# Multiplying numbers from One set with another set

• brisk11228
So in summary, the number S represents the sum of the products of all the even and odd integers between 1 and 30, which is 54,000.
brisk11228

## Homework Statement

Bob makes two sets: one with all the even integers between 1 and 30 inclusive, and another with all the odd integers inclusive. He called the sets Q and R. He multiplied each number from Q with each number in R. Then he added the 225 products together and called the result "S". What number does S represent?

(A) 8,000 (B) 18,000 (C) 36,000 (D) 54,000 (E) 86,000

## The Attempt at a Solution

Set Q = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29}
Set R = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30}

I noticed if I took 1 from Q and multiplied with every number in R, I get multiples of 2 from 2 to 30
Likewise, if I took 3 from Q and multiplied with every number in R, I get multiples of 6 from 6 to 90 and so on.

# from Q Range Sum (Added first term and last term and multiplied by 7 and then added the middle #)
1 2 to 30 32 * 7 + 16 = 240
3 6 to 90 96 * 7 + 48 = 720
5 10 to 150 160 * 7 + 80 = 1200
7 14 to 210 224 * 7 + 112 = 1680
9 18 to 270 288 * 7 + 144 = 2160

I stopped here because I noticed the sums were odd multiples of 240.

So then I found the first term which is 240 and the last term which would be 240 * 29 = 6960. The middle # here would be 3600.

6960 + 240 = 7200. There are 7 pairs of 7200 and the left out middle number 3600, thus the sum would be 54,000.

I was wondering if there is a shorter or easier or alternative method of solving this problem.

Yes. Multiply the sum of the odds by the sum of the evens. 225x240 = 54000.

And there is a formula you can use for those sums to make it even faster.

## What is meant by "multiplying numbers from one set with another set"?

Multiplying numbers from one set with another set refers to the mathematical operation of combining elements from two different sets to create a new set. This operation involves taking each element from the first set and multiplying it with every element from the second set to create a new set with all possible combinations.

## What types of sets can be multiplied together?

Any two types of sets can be multiplied together, as long as they contain elements that can be multiplied with each other. This includes integers, fractions, decimals, and even complex numbers.

## How is multiplying sets different from multiplying two individual numbers?

Multiplying sets involves creating a new set with all possible combinations of elements from two different sets. This is different from multiplying two individual numbers, which results in a single product.

## What is the result of multiplying two sets?

The result of multiplying two sets is a new set that contains all possible combinations of elements from the two original sets. For example, if set A contains the numbers 1 and 2, and set B contains the numbers 3 and 4, the result of multiplying A and B would be a new set with the elements 3, 4, 6, and 8.

## What are some real-life applications of multiplying sets?

Multiplying sets can be used in various fields, such as statistics, economics, and computer science. For example, in statistics, multiplying two sets can be used to calculate probabilities and in computer science, it can be used to create combinations for coding algorithms. In everyday life, multiplying sets can also be used to calculate discounts and taxes when shopping, or to determine the total number of possible outcomes in a game of chance.

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