Number in tens place

Can you figure out the digit in the tens place of the solution to 42015⋅92016 without using a calculator? By tens place I mean, for example if you have number 2451, the number in tens place here is 5. I know the answer, but I don’t know how to get it, so if you got … Read more

Finding all possible pairs of positive integer values

The ratio of the sum of two positive integers to their difference is $7:5$. If the the sum of the two numbers is at most $25$, find all possible values for the pair of numbers. Let $m$ be the first positive integer. Then $\frac{m}{6}$ is the second positive integer. This gives $m = 21.4$, but … Read more

How to understand the principles of the rule of three? By the way, who invented it?

I’m looking to learn all the basic math now, because now I’m an adult math looks much more interesting and easier than ever! As I saw no exact answer for my doubt here on Math SE I resolved to ask this question, which is about the rule of three. For example, a teacher gave me … Read more

Max value of $a-b$ given $\frac {a!}{b!}$ multiple of $4$ but not of $8$.

If $\frac{a!}{b!}$ is a multiple of $4$ but not a multiple of $8$,then what is the maximum value of $a-b$ ? My work : I’ve tried brute force method by trying different values for $a$ and $b$ to seek for some patters and it “seems” that the maximum value of $a-b$ is $3$. But of … Read more

If my salary grew from $1,200 a month to$1,300 a month, did I get $100/$1,200 = 8.3 % increase or $100/$1,300 = 7.7 % increase?

I’m math amateur. I was just given a raise at my job and my salary grew from $1,200 a month to$1,300 a month. I’m trying to figure out percentage growth in my salary. Did it grow $100$1,200=8.3% or did it grow $100$1,300=7.7% What’s the general rule for calculating percent growth when old value goes … Read more

Encoding 2 numbers into 1

Say we have two integers, a and b. I need a way to combine these numbers into one unique number x, such that they can both be recovered from x and no other numbers can be recovered from x There are plenty of ways to do this, but the problem is that I am using … Read more

How to calculate the price of a product without the sales tax, if we know the price including the tax and the rate of the tax?

The question is The price of a mobile phone is \$8800 inclusive of a 10% GST (General Sales Tax). What is the original price of the mobile phone? This is how I approached it: The Sale Price SP of the phone, i.e. it’s Original Price OP (sale price excluding GST) + GST on it, is … Read more

Is there a way to encode all decimal numbers between 0 and 1 into whole numbers?

Is there a way to encode ALL decimal numbers between 0 and 1 into whole numbers with a rationale that supports sum operations between the encoded numbers? so 1=0.1 2=0.2 3=0.3… 1+2 = 3 .. 0.2+0.1 = 0.3 .. 3 = 0.3 But in way that we could theoretically include ALL decimal numbers between 0 … Read more

Why shift the result of subtracting vectors?

Why do we shift the resulting vector after subtracting any two vectors a and b? I learned that when you add any two vectors a and b, the sum vector looks like the one that can be seen in the picture below (result could be found by adding the respective x and y coordinates of … Read more

Question about a puzzle I am making up: lim\lim_{x\to \infty} \sqrt[x]{-1}

Me and my friends enjoy setting each other puzzles, and one that I have come up with recently is the following: \lim_{x\to \infty} \sqrt[x]{-1} My idea is that by thinking of rooting something as rotation in the complex plane (where you are halving the angle in polar coordinates with each root), you will find that … Read more