X = ?

[absoluzation]

Today, yet another explosion occured Santa’s chemistry lab. Many beards were burnt, and many eyebrows were scorched. Over dinner, the mathematics pixy Calculus learns the following facts on the explosion from the three chemistry pixies Litmus, Nucleus, and Reductus:
Litmus recounts:“`Only a single pixy managed to survive the explosion unharmed. Exactly one pixy got away with only a burnt left eyebrow, exactly one with only a burnt right eyebrow, and exactly one with only a burnt beard.”
Nucleus is still very upset:“More than 95 % of the lab pixies suffered a burnt beard as well as a burnt left eyebrow.”
Reductus laments:“And more than 95 % of the lab pixies suffered a burnt beard as well as a burnt right eyebrow.”
Calculus ponders for a while about these informations and then observes:“Among all the lab pixies with a burnt left and a burnt right eyebrow, more than x % also have a burnt beard.”

What is the largest integer x for which the statement of Calculus will definitely be true?

Possible answers:
90 to 99

Can someone confirm whether it's 97 or not because that's my answer?

 

[Steven G]

We can confirm if the answer is 97% once we see your work.

 

[Deleted member 4993]

Today, yet another explosion occured Santa’s chemistry lab. Many beards were burnt, and many eyebrows were scorched. Over dinner, the mathematics pixy Calculus learns the following facts on the explosion from the three chemistry pixies Litmus, Nucleus, and Reductus:
Litmus recounts:“`Only a single pixy managed to survive the explosion unharmed. Exactly one pixy got away with only a burnt left eyebrow, exactly one with only a burnt right eyebrow, and exactly one with only a burnt beard.”
Nucleus is still very upset:“More than 95 % of the lab pixies suffered a burnt beard as well as a burnt left eyebrow.”
Reductus laments:“And more than 95 % of the lab pixies suffered a burnt beard as well as a burnt right eyebrow.”
Calculus ponders for a while about these informations and then observes:“Among all the lab pixies with a burnt left and a burnt right eyebrow, more than x % also have a burnt beard.”

What is the largest integer x for which the statement of Calculus will definitely be true?

Possible answers:
90 to 99

Can someone confirm whether it's 97 or not because that's my answer?

you have posted 7 puzzles without showing a line of work - just some wild guesses !!

 

[JeffM]

Set A, no injuries, number in set is 1
Set B, only one injury, number 3
Set C, three injuries, number p
Set D, only two injuries, l and r, number q
Set E, only two injuries, l and b, number r
Set F, only two injuries, r and b, number s

n = number of pixies

number of pixies with a burnt beard and left eyebrow = p + r

number of pixies with a burnt beard and right eyebrow = p + s

percentage of total with burnt beard and left eyebrow = u = (p + r) / n

percentage of total with burnt beard and right eyebrow = v = (p + s) / n

percentage with burnt beard out of those two burnt eyebrows = x% = x / 100 = p / q

We have eight unknowns, but it can be shown or is given that 6 including x are positive integers.

Moreover, we have four equations once we realize that

n = 4 + p + q + r + s.

So we can reduce the system to one in four unknowns.

Moreover, we have four independent inequalities, two involving an integer.

0.95 < u

0.95 < v

89 < x < 100

Finally, we are to find the largest possible value for x, not a unique value.

Is that the problem?

Ton of information to work with. What have you done with it?