Ranking Ordering And Comparisons MCQs

In a class of 65 students, Rohan ranks 18th from the top. What is his rank from the bottom?

47th
48th
49th
50th

Explanation: Use the rank conversion formula: Rank from bottom = Total students − Rank from top + 1. Substitute the given values and compute directly.

In a row of 45 students, A is 12th from the left and B is 15th from the right. When they interchange their positions, A becomes 31st from the left. What is B's new position from the right?

15th
31st
34th
12th

Explanation: First determine B's original position from the left using: Position from left = Total − Position from right + 1. After interchange, B occupies A's original position. Then convert B's new left position to a right position using the same formula rearranged: Position from right = Total − New position from left + 1.

In a row of students, Karan is 14th from the left and 18th from the right. How many students are in the row?

30
31
32
33

Explanation: Apply the overlap formula for dual ranking: Total number of students = Rank from left + Rank from right − 1. This accounts for the student being counted in both directions.

In a row of 60 students, A is 20th from the left and B is 25th from the right. How many students are between A and B?

14
15
16
17

Explanation: Convert both positions to the same directional reference (either both from left or both from right). Then apply: Students between = |Position of A − Position of B| − 1.

The average weight of 5 boxes is 24 kg. When a sixth box is added, the average increases to 26 kg. If the heaviest of the original five boxes weighs 30 kg, which of the following statements must be true about the new box?

It is lighter than the heaviest original box
It equals the average of the original five
It is the heaviest among all six boxes
It equals the median of the original five

Explanation: First compute the total weight of the original five boxes using Total = Average × Count. Then compute the new total weight with six boxes. The sixth box's weight equals the difference between the two totals. Compare this value with the known maximum of the original set.

Five friends A, B, C, D, and E have distinct ages. A is older than B. C is older than A. D is older than C. E is younger than B. B is not the youngest. Who is the youngest?

A
B
D
E

Explanation: Build the complete age chain by transitivity: start with the direct comparisons and link them sequentially. C > A and A > B gives C > A > B. D > C extends this to D > C > A > B. E < B places E at the end. The complete order is D > C > A > B > E.

In a group of six students P, Q, R, S, T, and U: P is taller than Q. R is taller than P. S is taller than R. T is taller than S. U is shorter than Q. Q is not the shortest. Who is the shortest?

P
Q
T
U

Explanation: Construct the height hierarchy by chaining the direct comparisons using transitivity. R > P and P > Q yields R > P > Q. S > R extends to S > R > P > Q. T > S gives T > S > R > P > Q. U < Q places U below Q. The full order is T > S > R > P > Q > U.

In a test with integer marks, A scored more than B but less than C. D scored less than B but more than E. The average marks of A, B, and C is 74. If C scored 84 and E scored 55, what is the maximum possible score of D?

65
66
67
68

Explanation: First compute the total of A, B, and C using Total = Average × 3. Subtract C's score to obtain A + B. Since A > B and both are integers, deduce the maximum possible value of B. Then apply the chain C > A > B > D > E to find the maximum integer value D can take while remaining strictly less than B and strictly greater than E.

In a class of 50 students, A is ranked 30th from the top in Mathematics and 30th from the top in Science. All marks are distinct. What is the minimum number of students who have scored more than A in both subjects?

0
8
9
10

Explanation: Determine the number of students above A in each subject. Then apply the principle of inclusion-exclusion for the minimum overlap: Minimum in both = (Above in Math) + (Above in Science) − (Total other students). This ensures the union does not exceed the available pool.

If the 15th of a month falls 3 days after Wednesday, what day of the week will the last day of the month be if the month has 31 days?

Saturday
Sunday
Monday
Tuesday

Explanation: First determine the day of the week for the 15th by counting forward from the given reference day. Then calculate the number of days between the 15th and the 31st. Find the remainder when divided by 7 and advance that many days from the 15th's day.

Five trains depart at different times: Train A departs at 6:00 AM, Train B departs 90 minutes after A, Train C departs 2 hours before B, Train D departs exactly halfway between A and B, and Train E departs 30 minutes after D. Which train departs last?

