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IMPORTANT
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A speaker talked for sixty minutes to a full auditorium. Twenty percent of the audience heard the entire talk and ten percent slept through the entire talk. Half of the remainder heard one third of the talk and the other half heard two thirds of the talk. What was the average number of minutes of the talk heard by members of the audience?

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Important Questions on Algebra

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IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.9>Q 4
All the students in an algebra class took a 100-point test. Five students scored 100, each student scored at least 60, and the mean score was 76. What is the smallest possible number of students in the class?
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IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.9>Q 5
In the sixth, seventh, eighth, and ninth basketball games of the season, a player scored 23, 14, 11, and 20 points, respectively. Her points per-game average was higher after nine games than it was after the first five games. Her average after ten games was greater than 18. What is the least number of points she could have scored in the tenth game?
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IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.9>Q 6
The mean of three numbers is 10 more than the least of the numbers and 15 less than the greatest. The median of the three numbers is 5. What is their sum?
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IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.9>Q 7
The mean, median, unique mode, and range of a collection of eight integers are all equal to 8. What is the largest integer that can be an element of this collection?
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IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.9>Q 8
The sequence a1, a2, a3, …, satisfies a1=19 and a9=99. Also, an is the arithmetic mean of the first n-1 terms whenever n≥3. What is a2?
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IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.9>Q 9
For positive integers m and n such that m+10<n+1, both the mean and the median of the set {m,m+4,m+10,n+1,n+2,2n} are equal to n. What is m+n?
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IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.9>Q 10
A list of 2018 positive integers has a unique mode, which occurs exactly 10 times. The least number of distinct values that can occur in the list is a three digit number xyz. What is y+z2?
HARD
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 1 - Algebra>EXERCISE - 1.9>Q 11
A, B, C are three piles of rocks. The mean weight of the rocks in A is 40 kg, the mean weight of the rocks in B is 50 kg, the mean weight of the rocks in the combined piles A and B is 43 kg, and the mean weight of the rocks in the combined piles A and C is 44 kg. What is the greatest possible integer value for the mean in kg of the rocks in the combined piles B and C?