is calculated by summing all the relevant data points and dividing by the total number of points. Average = \frac{Sum of Observations}{Number of Observations} Step-by-Step Solution: 1. Extract data for printer B: - Monday = 147 - Tuesday = 189 - Friday = 93 2. Calculate the sum: - Sum = 147 + 189 + 93 = 429 3. Calculate the average: - Number of days = 3 - Average = (429/3) = 143 Exam Strategy & Shortcut: Assume a base average, say 140. Find the deviations: Monday is +7, Tuesday is +49, Friday is -47. Sum of deviations = 7 + 49 - 47 = 9. Divide the sum of deviations by 3: 9 / 3 = 3. Add this to the assumed average: 140 + 3 = 143. This method avoids large additions. Common Pitfall: Adding the values correctly but forgetting to divide by 3, or miscounting the number of days specified. Final Answer: Therefore, the correct answer is 143.

Question 11

Accepted Answer

Concept & Weighted Averages: Calculate the specific volume of non-academic books for both publishers using their respective ratios, then compute their arithmetic mean. Average = \frac{Value 1 + Value 2}{2} Step-by-Step Solution: 1. Calculate Non-academic Books for R: - Total Books = 35700 - Ratio (Academic : Non-academic) = 11 : 6. Total parts = 17. - Non-academic = 35700 × ((6/17)) = 2100 × 6 = 12600. 2. Calculate Non-academic Books for S: - Total Books = 37800 - Ratio (Academic : Non-academic) = 5 : 13. Total parts = 18. - Non-academic = 37800 × ((13/18)) = 2100 × 13 = 27300. 3. Calculate the Average: - Average = (12600 + 27300/2) = (39900/2) = 19950. Exam Strategy & Shortcut: Notice the common factor when dividing by the ratio parts: 35700 / 17 = 2100 and 37800 / 18 = 2100. This makes calculation rapid. You can just sum the active ratio parts multiplied by this common factor: ((2100 × 6) + (2100 × 13)/2) = (2100 × 19/2) = 1050 × 19 = 19950. Common Pitfall: Using the academic portion of the ratio instead of the non-academic portion. Always map the requested category to its correct ratio position (the second number in this case). Final Answer: Therefore, the correct answer is 19950.

Question 12

Accepted Answer

Concept & Percentage Alterations: Apply the distinct percentage increase and decrease to the designated groups of publishers, sum the newly generated totals, and divide by the total number of publishers (7) to find the new average. New Average = \frac{New Total Sum}{Total Number of Entities} Step-by-Step Solution: 1. Group 1: P, Q, and R (Increased by 30%) - Original Sum = 31200 + 33800 + 35700 = 100700 - New Sum = 100700 × 1.30 = 130910 2. Group 2: M, N, O, and S (Decreased by 20%) - Original Sum = 28200 + 32200 + 29700 + 37800 = 127900 - New Sum = 127900 × 0.80 = 102320 3. Calculate New Overall Average: - New Total Books = 130910 + 102320 = 233230 - Total Publishers = 7 - New Average = (233230/7) = 33318.5714... Exam Strategy & Shortcut: When dividing 233230 by 7, observe the calculation: 233 / 7 = 33 with a remainder of 2. 22 / 7 = 3 with remainder 1. 13 / 7 = 1 with remainder 6. 60 / 7 = 8 with remainder 4. The result is 33318 with a fractional remainder (4/7). Because 33318 is provided as option (b) but is not the exact mathematical answer, marking "None of these" is the precise choice for decimal non-matches. Common Pitfall: Accidentally omitting a publisher when summing the "remaining publishers", or incorrectly calculating the new average by simply averaging the averages of the two separate groups. Final Answer: Therefore, the correct answer is None of these.

Question 13

Directions: Study the following bar-graph carefully and answer the questions given below:  <img    src="/api/images/average-export-of-pearls-for-given-period.png"   alt="average export of pearls for given period"   width="300"   height="200"   loadi…

Accepted Answer

Concept & Formula: To find the average of a given set of numbers, we sum all the values and divide by the total count. Average = \frac{Sum of all observations}{Number of observations} Step-by-Step Solution: • Total export from 2001 to 2007: = 5.2 + 6.5 + 7.8 + 9.9 + 10.8 + 9.5 + 11.4 = 61.1 crores • Number of years: 7 • Average export: = (61.1/7) = 8.7285... • Rounding off to two decimal places, we get 8.73. Exam Strategy & Shortcut: Instead of adding everything directly, you can pick an assumed mean (like 9) and sum the deviations. Deviations: -3.8 -2.5 -1.2 +0.9 +1.8 +0.5 +2.4 = -1.9 Average = 9 + ((-1.9/7)) = 9 - 0.27 = 8.73. Common Pitfall: A common mistake is misaligning the decimal points while summing up the values, leading to an incorrect total. Always align decimals vertically when adding. Final Answer: Therefore, the correct answer is 8.73.

