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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:
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:
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.
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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gurpreetsingh
Joined: 12 Oct 2009
Last visit: 15 Jun 2019
Posts: 2,266
Given Kudos: 235
Status:<strong>Nothing comes easy: neither do I want.</strong>
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
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27 Aug 2010, 11:03
Kudos
Bookmarks
Pkit
.
I cant see any bird
. I cant solve this even in 75 minutes. Are you sure this is complete?
27 Aug 2010, 11:08
Kudos
Bookmarks
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...
Posted from my mobile device
Posted from my mobile device