Train A
Train B
Train C
Train E

Explanation: Compute each departure time sequentially. Add or subtract the given intervals from the reference times. Convert all times to a common format (minutes since midnight) for comparison, then identify the maximum value.

In a 1000 metre race, X gives Y a start of 100 metres and beats him by 20 seconds. If X runs at 10 m/s, what is Y's speed?

6.5 m/s
7.0 m/s
7.5 m/s
8.0 m/s

Explanation: Calculate X's time to complete the full race using Time = Distance ÷ Speed. Y covers 100 metres less distance and finishes 20 seconds later than X. Apply Speed = Distance ÷ Time to Y's run, using Y's distance and Y's total time.

The ratio of ages of A and B is 3:5. After 8 years, the ratio becomes 5:7. What is the present age of A?

8 years
10 years
12 years
14 years

Explanation: Represent the present ages as 3k and 5k using the given ratio. After 8 years, both ages increase by 8. Set up the new ratio equation, cross-multiply to eliminate fractions, solve for k, then multiply by 3 to obtain A's present age.

In an examination, 40% of the students passed in Physics, 50% passed in Chemistry, and 25% passed in both. If 520 students passed in at least one subject, what is the total number of students?

700
750
800
850

Explanation: Apply the inclusion-exclusion principle for percentages: Percentage passing at least one subject = Physics% + Chemistry% − Both%. Equate this percentage to the given absolute number, then solve for the total by dividing the absolute number by the resulting percentage (converted to decimal).

A's income is 20% more than B's, and B's income is 25% more than C's. By what percentage is A's income more than C's?

40%
45%
50%
55%

Explanation: Choose a convenient base value for C's income (such as 100). Compute B's income by increasing the base by 25%. Then compute A's income by increasing B's result by 20%. Finally, compare A's income to C's base using the percentage increase formula: ((A − C) / C) × 100.

Which of the following fractions is the largest?

5/6
7/8
11/12
13/15

Explanation: Compare each fraction to 1 by computing the difference 1 − fraction. The fraction with the smallest difference from 1 is the largest. Convert all differences to a common denominator for direct comparison.

Arrange the following in ascending order: 0.7, 0.77, 0.707, 0.077, 0.0077. Which one is in the middle position?

0.077
0.7
0.707
0.77

Explanation: Align all numbers to the same number of decimal places by appending zeros where needed. Then compare digit by digit from left to right. After sorting, identify the element at the middle position of the odd-length list.

In a class of 80 students, the top 25% are assigned Grade A. If Ravi's rank is 18th from the top, what grade does he receive?

Grade A
Grade B
Grade C
Cannot be determined

Explanation: Calculate the cutoff rank for Grade A by finding 25% of the total number of students. Compare Ravi's rank to this cutoff. If his rank is numerically less than or equal to the cutoff, he falls in the top group.

In a class of 50 students, a student needs to be in the top 20% to qualify for a scholarship. By how many ranks must a student ranked 15th from the top improve to qualify?

3 ranks
4 ranks
5 ranks
6 ranks

Explanation: Compute the qualifying cutoff rank by taking 20% of the total students. The required improvement equals the difference between the student's current rank and the cutoff rank.

Five numbers are arranged in ascending order. The sum of the two smallest numbers is 30 and the sum of the two largest numbers is 50. If the average of all five numbers is 20, what is the median?

18
20
22
24

Explanation: Let the five numbers in ascending order be a, b, c, d, e. Use the given sums to express a + b and d + e. The total sum equals the average multiplied by 5. Substitute the known pair sums into the total equation and solve for c, which is the median of an odd-count ordered set.

In a row of 40 students, A is 15th from the left. If 5 students to A's left leave, what is A's new rank from the left?

10th
11th
12th
15th

Explanation: When students to the left of a given position leave, the position shifts left by exactly the number of students who departed. Subtract the number of departing students from the original rank.

In a row of 30 students, B is 15th from the left. If 5 new students join at the right end, what is B's new rank from the right?

15th
16th
20th
21st

Explanation: First determine B's original rank from the right using the formula: Right rank = Total − Left rank + 1. When new students are added to the right end, the left rank of existing students remains unchanged but the total increases. Recompute the right rank with the new total, or simply add the number of new students to the original right rank.

