ID 861

Numbers and Arithmetic K11The speed of light is 3 x 105 kilometers/second.

If the sun is 1.5x 108 kilometers from Earth, how many seconds does it take light to reach the Earth?



ID 1244

Numbers and Arithmetic K11The North American emergency telephone number is 911.

How many three-digit integers are exactly 911 more than a two-digit integer?



ID 1388

Numbers and Arithmetic K11Choose the answer without using a calculator.

Which number is evenly divisible by 8?



ID 1408

Numbers and Arithmetic K11How many sets of at least two consecutive positive integers have a sum of 15?



ID 1820

Numbers and Arithmetic K11What is the sum of all the digits (not numbers) in the sequence 1, 2, 3, 4, . . . 98, 99?



ID 1894

Numbers and Arithmetic K11How many three-digit numbers which are multiples of 7 end with the digit 4?



ID 2185

Numbers and Arithmetic K11The date July 31, 1370 in MM/DD/YYYY format is a palindrome that may be read the same way in either direction (the same forwards as backwards).
07/31/1370

How many such dates are there from June 1, 1352 to June 1, 2012?



ID 2212

Numbers and Arithmetic K11We use the decimal number system with base 10.
The binary numeral system (base 2) is widely used for digital computations.

In a number system, 17 is a prime number.
A prime number is a positive integer that has no positive divisors other than 1 and itself.

What is the base of the number system?



ID 2224

Numbers and Arithmetic K11How many two-digit numbers have exactly five divisors including 1 and themselves?



ID 2274

Numbers and Arithmetic K11Make 33 by using three 3s and any math operators.
How many times do you use the plus sign (+) in the expression?



ID 2277

Numbers and Arithmetic K11The sum of two prime numbers is equal to 888.
There are several options. We look for two numbers with maximum product.

What is one of the numbers?



ID 3176

Numbers and Arithmetic K11The last digit of the number 9100 is



ID 3191

Numbers and Arithmetic K11The typical healthy resting heart rate in adults is 60–80 beats per minute.
If you live 80 years, how many times will your heart beat?



ID 3536

Numbers and Arithmetic K11Pairs of primes separated by a single number are called prime pairs. Examples are 809 and 811.

The number between a 3-digit prime pair is always divisible by:



ID 3539

Numbers and Arithmetic K11Find the last 3 digits of the sum of

1 + 11 + 111 + . . . + 111 . . . 111,

where the last number has 99 ones.



ID 3591

Numbers and Arithmetic K11A number is palindromic, if it is the same backwards as forwards.

Of the largest palindrome made from the product of two two-digit numbers, find one of the numbers.



ID 3686

Numbers and Arithmetic K11If you sum all the numbers between 1 and 11111, what number is the result?

By the way, 1 is odd.



ID 3699

Numbers and Arithmetic K11Which is not correct?

Remember that
3! = 1 x 2 x 3



ID 3946

Numbers and Arithmetic K11You can throw an unlimited number of darts at the dartboard.
Some total scores are impossible to obtain, such as all numbers less than 5 as well as 6, 8, and 9.

What is the highest whole number score that is impossible to obtain?

The Dart Problem by Bill Graham in Games Magazine (August 2003)



ID 3952

Numbers and Arithmetic K11How many sets of three consecutive integers whose product is equal to their sum are there?



ID 4045

Numbers and Arithmetic K11If the sum of three distinct positive integers is 33, what is the maximum possible product of the numbers?



ID 4340

Numbers and Arithmetic K11The product of two integers is 1000.
Neither of the numbers contains a zero.

Find the sum of the integers.



ID 4684

Numbers and Arithmetic K11What is a mystery number if you add it to 1, then multiply by 2, then add 3, then multiply by 4, you get 5?



ID 4760

Numbers and Arithmetic K11The product of 99 integers is 99.

What is the largest possible value the sum of the numbers can have?



ID 4932

Numbers and Arithmetic K11What is the smallest number greater than 2000 that is evenly divisible by all of 2, 3, 4, 5 and 6?



ID 5000

Numbers and Arithmetic K11How many digits are in the number 2015?



ID 5030

Numbers and Arithmetic K11What is the smallest 7-digit prime number?

A prime number is a natural number that has no positive divisors other than 1 and itself.



ID 5169

Numbers and Arithmetic K11Leslie Green asks:

Find the ratio A/B where A is the number of elements in the set of all positive integers
and B is the number of elements in the set of all even positive integers.



ID 5190

Numbers and Arithmetic K11As n goes to infinity, what is the limit of n / (n-1)?



ID 5206

Numbers and Arithmetic K11The product of real positive numbers a, b, c, and d is equal to 1.

What is the minimum value of their sum?



ID 5267

Numbers and Arithmetic K11The sum of the digits of a four-digit number is 11.
All the digits are different.

What is the sum of the first two digits?