ID 685

ID 688

ID 756

ID 766

ID 1020

ID 1070

ID 1207

ID 1212

ID 1554

ID 1839

ID 1881

What is the difference between the sum of the first 2012 even positive numbers and the sum of the first 2012 odd positive numbers?

ID 1980

A man is eating a pizza.

During the first day he eats a half of the pizza.

On the second day he eats 1/3 of the remaining part of the pizza.

The third day he eats 1/4 of what is left, and the fourth day he eats 1/5 of what still remains.

He then stops because the last piece was not fresh.

What fraction of the original pizza is still available?

ID 2028

An abundant number is a positive integer whose factors (other than the number itself) have a sum greater than the number.

Which number is not abundant?

ID 2229

When freezing, milk increases its volume by 1/15.

How will the frozen milk volume decrease when it melts?

ID 2268

ID 2276

A number is said to be perfect if it is equal to the sum of its proper divisors, that is all divisors excepting the number itself.

For example, 6 is a perfect number because 1 + 2 + 3 = 6 .

What is the largest 3-digit perfect number?

ID 2283

A prime number is an integer number that has no positive divisors other than 1 and itself.

Which is not a prime number?

ID 3221

ID 3318

The North American emergency telephone number is 911.

It is a prime number.

A prime number is an integer that has no positive divisors other than 1 and itself.

What is the next prime number?

ID 3356

ID 3392

Multiply all the digits of each license plate without using a calculator.

Find the plate with the smallest total.

ID 3412

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ID 3537

ID 3649

What is the smallest possible difference between two integer numbers that, when multiplied together, produce12345?

ID 3774

ID 3779

Fill in each empty place between the numbers with one of the symbols +, -, x or /, with each symbol used exactly once.

No parentheses are allowed.

What is the least possible absolute value of the result?

ID 3784

ID 3918

ID 3964

Write natural numbers 1, 2, . . .100 in a row so that the difference between any two adjacent numbers is smaller than N.

Find the maximum possible N.

ID 4039

In a class, 7 students walk to school, two fifths ride the bus, and 32% are dropped off by their parents.

What number is the largest?

ID 4040

In a class, 7 students walk to school, two fifths ride the bus, and 32% are dropped off by their parents.

How many students ride the bus?

ID 4051

How many digits are there in the largest positive integer, in which each digit is at least the sum of all the digits to its left?

ID 4182

What is the smallest result that can be achieved?

AB6 + BC7

Different letters in the expression are replaced with different numbers from 0 to 9 and there are no leading zeros.

The question is typical for PISA Test.

PISA stands for Programme for International Student Assessment.

ID 4235

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ID 5378

The maximum capacity of the Wembley Stadium, London, England, is 90,000.

The stadium contains 2,618 toilets, more than any other venue in the world.

There are 78,540 people in the stadium now.

If they all go to the toilets and they are evenly distributed, how long will be the queue?

We suppose that there is 1 seat per toilet.

ID 5422

The ratio of two numbers is 3 : 5.

The difference between the numbers is 8.

What is the sum of the two numbers?

ID 5436

Gerry writes the first 5 integers.

He puts either sign "+" or "x" between the numbers.

What is the largest result he can get?

He does not use parentheses (brackets).

ID 5439

ID 5644

How many positive integers that are strictly less than one hundred are evenly divisible by both 2 and 3?

ID 5758

ID 6034

ID 6248

ID 6533

Put four operations signs between the numbers 5, 4, 3, 2, and 1 to make the lowest possible result.

What will it be?

Don't change the order of the numbers, use all four signs, and don't use brackets.

ID 6598

ID 6725

Spotting patterns is very important.

Can you spot which number doesn't fit the pattern?

1, 2, 5, 14, 42, 122, . . .

Author: Leslie Green

ID 6976

Cross out 5 digits from the number

54321543215432154321

so that the remaining number is as small as possible.

What are the first five digits of the result?

ID 7028

ID 7192

*Do this in your head. No pen, paper, or calculator.*

Start with 3

multiply the result by 3

add one

multiply the result by 3

add one

Which is the correct answer?

ID 7325