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PS: Two russian mathematicians

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PS: Two russian mathematicians [#permalink] New post 27 Aug 2010, 09:02
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Today my girl-friend asked me to solve this problem.
She knows that I am preparing for the GMAT and tries to help me by giving me hard logical problems to solve.
This one I cracked in about 7-8 minutes.
source: math competition problem for 5th grade kids. (well, it's debatable as for me).

Once two mathematicians (A and B) met each other. They had the following conversation:
A:-Hi, how are you?
B:-I am fine, thanks, I have two nice preschool sons.
A:-Wou, great. How old they are?
B:-Product of their ages equals to the number of birds sitting on this fence, and the smallest boy is similar to me.
A:-Aha, I know their ages now.
What are the boys' ages?


Assume the numbers are integers.

I will post the answer later :-D .

kudos appreciated ;)


Solution:
[Reveal] Spoiler:
Let:
a- years of an older boy
b- year of yanger boy
Prescolar age is up to 6-7 years, well it even could be 5 years.
Thus product of a*b could be any number from 1 (1*1) to 49 (7*7).
N-number of birds on fence.
Additional information as per DS question is:
1) smaller boy is similar to me
2) N does not equal to 0.


We know that a>b, and a*b=N.
Considering that birds are on fence, thus neither a , nor b equals to 0.
Put yourself in shoes of the "A" guy, who counted birds. He counted the number of birds, and than he compared that number to a product of any two numbers. In his mind, N is formed by some different pairs of figures: let say (a1;b1), (a2;b2), (a3;b3) -the combination of possible values is limited. (for example he counted 12 birds on fence, so possible sollutions are only two pairs 2;6, 3;4, and not 1;12. - but in this case there is no clue what are the boys' ages). After he understood that one of child is smaller, THIS FACT was sufficient for him to conclude about the ages.
So, in his possible solutions (pairs of figures) were a pair of two equal numbers and a pair of non-equal numbers. Factor of two equal numbers is a perfect square. Perfects squares are 4,9,16,25,36,49 - up to 7.

Possible pairs are:
4- (2;2) and (4;1)
9- (3;3) and (9;1)
16-(4;4), (1;16), (2;8)
From these pairs only first pair of figures has prescolar ages. So boys' ages are 4 and 1.

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Last edited by PTK on 05 Sep 2010, 09:48, edited 3 times in total.
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Re: PS: Two russian mathematicians [#permalink] New post 27 Aug 2010, 10:03
Pkit wrote:
Today my girl-friend asked me to solve this problem.
She knows that I am preparing for the GMAT and tries to help me by giving me hard logical problems to solve.
This one I cracked in about 7-8 minutes.
source: math competition problem for 5th grade kids. (well, it's debatable as for me).

Once two mathematicians (A and B) met each other. They had the following conversation:
A:-Hi, how are you?
B:-I am fine, thanks, I have two nice preschool sons.
A:-Wou, great. How old they are?
B:-Product of their ages equals to the number of birds sitting on this fence....and the smallest boy is similar to me.
A:-Aha, I know their ages now.
What are the boys' ages?


I will post the answer later :-D .

kudos appreciated ;)


I cant see any bird :(. I cant solve this even in 75 minutes.
Are you sure this is complete?
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Re: PS: Two russian mathematicians [#permalink] New post 27 Aug 2010, 10:08
The only thing suspicious is the .... 4 dotted spots.. Perhaps they are the birds? If so a x b = 4 and as for similar to me... Not sure about that...

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Re: PS: Two russian mathematicians [#permalink] New post 27 Aug 2010, 10:11
nice catch

a*b = 4 then the only possible solution is 4 and 1 as both can not be equal. It is mentioned that smallest is similar to him. That means they are not twins.
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Re: PS: Two russian mathematicians [#permalink] New post 27 Aug 2010, 10:15
gurpreetsingh wrote:
nice catch

a*b = 4 then the only possible solution is 4 and 1 as both can not be equal. It is mentioned that smallest is similar to him. That means they are not twins.


