A weird math problem

[bindwood]

carol's age in years, can be expressed by reversing the digits in her father's age, in years. the sum of the digits in each age is 10.
the positive difference between carol's age in years, and her fater's age in years___36
a.>
b.<
c.=
d.uncertain

In my opinion, there are four pairs: (19,91),(28,82),(37,73),(46,64). the differences are 72,54,36,18 respectively. so I choose d. But the answer is b, I was confused. Am I wrong or the answer is incorrect? Can you throw some ideas? Any help would be much appreciated. thnx.

[daveb]

If what you wrote is the exact wording of the problem then you are correct.

[Kalouste]

Male androgens progressively decline with age and that can mean you cannot have babies after the age of 50. What does this have to do with your problem? Well:

(19,91),(28,82),(37,73),(46,64) the differences are 72,54,36,18

So I guess we can focus on (37,73),(46,64) only*. Hence, the positive difference between carol's age in years, and her fater's age in years could be <=36 because her father could had her in the ages of 18 or 36.

*This pair also doesn't make any sense: (55, 55), yet mathematically it can be consider...

[daveb]

1) This is a math problem, not a biology problem
2) Just because they decline with age doesn't imply it can't happen. Plenty of 50+ men father children

[Kalouste]

1) This is a math problem, not a biology problem
2) Just because they decline with age doesn't imply it can't happen. Plenty of 50+ men father children

a.>
b.<
c.=
d.uncertain

Let's see it in another way. You can be a father at the age of 18. That's undoubtable. Same goes to 36. About 54, let's say you also can. But 72? I don't think so.

The answer b

The answers a, c and d don't make sense because at 72 it's logically (rather than mathematically) impossible to conceive a child. "Greather than" includes the age of 72, even though 54 can be possible, like you said: so if 72 cannot be, hypothesis a cannot be either. "Equals" 36 doesn't comprehends the age of 18. And surely it's not "uncertain". Remains hypothesis b, which could be true because you assure that her father had her at 18, whereas you cannot make such assumption for hypothesis a.

About being or not a biology problem, it's not. But one thing is certain: it worked out, don't you agree?

[uart]

a.>
b.<
c.=
d.uncertain

Let's see it in another way. You can be a father at the age of 18. That's undoubtable. Same goes to 36. About 54, let's say you also can. But 72? I don't think so.

The answer b

The answers a, c and d don't make sense because at 72 it's logically (rather than mathematically) impossible to conceive a child. "Greather than" includes the age of 72, even though 54 can be possible, like you said: so if 72 cannot be, hypothesis a cannot be either. "Equals" 36 doesn't comprehends the age of 18. And surely it's not "uncertain". Remains hypothesis b, which is true because you assure that her father had her at 18 or 36, whereas you cannot make such assumption for hypothesis a.

About being or not a biology problem, it's not. But one thing is certain: it worked out, don't you agree?

Nonsense! The answer is d. Even if you do rule out the (19,91) solution for biological reasons it still leaves (28,82), (37,73), (46,64) with differences of 54, 36 and 18.

[daveb]

The statistics here http://www.idph.state.il.us/health/trivia/vit02.htm show that just in Illinois the oldest father was 83 and the youngest was 14. If you want to state that all others do not make logical sense, then you need to provide proof of those extraordinary claims. From a mathematical perspective, the correct answer is d. Just because your logic brings about the supposed correct answer of less than does not mean your thought processes are correct.

[Kalouste]

Even if you do rule out the (19,91) solution for biological reasons it still leaves (28,82), (37,73), (46,64) with differences of 54, 36 and 18

I can understand your outlook and, leaving biology out of the question, the answer is of course d. But it was said that the correct answer was b. I just tried to give a reasonable explanation that may or not be correct. It's just a hypothesis.

Same way (55,55) is not a valid combination because no daughter and father have the same age, I figured out that other combinations may not be valid as well. If you gird to a strictly mathematically point of view (55,55) can be considered a valid combination! But, as I said, I clearly understand your perspective. Without the biology, the answer is d. With the biology, we can try to explain why it could be b.

[bindwood]

thank you very much for the help, esp the data provided. Then can we just say the difference is less than 36 with the probability p1, or equals to 36 with the probability p2, or even greater than 36 with the probability
p3, where p1,p2,p3 from 0 to 1 (exclusive). Apparently p2>p1>>p3. Then a fuzzy set can be used to describe the result: {a/p1,b/p2,c/p3}, which leads to the answer d. I apologize if its nonsense.