Seven numbers are arranged in ascending order. The average of the first three is 12 and the average of the last three is 24. If the median is 18, what is the average of all seven numbers?

16
17
18
19

Explanation: For seven numbers in ascending order, the median is the 4th number. Compute the sum of the first three using their average, the sum of the last three using their average, and add the median. Divide the total sum by 7 to obtain the overall average.

In a 100 metre race, A beats B by 10 metres. In another 100 metre race, B beats C by 10 metres. By how many metres will A beat C in a 100 metre race?

15 metres
19 metres
20 metres
21 metres

Explanation: When A completes 100 m, B completes 90 m. When B completes 100 m, C completes 90 m. Scale C's distance proportionally to B's 90 m: C covers 90 × (90/100) = 81 m. Therefore, when A finishes 100 m, C has run 81 m. The gap is 100 − 81.

In an examination, five students scored distinct marks. A scored more than B but less than C. D scored less than E but more than C. B scored more than 60% marks. Which student definitely scored the highest?

A
C
D
E

Explanation: Chain the inequalities by transitivity. A > B and C > A gives C > A > B. D > C extends to D > C > A > B. E > D gives E > D > C > A > B. The leftmost element in the complete chain is the highest scorer.

In a class of 60 students, a student's rank is 25th from the top. If 15 students ranked below him leave the class, what is his new rank from the bottom?

15th
20th
21st
25th

Explanation: When students below a given rank leave, the rank from the top remains unchanged because the number of students above is unaffected. Compute the new total by subtracting the departing students from the original total. Then apply the conversion formula: Rank from bottom = New total − Rank from top + 1.

Five positive integers are arranged in ascending order. The product of the two smallest is 12 and the product of the two largest is 60. If the middle number is 5 and the sum of all five is 28, what is the largest number?

8
10
12
15

Explanation: Factor the product of the two smallest numbers into pairs of positive integers, keeping only the pair where both are less than the median. Sum all five numbers and subtract the known values to obtain the sum of the two largest. Use the product and sum of the two largest to form a quadratic equation whose roots are those two numbers. Select the larger root.

In a class of 120 students, 70% passed in History and 60% passed in Geography. If 30% of the students failed in both subjects, what percentage of students passed in both subjects?

40%
50%
60%
70%

Explanation: Let x be the percentage that passed in both. Express the percentage that passed only History as 70 − x and only Geography as 60 − x. The four groups (only H, only G, both, neither) must sum to 100%. Set up the equation and solve for x.

Six friends P, Q, R, S, T, and U have distinct integer heights in cm. P is taller than Q but shorter than R. S is taller than R but shorter than T. U is shorter than Q. The average height of all six is 165 cm, the average of P and R is 160 cm, and the average of S and T is 180 cm. What is the maximum possible height of U?

150 cm
152 cm
154 cm
156 cm

Explanation: Establish the height order by transitivity: T > S > R > P > Q > U. Compute the total height of all six from the overall average. Subtract the sums of P+R and S+T (derived from their averages) to obtain Q+U. Use the chain constraints Q < P and U < Q to bound Q. Since Q+U is fixed and U < Q, express U in terms of Q and find the maximum integer U that satisfies all strict inequalities.

A can complete a piece of work in 15 days and B can complete the same work in 10 days. They start working together, but B leaves after 2 days. How many more days will A take to finish the remaining work alone?

8 days
10 days
12 days
15 days

Explanation: First find the combined work rate per day: 1/15 + 1/10 = 1/6. In 2 days working together, they complete 2 × (1/6) = 1/3 of the work. The remaining work is 2/3. A's individual rate is 1/15 per day. Divide the remaining work by A's rate: (2/3) ÷ (1/15) = (2/3) × 15 = 10 days.

In a class of 90 students, the top one-third get Grade A, the next one-third get Grade B, and the rest get Grade C. If Priya is 28th from the top and Rahul is 35th from the bottom, which statement is definitely true?

