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How old is Ann?

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Re: How old is Ann?

#51

Post by HarHarVeryFunny »

Ann is 18.

I think what makes it confusing is the "variable overloading" referring to both the current ages of Mary and Ann (M & A), and their ages at some point in the past "when Mary was as old as Ann is now" (M' & A').

So, what we're given is:

M = 24

M' = A

M = 2A' => A' = M/2 = 12

Since the age gap between Mary and Ann is constant, we know:

M - A = M'- A'

So, substituting in the known values:

24 - A = A - 12

2A = 36

A = 18

We can double check the result. Since Mary (24) is 6 years older than Ann (18), then when Mary was 18 Ann would have been 12, so Mary is now twice that age as given.

Re: How old is Ann?

#52

Post by quickthrowman »

judofyr wrote: post #9

Rephrasing it makes it easier to grasp: Mary is 24 years old. When Mary was Ann’s current age, Ann was 12 years old (half Mary’s current age). This makes it a bit easier to realize that Ann’s age has to be right in the middle of 12 and 24.

I figured it out by knowing that Ann had to be 12 in the past since Mary is 24 now which is twice Ann’s age. 6 years have passed since Ann was 12 and Mary was 18 making them 18 and 24, respectively.

Re: How old is Ann?

#53

Post by losvedir »

tempfile wrote: post #40
judofyr wrote: post #9

Rephrasing it makes it easier to grasp: Mary is 24 years old. When Mary was Ann’s current age, Ann was 12 years old (half Mary’s current age). This makes it a bit easier to realize that Ann’s age has to be right in the middle of 12 and 24.

> This makes it a bit easier to realize that Ann’s age has to be right in the middle of 12 and 24. How did you actually make that deduction? I can only see it by writing down an equation. I can't see anything in the problem that directly implies it.

> How did you actually make that deduction?

Think of it on a number line. Mary is 24 now, Ann was 12 then. There's a point somewhere between the two, representing Mary's age at that time.

     ---*-------*---------------*--------
        12      ?               24
The problem states that time has passed such that Mary has aged to 24 and Ann has aged to that point. You can think of time passing as a line growing out of each of them:

     ---*===----*===------------*--------
        12      ?               24
Since time progresses equally for both of them, and Ann is now that mystery age, and Mary is now 24, you can see that the distance from "12" to "?" has to be the same distance as "?" to "24".

Re: How old is Ann?

#54

Post by seemaze »

losvedir wrote: post #53
tempfile wrote: post #40

Earlier quoted context omitted.

> This makes it a bit easier to realize that Ann’s age has to be right in the middle of 12 and 24. How did you actually make that deduction? I can only see it by writing down an equation. I can't see anything in the problem that directly implies it.

> How did you actually make that deduction? Think of it on a number line. Mary is 24 now, Ann was 12 then. There's a point somewhere between the two, representing Mary's age at that time. ---*-------*---------------*-------- 12 ? 24 The problem states that time has passed such that Mary has aged to 24 and Ann has aged to that point. You can think of time passing as a line growing out of each of them: ---*===----*===-…

That's pretty much how I approached it;

                   A1   M1
              A0   M0
    +----+----+----+----+----+
    0    6    12   18   24

Re: How old is Ann?

#55

Post by zephen »

tempfile wrote: post #38
zephen wrote: post #17

Earlier quoted context omitted.

> I can't see a way to do it without algebra. This is related to "When all you have is a hammer, everything looks like a nail." It's slightly different, because you've supercharged your hammer. Everything you ever understood about how to solve word problems has been subsumed into what your brain labels as "algebra." But look at it this way: 1) Did you use algebra to convert the problem to algebraic form? Probably not…

Sorry to say, the first half of this comment is almost gibberish. It became algebra when I introduced an unknown variable and wrote down an equation. I can't see a way to solve the problem without doing that. > If X is Ann's current age, then the problem setup is: 24 - x = x - 12 How did you get this equation from the problem statement? The equation is of course correct, but I don't see how you would derive it, other…

> Sorry to say, the first half of this comment is almost gibberish.

In what way?

> It became algebra when I introduced an unknown variable and wrote down an equation.

But a lot of people, including me, can solve it without writing down any equation.

> I can't see a way to solve the problem without doing that.

Ah. So it's gibberish because of your limitations? That's... not how this usually works. (Although, to be fair, it's often the case that people of limited intellectual means lash out with unkind comments such as "gibberish" so maybe this is how it works.)

> How did you get this equation from the problem statement?

"Mary is 24 years old. She is twice as old as Ann was when Mary was as old as Ann is now. How old is Ann?"

We know that there is a delta between Mary's current age (24) and what I called X in my previous comment (Ann's current age AKA Mary's prior age). That would be 24 - X.

We also know that at some previous time, Ann was 12 (half of 24) when Mary was (Ann's current age AKA Mary's prior age).

Some of us just take the mental shortcut that the in between age has to be the average of 24 and 12 (because the delta doesn't change[1], so the delta must have been the same before as it is now), but if forced to write it down into algebra, we can say that this second statement is X - 12.

And then of course, again, because the delta doesn't change, and the delta is equal to both x-12 and 24-x, those expressions must be equal to each other.

[1] Except of course, the delta could wobble a bit for birthdays being on different dates within the year. In simple puzzles like this, of course, that +/- 1 year possibility is usually ignored.

Re: How old is Ann?

#56

Post by OvidStavrica »

How interesting!

This discussion itself offers insight on the actual need for technical professionals to be able to logically reason through non-obvious [information] structures.

I've anecdotally suspected that the ability to synthesize information into a navigable data structure and subsequently analyze it, both from internal and external POV, is not a hard requirement for the majority SWE positions.

Re: How old is Ann?

#58

Post by anigbrowl »

It's amazing to me how much effort people invest in elaborating wrong answers.

The key insight here is to remember that time moves the same for both Mary and Ann. Let's call the number of years between past and present X. Then

24 - X = 12 + X => 24 - 12 = 2X => X = 6.

Re: How old is Ann?

#60

Post by Brendinooo »

sebmellen wrote: post #45

This may help people: > Mary is 24 years old. She is twice as old as Ann was (12) when Mary was as old (18) as Ann is now (18). How old is Ann? So 6 years ago, Mary was 18, and Ann was 12. Today, Mary is twice the age that Ann was (12 * 2) at the time that she (Mary) was 18, making her 24. What makes it confusing is that the sentence is comparing Mary’s present age with Ann’s past age (which I did not catch until mul…

Yeah, I had to spell it out to get it to click for me

> mary is 24

> 8 years apart: ann is 16 now, when ann was 12 mary was 20

> 6 years apart: ann is 18 now, when ann was 12 mary was 18

> 4 years apart: ann is 20 now, when ann was 12 mary was 16

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