HARD
IOQM - PRMO and RMO
IMPORTANT
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Find the largest possible value of n such that there exist n consecutive positive integers whose sum is equal to 2010

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Important Questions on Number System

MEDIUM
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 51
Let S be the set of all integers n such that 8n3-96n2+360n-4002n-7 is an integer. Find the value of ∑n∈Sn.
MEDIUM
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 52
Find the sum of all positive integers p such that the expression x-px-13+4 can be expressed in the form x+qx+r for distinct integers q and r.
HARD
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 53
Let Pk=1+1k-1k2-1k3, where k is a positive integer. Find the sum of all the digits of least positive integer n such that the product P2P3⋯Pn exceeds 2010 .
EASY
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 54
What is the sum of the digits of the square of 111,111,111?
HARD
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 55
Let a, b, c, and d be real numbers with a-b=2,  b-c=3 and c-d=4. What is the sum of all possible values of a-d?
HARD
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 56
Let k=20082+22008. What is the units digit of k2+2k? 
EASY
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 57
The numbers from 1 to 8 are placed at the vertices of a cube in such a manner that the sum of the four numbers on each face is the same. What is this common sum?
MEDIUM
IOQM - PRMO and RMO
IMPORTANT
Non-Routine Mathematics Resource Book-1 for PRMO>Chapter 2 - Number System>EXERCISE - 2.3>Q 58
The Saxena family consists of a mother, a father, and some children. The average age of the members of the family is 20, the father is 48 years old, and the average age of the mother and children is 16. How many children are in the family?