Priya and Rahul have the same grade
Priya is ranked higher than Rahul
Rahul is in Grade A
Priya is in Grade C

Explanation: Divide the class into three equal groups by rank to determine the grade boundaries. Convert Rahul's bottom rank to a top rank using the conversion formula. Compare both students' top ranks to determine their relative standing and grade assignment.

In a row of students, A and B interchange positions. After interchange, A's position from the left becomes 18th and B's position from the right becomes 20th. If A was originally 12th from the left, what is the total number of students?

28
29
30
31

Explanation: After interchange, A occupies B's original position. Therefore B's original left rank equals A's new left rank. After interchange, B occupies A's original position. Convert B's new right rank to a left rank and set it equal to A's original left rank. Solve for the total.

In a row of 80 students, A is 25th from the left, B is 35th from the right, and C is 40th from the left. How many students are between A and C, and between C and B combined?

17
18
19
20

Explanation: Convert all positions to the same directional reference. Compute the gap between each adjacent pair using the formula: Students between = |Position difference| − 1. Sum the individual gaps to obtain the combined count.

The average weight of 8 people in a lift is 65 kg. When two people step out, the average of the remaining 6 becomes 62 kg. If the person who stepped out first was the heaviest at 80 kg, what is the worst possible rank of the second person who stepped out?

5th
6th
7th
8th

Explanation: Compute the total weight before and after using Total = Average × Count. The difference gives the combined weight of the two people who left. Subtract the known heaviest person's weight to find the second person's weight. To minimize their rank from the heaviest, maximize the number of people heavier than them among the remaining six. Use the remaining total and count to verify how many can exceed this weight while keeping all weights positive.

Five friends have distinct integer ages. A is older than B. C is younger than B but older than D. E is older than A. In 10 years, the sum of A's and B's ages will be 70. If D is currently 15 years old, what is the maximum possible current age of C?

20 years
22 years
23 years
24 years

Explanation: Establish the age order by transitivity: E > A > B > C > D. From the future sum condition, derive the present sum of A and B. Since A > B and both are integers, determine the maximum possible value of B. Then apply the constraint C < B along with C > D to find the maximum integer value C can take.

If 1st March 2024 is a Friday, what day of the week will 15th May 2024 be?

Monday
Tuesday
Wednesday
Thursday

Explanation: Count the exact number of days from the reference date to the target date, accounting for the full month lengths of March (31) and April (30). Divide the total day count by 7 and advance the remainder from the starting day.

A train leaves station X at 8:00 AM and reaches station Y at 11:30 AM. Another train leaves Y at 9:30 AM and reaches X at 12:00 PM. If both trains travel at constant speeds, at what time do they cross each other?

10:00 AM
10:10 AM
10:20 AM
10:30 AM

Explanation: Compute each train's travel time and derive their speeds as fractions of the total distance per hour. Determine how far the first train has traveled by the time the second train starts. The remaining distance is covered by both trains approaching each other; divide this remaining distance by the sum of their speeds to find the meeting time after the second train's departure.

In a circular track of 400 m, A completes a lap in 80 seconds and B completes a lap in 100 seconds. If they start together from the same point and run in the same direction, after how many seconds will they meet at the starting point for the first time?

200 seconds
400 seconds
600 seconds
800 seconds

Explanation: Two runners meet at the starting point only when the elapsed time is an exact multiple of both lap times. Compute the least common multiple of the two lap times by prime factorizing each, taking the highest power of each prime, and multiplying.

Which of the following is the smallest: 7/11, 5/8, 9/14, 11/17?

7/11
5/8
9/14
11/17

Explanation: Compare fractions by cross-multiplying pairs. For two fractions a/b and c/d, compare ad and bc. If ad < bc, then a/b < c/d. Systematically compare each fraction against the others to identify the minimum.

Four numbers are arranged in descending order. The average of the first two is 28 and the average of the last two is 16. If the average of the middle two is 22, what is the average of all four numbers?

20
21
22
24

Explanation: Let the four numbers in descending order be a, b, c, d. Compute the sum of the first pair from their average and the sum of the last pair from their average. The total sum of all four numbers is simply the sum of these two pairs. Divide by 4 to obtain the overall average.

In a row of 40 students, C is 18th from the left. If 4 students join at the left end and 6 students join at the right end, what is C's new rank from the right?

