Practice Questions
Concept Explanation
Marks problems use standard average formulas. Common patterns include finding a missing score, required score for a target average, and combined class averages.
Key Formulas
- Total marks = Average × Number of subjects/tests
- Required score = (Target average × n) − Sum of known scores
- Combined class average = Total marks of all students / Total students
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Q1 EasyA student was asked to find the arithmetic mean of the numbers 3, 5, 7, 9 and 11. He found the mean to be 17 by mistake instead of 11. His answer was how much more than the correct answer?ExplanationFormula: Average = Sum / n. Correct sum = 3 + 5 + 7 + 9 + 11 = 35, so correct mean = 35/5 = 7. Wrong sum uses 17 instead of 11: wrong sum = 35 − 11 + 17 = 41, wrong mean = 41/5 = 8.2. Excess = 8.2 − 7 = 1.2. Shortcut: excess = (17 − 11)/5 = 6/5 = 1.2. Hence the answer is 1.2 more.
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Q2 EasyA student scores 72, 78, 84, 88 and 93 in five subjects. What is the average marks?ExplanationFormula: Average = Sum / 5. Sum = 72 + 78 + 84 + 88 + 93 = 415. Average = 415/5 = 83.
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Q3 EasyIn five papers of 100 marks each, a student averages 82%. Total marks scored are:ExplanationTotal marks = average × number of papers = 82 × 5 = 410.
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Q4 MediumThe average marks of 10 students is 60. Later it was found that marks of one student 48 were misread as 84. The correct average is:ExplanationFormula: Correct average = (Wrong sum − wrong entry + correct entry) / n. Wrong sum = 10 × 60 = 600. Correct sum = 600 − 84 + 48 = 564. Correct average = 564/10 = 56.4. Alternatively, change in average = (48 − 84)/10 = −3.6, so 60 − 3.6 = 56.4.
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Q5 MediumA batsman's average for 40 innings is 50 runs. If the highest score of 172 and the lowest score of 20 are excluded, then the average of the remaining innings is:ExplanationFormula: Remaining average = (Total runs − excluded runs) / remaining innings. Total runs = 40 × 50 = 2000. Excluded = 172 + 20 = 192. Remaining sum = 2000 − 192 = 1808 over 38 innings. Average = 1808/38 = 47.5789… ≈ 47.58 runs.
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Q6 MediumThe mean of 100 items was found to be 30. Later it was discovered that two items 40 and 25 were wrongly taken as 30 and 15. The correct mean is:ExplanationFormula: Correct mean = (Wrong sum − wrong entries + correct entries) / n. Wrong sum = 100 × 30 = 3000. Correction = −(30 + 15) + (40 + 25) = −45 + 65 = +20. Correct sum = 3020. Correct mean = 3020/100 = 30.2.
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Q7 MediumThe average of 5 consecutive numbers is n. If the next two numbers are also included, the average will:ExplanationFive consecutive numbers with average n are: (n − 2), (n − 1), n, (n + 1), (n + 2). The next two are (n + 3) and (n + 4). New sum = 5n + (n + 3) + (n + 4) = 7n + 7 = 7(n + 1). New average = 7(n + 1)/7 = n + 1. So the average increases by 1.
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Q8 MediumA student needs an average of 80 in 5 tests. Marks in the first four tests are 74, 78, 82 and 76. What minimum marks are needed in the fifth test?ExplanationRequired total = 80 × 5 = 400. Known sum = 74 + 78 + 82 + 76 = 310. Fifth score = 400 − 310 = 90.
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Q9 MediumThe average marks of 12 students is 58. One student's marks are revised from 42 to 66. What is the new average?ExplanationOld sum = 12 × 58 = 696. Increase = 66 − 42 = 24. New sum = 720. New average = 720/12 = 60. Or: average rises by 24/12 = 2 → 58 + 2 = 60.
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Q10 MediumAfter 9 tests a student's average is 68. After the 10th test the average becomes 70. What was scored in the 10th test?ExplanationOld sum = 9 × 68 = 612. New sum = 10 × 70 = 700. Tenth score = 700 − 612 = 88.
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Q11 MediumClass A has 30 students with average marks 62 and Class B has 20 students with average 72. What is the combined average?ExplanationCombined average = (n₁A₁ + n₂A₂)/(n₁ + n₂) = (30 × 62 + 20 × 72)/50 = (1860 + 1440)/50 = 3300/50 = 66.
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Q12 MediumA student scored 65, 70, 75 and 80 in four tests. What score in the fifth test gives an overall average of 76?ExplanationRequired total = 76 × 5 = 380. Known sum = 65 + 70 + 75 + 80 = 290. Fifth score = 380 − 290 = 90.
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Q13 HardIn seven given numbers, the average of the first four is 4 and that of the last four is 7. If the average of these seven numbers is 5.2, the fourth number is:ExplanationFormula: Fourth number = (Sum of first four + Sum of last four) − Sum of all seven, because the fourth is counted twice. First four sum = 4 × 4 = 16. Last four sum = 4 × 7 = 28. Combined = 44. Total of seven = 5.2 × 7 = 36.4. Fourth number = 44 − 36.4 = 7.6.
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Q14 HardAverage marks of 14 students is 55. If the highest score 85 and the lowest score 25 are removed, the average of the remaining students is:ExplanationOld sum = 14 × 55 = 770. Remaining sum = 770 − 85 − 25 = 660 over 12 students. Average = 660/12 = 55.
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DS1 Easy
What is the student's average in four tests?
Statement IThe marks scored are 70, 74, 78 and 82.
Statement IIThe total marks in the four tests is 304.
ExplanationStatement I: sum = 304, average = 304/4 = 76. Statement II: average = 304/4 = 76. Either statement alone is sufficient. -
DS2 Easy
During a screening round, what is the combined class average?
Statement IClass A has 25 students with average marks 58.
Statement IIClass B has 35 students with average marks 62.
ExplanationBoth class sizes and averages are needed. Combined = (25 × 58 + 35 × 62)/60 = (1450 + 2170)/60 = 60.333…
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DS3 Medium
What fifth-test score is needed for an average of 80?
Statement IThe average of the first four tests is 76.
Statement IIThere are five tests in total and the target average is 80.
ExplanationNeither alone fixes the fifth score. Together: required total = 80 × 5 = 400; current total = 76 × 4 = 304; fifth = 96. -
DS4 Medium
In a quantitative interview round, is the student's average above 70?
Statement IThe student scored 68, 72, 74 and 76 in four tests.
Statement IIThe total marks in four tests is 290.
ExplanationStatement I: sum = 290, average = 72.5 > 70. Statement II: average = 290/4 = 72.5 > 70. Either alone answers the yes/no question.