Question 14

Directions: Study the following bar-graph carefully and answer the questions given below:  <img    src="/api/images/average-export-of-pearls-for-given-period.png"   alt="average export of pearls for given period"   width="300"   height="200"   loadi…

Accepted Answer

Concept & Logic: First, determine the overall average for the given period. Then, count the number of data points (years) that have a value strictly greater than that average. Step-by-Step Solution: • Find the Average: From the first question, we calculated the total export to be 61.1 crores over 7 years. • Average = (61.1/7) \approx 8.73 crores. • Compare each year to the average: - 2001: 5.2 8.73 (Above) - 2005: 10.8 > 8.73 (Above) - 2006: 9.5 > 8.73 (Above) - 2007: 11.4 > 8.73 (Above) • Count: There are exactly 4 years (2004, 2005, 2006, 2007) where the export is greater than the average. Exam Strategy & Shortcut: If you've already calculated the average in a previous question of the set, reuse that value! Simply scan the bar graph for bars crossing the imaginary line at y = 8.73. Common Pitfall: Forgetting the exact average or recalculating it and making an arithmetic error. Always write down intermediate values like the average when doing set-based questions. Final Answer: Therefore, the correct answer is 4.

Question 15

Directions: Study the following pie-chart and bar diagram and answer the following questions Percentage-wise Distribution of students in 6 Different Schools. Total number of students = 6000.  <img    src="/api/images/percentage-wise-distribution-of-…

Accepted Answer

Concept & Logic: A ratio compares quantities of identical units. We need to sequentially extract the exact values for the three requested groups and divide them by their greatest common divisor (GCD) to find the simplest form. Step-by-Step Solution: • Number of boys in School C: Given directly in the bar chart as 900. • Number of girls in School B: - Total students in B = 9% of 6000 = 9 × 60 = 540. - Number of boys in B = 400. - Number of girls in B = 540 - 400 = 140. • Total number of students in School E: - 29% of 6000 = 29 × 60 = 1740. • Required Ratio: - 900 : 140 : 1740 - Cancel the common zero (divide by 10): 90 : 14 : 174 - Divide by 2: 45 : 7 : 87 Exam Strategy & Shortcut: Once you get the sequence 900 : 140 : 1740, check the options. The middle term 140 simplifies to 14, then 7. Look for options with 7 in the middle. This immediately eliminates (b) and (d). Dividing 174 by 2 gives 87, leaving (c) as the only valid choice. Common Pitfall: Misordering the terms of the ratio. Always build the ratio in the exact sequence requested by the question prompt: (Boys C) : (Girls B) : (Total E). Final Answer: Therefore, the correct answer is 45 : 7 : 87.

Question 16

Directions: Study the following pie-chart and bar diagram and answer the following questions Percentage-wise Distribution of students in 6 Different Schools. Total number of students = 6000.  <img    src="/api/images/percentage-wise-distribution-of-…

Accepted Answer

Concept & Formula: To find what percentage one value (X) is of another value (Y), we use the formula: Percentage = ( (X/Y) ) × 100 Step-by-Step Solution: • Find Value X (Girls in School A): - Total students in A = 12% of 6000 = 12 × 60 = 720. - Number of boys in A = 500. - Number of girls in A = 720 - 500 = 220. • Find Value Y (Total students in School B): - Total students in B = 9% of 6000 = 9 × 60 = 540. • Calculate Percentage: - Required % = ( (220/540) ) × 100 - = ( (22/54) ) × 100 - = ( (11/27) ) × 100 \approx 40.74% • The question asks for the approximate percentage. Looking at the options (55, 50, 35, 45, 40), the closest value is 40. Exam Strategy & Shortcut: To quickly estimate (220/540), notice that 10% of 540 is 54. Multiply 54 by 4 to get 40%: 54 × 4 = 216. Since 220 is very close to 216, the answer is roughly 40%. No long division is necessary. Common Pitfall: Setting up the percentage fraction backwards (e.g., dividing total students in B by girls in A). The phrase "is what percentage of [Value Y]" implies [Value Y] is the denominator. Final Answer: Therefore, the correct answer is 40.

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