25th
27th
29th
31st

Explanation: When students join at the left end, every existing student's left rank increases by that number. When students join at the right end, the total increases but existing students' left ranks are unaffected. Compute the new left rank and new total, then apply the conversion formula. Alternatively, add only the right-end arrivals to the original right rank.

The ages of four siblings are distinct integers in arithmetic progression. The youngest is 8 years old. In 6 years, the average of the ages of the eldest and the youngest will be equal to the present age of the second eldest. What is the present age of the eldest?

36 years
40 years
44 years
48 years

Explanation: Represent the four ages in arithmetic progression as a, a+d, a+2d, a+3d. Set the youngest equal to the given value. Express the future ages of the eldest and youngest, compute their average, and equate it to the present age of the second eldest. Solve for the common difference d, then compute the eldest sibling's present age.

Three positive numbers are in the ratio 2:3:5. If the sum of their squares is 608, what is the largest number?

16
18
20
24

Explanation: Express the three numbers as 2k, 3k, and 5k using the given ratio. Square each term and sum them. Set the result equal to the given total and solve for k², then take the positive root. Multiply by 5 to obtain the largest number.

In a class of 100 students, a student is ranked 40th from the top. The top 30% are declared pass with distinction, the next 40% pass, and the rest fail. If the student improves his rank by exactly 15 positions, what will be his new category?

Fail
Pass
Pass with distinction
Cannot be determined

Explanation: Compute the rank boundaries for each category by taking the respective percentages of the total. Determine the student's new rank after the improvement. Compare the new rank to the category boundaries to identify the new classification.

The average weight of 7 people is 68 kg. When the heaviest person leaves, the average of the remaining 6 becomes 66 kg. When the lightest person also leaves, the average of the remaining 5 becomes 67 kg. What is the weight of the heaviest person?

76 kg
78 kg
80 kg
82 kg

Explanation: Compute the total weight of all seven people. Compute the total after the heaviest leaves by multiplying the new average by the new count. The heaviest person's weight is the difference between the original total and this new total.

In a row of 50 students, A is 20th from the left and B is 30th from the left. How many students are between A and B, excluding A and B themselves?

8
9
10
11

Explanation: When both positions are given from the same directional reference, subtract the smaller rank from the larger rank and subtract one additional unit to exclude the endpoints themselves.

In an examination of 150 students, the top 10% receive a merit certificate. If a student is ranked 25th from the top, by how many ranks must he improve to receive the certificate?

8 ranks
9 ranks
10 ranks
11 ranks

Explanation: Calculate the cutoff rank for the merit certificate by finding 10% of the total number of students. The required improvement is the difference between the student's current rank and this cutoff rank.

A cyclist covers 48 km in 4 hours. A motorist covers the same distance in 2 hours. If they start from the same point at the same time and travel in the same direction, after how many hours will the motorist be exactly 24 km ahead of the cyclist?

1 hour
2 hours
3 hours
4 hours

Explanation: Compute each traveller's speed using Speed = Distance ÷ Time. Since they move in the same direction, the relative speed is the difference of their individual speeds. Divide the required lead distance by this relative speed to obtain the time.

In a class of 60 students, the top one-fourth are declared excellent in a subject, the next one-third are declared good, and the rest are average. If a student is ranked 14th from the top in Mathematics and 36th from the top in Science, and the final category is based on the better of the two ranks, what is the student's category?

Excellent
Good
Average
Cannot be determined

Explanation: Compute the cutoff ranks for each category by taking one-fourth and one-third of the total. Determine the student's category in each subject separately by comparing their rank to these cutoffs. The better rank corresponds to the better category, which becomes the final classification.

Which of the following is the greatest: 0.625, 5/7, 0.72, 11/15?

0.625
5/7
0.72
11/15

Explanation: Convert all values to a common format, either all decimals or all fractions with a common denominator. For decimal conversion, divide the numerator by the denominator for each fraction. Then compare the decimal values digit by digit.

In a row of 50 students, A and B interchange positions. After interchange, A is 18th from the left and B is 22nd from the right. What was B's original rank from the right?