Spots does not have any matter here.
this was just a random, (instead of putting 3 dots, I put 4).
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Re: PS: Two russian mathematicians [#permalink] New post 27 Aug 2010, 10:17
mainhoon wrote:
The only thing suspicious is the .... 4 dotted spots.. Perhaps they are the birds? If so a x b = 4 and as for similar to me... Not sure about that...

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number of spots is random. there is no connection.
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Re: PS: Two russian mathematicians [#permalink] New post 27 Aug 2010, 10:27
also he said smallest. If there are two boys then it should be smaller not smallest.
Grammatical mistake.
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Re: PS: Two russian mathematicians [#permalink] New post 27 Aug 2010, 10:43
Preschool sons... What age do they go to school now? 5?

Ages can be anything I guess not necessarily integers?

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Re: PS: Two russian mathematicians [#permalink] New post 27 Aug 2010, 11:56
ages integers
up to 6-7 years is prescolar age.
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Re: PS: Two russian mathematicians [#permalink] New post 27 Aug 2010, 15:01
You might as well post the solution I dint think anyone knows

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Re: PS: Two russian mathematicians [#permalink] New post 27 Aug 2010, 16:19
You should post the solution now. Even birds have left the fence. :)

Highly irrelevant Gmat question but I m curious to know the solution.
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Re: PS: Two russian mathematicians [#permalink] New post 27 Aug 2010, 20:19
This is by far the most interesting question I have seen being posted.....

Am totally clueless about this one. :lol:
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Re: PS: Two russian mathematicians [#permalink] New post 27 Aug 2010, 22:52
Vox populi :)

Guys, pm me and will send you the solution.

Please provide solution and not a guess. :-D

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Last edited by PTK on 27 Aug 2010, 23:05, edited 2 times in total.
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Re: PS: Two russian mathematicians [#permalink] New post 27 Aug 2010, 22:56
gurpreetsingh wrote:
You should post the solution now. Even birds have left the fence. :)

Highly irrelevant Gmat question but I m curious to know the solution.


Well, you will see that this is highly relevant GMAT question

Quote:
also he said smallest. If there are two boys then it should be smaller not smallest.
Grammatical mistake.


Thanks for correcting me.
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Re: PS: Two russian mathematicians [#permalink] New post 27 Aug 2010, 23:25
Very tough problem. :!:
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Re: PS: Two russian mathematicians [#permalink] New post 28 Aug 2010, 00:41
Pkit wrote:
ages integers
up to 6-7 years is prescolar age.



Is there a range ? Like, preschool kids age ranges from 3-5 or something like that ?
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Re: PS: Two russian mathematicians [#permalink] New post 28 Aug 2010, 00:46
nitishmahajan wrote:
Pkit wrote:
ages integers
up to 6-7 years is prescolar age.



Is there a range ? Like, preschool kids age ranges from 3-5 or something like that ?


yes,
so prescolar age I understand from birth up to 1 grade in school.
in Europe children go to school at the age of 6-8 years.

for the sake of simplicity take range from 1 to 7. (0 is not allowed as there WERE birds, so Ndoeas not equal to 0).
Assume that numbers are integers.
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Re: PS: Two russian mathematicians [#permalink] New post 30 Aug 2010, 09:43
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Re: PS: Two russian mathematicians [#permalink] New post 31 Aug 2010, 02:14
I appreciate your post but GMAT will never ask this question and if it asks i dont want to get 800...ha...ha...h.a.... Eager to see the solution....
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Re: PS: Two russian mathematicians [#permalink] New post 05 Sep 2010, 09:50
amitjash wrote:
I appreciate your post but GMAT will never ask this question and if it asks i dont want to get 800...ha...ha...h.a.... Eager to see the solution....


I have posted the solution in spoiler.
As you see the problem tests perfect square and basic counting (pairs, product of integers, etc).
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Re: PS: Two russian mathematicians   [#permalink] 05 Sep 2010, 09:50
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