Tag Archives: remainder

TV Game Show

Posted on February 17, 2017 by mvtrinh

On a television show, a player receives points for answering an easy question and points for a hard one. What is the largest integer that cannot be a contestant’s total score of the game? Source: NCTM Mathematics Teacher, October 2006 … Continue reading →

Posted in Problem solving | Tagged division, grade 8, integers, multiple, NCTM Mathematics Teacher, number sense, remainder, subtraction | Leave a comment

Largest of Five Integers

Posted on January 8, 2017 by mvtrinh

A set contains five integers. When distinct elements of this set are added together, two at a time, the complete list of different possible sums is , and . What is the largest of the five integers in the set? … Continue reading →

Posted in Problem solving | Tagged combinatorics, counting, even numbers, grade 8, inequality, integers, multiple, NCTM Mathematics Teacher, number sense, odd numbers, parity, remainder, rich problem, system of equations | Leave a comment

Largest Divisor

Posted on March 4, 2016 by mvtrinh

Select any prime number greater than . Square it and subtract . What is the largest number that must be a divisor of the result? Source: NCTM Mathematics Teacher, January 2006 SOLUTION Suppose is a prime number greater than . … Continue reading →

Posted in Problem solving | Tagged consecutive integers, divisor, grade 8, NCTM Mathematics Teacher, prime, remainder | Leave a comment

Pennies on Table

Posted on December 29, 2015 by mvtrinh

Some pennies are piled on a table. If you put them into piles of size , or , you always end up with penny left over. There is more than penny on the table. What is the fewest number of … Continue reading →

Posted in Problem solving | Tagged division, grade 6, Least common multiple, NCTM Mathematics Teacher, number sense, prime factorization, remainder | Leave a comment

Find All Integers

Posted on October 26, 2015 by mvtrinh

Find all integers such that is also an integer. Source: NCTM Mathematics Teacher, December 2005 SOLUTION The expression is an integer if is a divisor of . The divisors of are: Eight integers make the expression also an integer. Answer: 8

Posted in Problem solving | Tagged divide, divisor, grade 6, integers, NCTM Mathematics Teacher, number sense, prime factorization, remainder | Leave a comment

Sum of Terms

Posted on October 19, 2015 by mvtrinh

In the sequence of numbers , each term (starting with the third) is equal to the term preceding it minus the term preceding that one. What is the sum of the first terms of this sequence? Source: NCTM Mathematics Teacher, … Continue reading →

Posted in Problem solving | Tagged division, grade 6, NCTM Mathematics Teacher, remainder, sequence | Leave a comment

More Remainders

Posted on August 24, 2015 by mvtrinh

How many positive integers have a remainder when is divided by ? Source: NCTM Mathematics Teacher, November 2006 SOLUTION If divided by has a remainder , there exists a quotient such that and . which implies that the number of … Continue reading →

Posted in Problem solving | Tagged divisor, grade 6, NCTM Mathematics Teacher, number sense, prime factorization, quotient, remainder | Leave a comment

Remainder

Posted on August 7, 2015 by mvtrinh

What is the remainder when is divided by ? Source: NCTM Mathematics Teacher, November 2006 SOLUTION If a polynomial is divided by a polynomial , there exists a quotient polynomial and a remainder polynomial such that with . Though tedious … Continue reading →

Posted in Problem solving | Tagged grade 8, long division, NCTM Mathematics Teacher, polynomial, quotient, remainder, synthetic division | Leave a comment

Pairs of Digits

Posted on December 20, 2014 by mvtrinh

How many pairs of decimal digits exist with the property that if is an integer ending in those two digits, then ends in the same two digits? Repetition of the digits in a pair is allowed. Source: NCTM Mathematics Teacher, … Continue reading →

Posted in Problem solving | Tagged grade 8, guess and check, modulo arithmetic, number sense, remainder, square | Leave a comment

ISBN

Posted on June 2, 2014 by mvtrinh

Commercially published books bear a 10-digit identification number called an ISBN. Let denote the digits from left to right. Each ISBN has the property that is divisible by . Given the correct ISBN , how many possible pairs of digits … Continue reading →

Posted in Problem solving | Tagged Diophantine equation, divisibility, grade 6, linear equation, number sense, remainder | Leave a comment