30th
31st
32nd
33rd

Explanation: After interchange, A occupies B's original position, so B's original left rank equals A's new left rank. Apply the rank conversion formula to B's original left rank to obtain B's original right rank: Original right = Total − Original left + 1.

Four distinct positive integers are arranged in ascending order. The sum of the first two is 10 and the product of the last two is 80. If the average of all four is 7, what is the third number?

6
7
8
10

Explanation: Let the four numbers be a, b, c, d in ascending order. Compute the total sum from the average. Subtract the sum of the first two to obtain c + d. Use the given product of the last two to form a quadratic equation. Solve for c and d, selecting the smaller root as the third number.

In a class of 200 students, a student is told he is in the 85th percentile. What is his rank from the top?

20th
25th
30th
35th

Explanation: The 85th percentile indicates that 85% of the students scored below him. Calculate this number: 85% of 200 = 170 students. Since 170 students are below him, his rank from the bottom is 171st. Convert this to a top rank using the standard formula: Total students − Rank from bottom + 1 (200 − 171 + 1 = 30).

Two runners start together on a circular track of 600 m. The faster runner completes a lap in 2 minutes and the slower in 3 minutes. How many laps will the faster runner have completed when he overtakes the slower runner for the first time?

2
3
4
5

Explanation: Compute each runner's speed in metres per minute. For same-direction motion on a circular track, the faster runner gains one full lap when the distance gained equals the track length. Divide the track length by the relative speed to find the time required, then divide by the faster runner's lap time.

In a row of 50 students, A is 20th from the left. If 5 students from the left end and 8 students from the right end leave, what is A's new rank from the right?

21st
22nd
23rd
24th

Explanation: When students leave from the left end, subtract that number from the original left rank. When students leave from the right end, subtract that number from the original right rank. Alternatively, compute the new total and new left rank, then apply the conversion formula.

Seven people have distinct heights arranged in ascending order. The average height of the tallest three is 180 cm and the average of the shortest three is 160 cm. If the overall average height of all seven is 170 cm, what is the median height?

165 cm
168 cm
170 cm
172 cm

Explanation: For seven values in ascending order, the median is the 4th value. Compute the total height of all seven from the overall average. Compute the total of the tallest three and the shortest three from their respective averages. Subtract both from the grand total to isolate the median.

In a row of 45 students, A is 15th from the left, B is 20th from the left, and C is 30th from the left. If A and B interchange positions, and then B and C interchange positions, what is C's final rank from the right?

29th
30th
31st
32nd

Explanation: Track the position of the target student through each interchange step by step. After the first swap, note the intermediate positions. After the second swap, determine the final left position. Convert this final left position to a right position using the total count.

Three numbers are in the ratio 4:5:6. If the sum of the largest and smallest is 50 more than the middle number, what is the sum of all three numbers?

120
135
150
165

Explanation: Express the three numbers as 4k, 5k, and 6k. Write the given condition as an equation: (Largest + Smallest) = Middle + 50. Substitute the expressions in terms of k and solve. Then compute the sum of all three terms.

In a class of 48 students, the average marks of the top 12 students is 85 and the average of the remaining 36 students is 65. If the student ranked 13th scored exactly 5 marks more than the average of the remaining 36 students, what is the difference between the average of the top 12 and the marks of the 13th ranked student?

10
12
15
20

Explanation: Identify the average of the remaining 36 students. Add the given margin to obtain the 13th ranked student's marks. Subtract this value from the average of the top 12 to find the required difference.

Five students A, B, C, D, and E have distinct integer marks out of 100. A scored more than B but less than C. D scored less than E but more than C. The average of A, B, and C is 70. The average of C, D, and E is 80. What is the maximum possible score of B?

65
67
69
71

Explanation: Establish the mark order: E > D > C > A > B. Compute the totals of the two groups from their averages. From the second group, derive the constraint D + E = 240 − C. Since D > C and E > D with distinct integers, D + E ≥ 2C + 3, which bounds C from above. From the first group, A + B = 210 − C. To maximize B, minimize A and C while maintaining A > B and C > A. Test the boundary values to find the maximum integer B that satisfies all strict inequalities and the total mark constraint.

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