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Is "twice bigger" the same as double?


We often find phrases with expressions like "something is x times larger than another. "Here are some examples:

The budget for health this year will be $ 600 million, ie, twice bigger than the $ 300 million last year.

This year, Flamengo spent R $ 100 million in hiring, value four times bigger than last year, which was $ 25 million.

The company built a 60 meter high building, three times higher than the neighboring building, which has 20 meters.

Many people consider that there may be an error in these sentences. They say, for example, that for the budget to be twice as large as R $ 300 million, it should be R $ 900 million (R $ 300 million twice as much). Similarly, they think that a 60-meter-high building should not be considered three times taller than a 20-meter building, but only twice as tall.

But in fact, this is a mathematical rather than a linguistic operation. In mathematics, when we say "twice as long," it is the same as saying "double." That is, it would be the equivalent of adding twice the reference or starting value.

Note that it makes no sense to say "A is once greater than B" because any value multiplied by 1 results in the starting or reference value itself.

Example: 100x1 = 100

So in mathematics, when you say that "A is twice as large as B" means that A is twice B, or A = 2 * B.

This means that a 40 meter high building is twice (or twice as high) a 20 meter high building or twice as large (remembering that there is no "once larger" since the "once" is the building itself). that already exists).

Question Example

There was even a math Olympiad that posed the following question:

How many times is double 50 greater than half of 10?
a) 20
b) 19
c) 15
d) 10
e) 5

Since twice 50 is 100 and half 10 is 5, it would be the equivalent of asking: "How many times 100 is greater than 5?"

Probably many people would choose the alternative B. But from a mathematical point of view, the answer is the letter The, 20 times.