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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?

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.

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 .

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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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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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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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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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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