In the figure below, PQRS is a rectangle. What is the value of a + b + c.Solution:

Using Pythagoras Theorum, we know that:

--- --- ---

And

Replace to , we get and .

Answer:

If each large ball weighs times the weight of each little ball, what is the minimum number of balls that need to be added to the right-hand side to make the scale balance? You may not remove balls, but only add small and/or large balls to the right-hand side.Solution:

Which means we can assume the weight for small ball is 3 and large ball is 4.

The weight for right-hand side The weight for left-hand side And we need to add __①__ to right-hand side.

Assuming we are adding small ball and large ball: --- ②To get minimum number of balls, add as many large ball as possible. The maximum large ball to add is .From ②,

Answer:

Solution:

Since the remainders are equal, this means the difference of 31513 and 344369, , is divisible by the three-digit number.

You can use the division-by-prime method to obtain the factors for .

So the three-digit number can be 102, 119, 136, 168, 204, 238, 357, 408, 476, 714 and 952.Use either one of these to find the remainder.

Answer:

When 31513 and 34369 are each divided by a certain three-digit number, the remainders are equal. Find this remainder.

Solution:

Let’s rewrite the expression to We know that the biggest digits must go to and ; go to and ; and go to and ; and .And we will get the largest product if the sum of the digits for and are the same.Therefore, and

Answer:

Fill the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 into the boxes

so that the expression will produce the largest product. (Each digit can be used only once)