What are the chances of solving this problem?

maths is not always something used for real life. as GH Hardy said - ''Pure mathematics is on the whole more distinctly useful than applied mathematics." this question is intended to clear the Theory of percentages and the theory of square roots. And i haven't seen even 2% of maths taught in any school of the world being used in real life. what the heck will polynomials, their degrees,their graphs do in real life?And IMO is purely pure mathematics.Trigonometry for exams is more of proofs than of heights and distances(well in India, at least!).Calculus is so taught that it fails to deliver it's actual use in physics and other branches of science. All in all, in that sense, here it seems to me that pure (here by pure i mean not used in real life) mathematics holds more significance than real life mathematics. there are many other subjects(physics, chemistry) derived from real life but taught in a pure subject context.

Knowing that 100% = 1 is very important to know.

best comment I've seen on this...thank you

According to Wikipedia, "a percentage is a number or ratio expressed as a fraction of 100." So, mathematically, a percentage can stand by itself as a pure, absolute number.

This is important, because this means we can manipulate a percentage just like we do real numbers. For instance, $\sqrt{100\% \times 25} = \sqrt{100\%} \times \sqrt{25} = 100\% \times 5$ ; this implies that the square root of 100% is 100%, not 20%.

Another example is $\sqrt{64\% \times 100} = \sqrt{64\%} \times \sqrt{100} = 80\% \times 10 = 8$ which is perfectly fine since the square root of 0.64 is 0.8

If you're wondering who the heck manipulates percentages like that, look at fluid mechanics. They often use dimensionless numbers and sometimes express them in percentages. And (especially in engineering applications) the numbers are often subject to more bizarre treatments (cosine of a percentage, anyone?)

According to me it shud b 1.... since 100% is 100/100=1.... so sq. Root of 1=1

1 is a whole number. This tests whether you can understand that 100% = 1, a whole number.

you are right!

U just think that 100% is 1 because that's Wut it is, and the √1 is 1 so √100% is 100%

actually a% means 'a' parts per 100, so if there are x parts in n* 100, a% would become x/n. in this solution, x is 100 and n is 1, therefore x/n=100. and so the solution is justified as 100% equals 1(100/100=1). after taking the square root of 1, result is 1, which again means 100/100 or 100%'.

i also agree with your comments

I don't believe that is relevant to the solution. What is the square root of 49 doors? You can't quantify a square root of an object, only of a number.

How exactly does one multiply doors?

i think you fail to understand the context and purpose of the question.

yes, divide 100 by 100 what will be the answer = " 1 " as 100/100 = 1

I don't think so. You can solve it, but the chances of not solving it is 3x the chance of solving it. Thus, 1/(1+3x1) = 1/4 or 25%. However, there was no 25%, so I chose the one closest to it, i.e., 10%.

it can be made dimensional by converting 100% to an integer(1)

Purely wrong... 100% means (100/100 100) or (5/5 100) or (10/10*100) . Thus 100% of 5 is 5 and of 10 is 10. IN ALL THE CASES SQ.ROOT WOULD BE DIFFERENT. THUS THERE CANNOT BE ANY ROOT OF PERCENTAGES , AS THEY ARE RELATIVE IN NATURE WHEREAS ROOT IS OF ANY CERTAIN NUMBER

no mate , you are wrong. 29% is not equal to (29/100)*100 = 29 , here a =29. actually a% means that a parts out of hundred i.e. a/100

Agreed Elliot that the 'answer' is not the answer to the question set which is a probability question rather than a question on recognising 100%=1. (Which even then has two possible square roots)

the question needs more pratical approach than formulaes..

The function $f(x)=\sqrt{x}$ is injective. Its domain and range are both 'all non-negative real numbers' (assuming the function is from reals to reals).

Therefore $\sqrt{1}=1$ and thus $\sqrt{1} \neq -1$ .

The fact that $1^2=1$ and as well $(-1)^2=1$ is a different matter.

Percentage is per-cent which means parts per hundred. One-hundred percent is equal to 100/100 fraction: 100% = 100/100 = 1

Just as 50% is half, i.e 1/2

100% is whole, i.e. 1/1

1/1 = 1 and the sqrt1 = 1

Because 0.99 is 99 percent. :)

Vubon: Percent means how many parts out of 100. 10 % means 10 parts out of 100 i.e. 10/100 = 0.1. Sameway, 100 % = 100/100 = 1. Hope that helps.

100% is equal to 100÷100 i.e. 1

1 is a whole unit.

You can't say "100% of a cat is not 1" any more than you can say "3 apples is not 3" or "five hours is not hour" - you're dropping information, of course it sounds like nonsense.

100% of a cat is 1 cat. 100% of 49 is one 49 - weird phrasing, but accurate. Or in actual numbers:

$50\% of 49 = 50\% \times 49 = \frac{50}{100} \times 49 = 0.5 \times 49 = 24.5$ $100\% of 49 = 100\% \times 49 = \frac{100}{100} \times 49 = 1 \times 49 = 1$

100% of 49 does not equal 1 just like you say... but then, nobody claimed it was. And to put any debate to rest:

$\sqrt{100\% \times 25} = \sqrt{25} = 5$ $\sqrt{100\% \times 25} = \sqrt{100 \%} \times \sqrt{25} = x \times 5$

Therefore: $x \times 5 = 5$

Solve for X.

another brilliant mind...thank you,John

But 100% in decimal form is equal to 1, therefore the question is really asking what is the square root of 1. Since the square root of 1 is 1, it follows that the square root of 100% is 100%.

You're right that a square root of a number times itself equals that number .... And the square root of 100 does equal 10 ... But you can't just say the sqrt of 100% is 10%. That's like saying the sqrt of 100a^2 is 10a^2.

Think of 100 % as 100 * 1%. If u take the sqrt its 10 * sqrt of 1%. What's the sqrt of 1%? Well 1% can be viewed as 0.01. When u make $500 and joe asks for 1% of that, u calculate $500 * 0.01 = $5. That's how u know to give $5. The square root of 0.01 is 0.1.

10 * 0.1 = 100 * 0.01 and both are equal to 1.

So you're telling me that sqrt(1)= 1/10 ?

This doesn't make sense Samuel. True, 10x10=100. But 10% times 10% doesn't equal 100% because 10% is really equivalent to ".1" not "10" So.... "10% x10%" is really the same as ".1 x .1" which equals .01 not 100

Using the logic of "the number times itself that equals the original number." 10% times 10% is 1% so even then sticking to your logic, you wouldn't have gotten he correct answer.

10%= 0.10, 0.10 X 0.10 = 0.01. So actually 10% X 10% equals 1%. multiplying fractions, decimals, and percentages works out a bit differently than whole numbers.