Hard DS: Two russian mathematicians : GMAT Data Sufficiency (DS)
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# Hard DS: Two russian mathematicians

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Hard DS: Two russian mathematicians [#permalink]

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27 Aug 2010, 08:58
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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.
A:-But this information is not sufficent.
B:- ...and the smaller boy is similar to me.
A:-Aha, I know their ages now.
What are the boys' ages?

Assume that numbers are integers.

I will post the answer later .

p.s. Please provide solution and not just a random guess.

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.

kudos appreciated
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Last edited by PTK on 05 Sep 2010, 09:36, edited 3 times in total.
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Re: Hard DS: Two russian mathematicians [#permalink]

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27 Aug 2010, 22:44
Guys, look at this question as a purely DS question.
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Re: Hard DS: Two russian mathematicians [#permalink]

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27 Aug 2010, 23:23
Any clues how to solve this?
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Re: Hard DS: Two russian mathematicians [#permalink]

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27 Aug 2010, 23:43
B:- ...and the smaller boy is similar to me.
What does this weird phrase mean?
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Re: Hard DS: Two russian mathematicians [#permalink]

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27 Aug 2010, 23:46
Financier wrote:
B:- ...and the smaller boy is similar to me.
What does this weird phrase mean?

well, this is the clue, which helped "A" arrive to solution.
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Re: Hard DS: Two russian mathematicians [#permalink]

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28 Aug 2010, 01:55
If this is a DS question then both statements are not sufficient even if taken together.

Thus E.
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Re: Hard DS: Two russian mathematicians [#permalink]

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28 Aug 2010, 07:42
E

B is lying, he doesn;t know there age
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Re: Hard DS: Two russian mathematicians [#permalink]

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28 Aug 2010, 08:01
1
KUDOS
onedayill wrote:
B is lying, he doesn;t know there age

funny

nope, it is not E.
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Re: Hard DS: Two russian mathematicians [#permalink]

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29 Aug 2010, 02:52
1
KUDOS
Just giving it a shot! Dunno if it's right though....

Clue 1:- PRESCHOOL.
So i assume they are below three years old and its been mentioned they are integers.

So the options are (1,2) (1,1) (2,2)

Clue 2: "The smaller boy is similar to me." This means one is older than the other

The answer could be only 1,2.
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Re: Hard DS: Two russian mathematicians [#permalink]

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29 Aug 2010, 03:47
ramgmat wrote:
Just giving it a shot! Dunno if it's right though....

Clue 1:- PRESCHOOL.
So i assume they are below three years old and its been mentioned they are integers.

So the options are (1,2) (1,1) (2,2)

Clue 2: "The smaller boy is similar to me." This means one is older than the other

The answer could be only 1,2.

Good! I like you way of judgement, you are nearby.

But:
1.Why you assume that they are below 3 years old? what if one of them is 5,6 or even 7 years old?
2.In your options there are three different pairs (1,2) (1,1) (2,2), BUT product of this numbers gives us different number of birds, ie 2, 1 and 4 respectively. But number of birds is defined and it is N.

thanks for kudos
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Re: Hard DS: Two russian mathematicians [#permalink]

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30 Aug 2010, 20:05
Pkit wrote:
ramgmat wrote:
Just giving it a shot! Dunno if it's right though....

Clue 1:- PRESCHOOL.
So i assume they are below three years old and its been mentioned they are integers.

So the options are (1,2) (1,1) (2,2)

Clue 2: "The smaller boy is similar to me." This means one is older than the other

The answer could be only 1,2.

Good! I like you way of judgement, you are nearby.

But:
1.Why you assume that they are below 3 years old? what if one of them is 5,6 or even 7 years old?
2.In your options there are three different pairs (1,2) (1,1) (2,2), BUT product of this numbers gives us different number of birds, ie 2, 1 and 4 respectively. But number of birds is defined and it is N.

thanks for kudos

Based on whatever information is posted till now, we can guess that age of the younger son is 1. Hence whatever is the age of the other son, their product is the same as the number of birds.

Hence if based on these two statements.

1) -- B:-Product of their ages equals to the number of birds sitting on this fence.

2) -- B:- ...and the smaller boy is similar to me.

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Re: Hard DS: Two russian mathematicians [#permalink]

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31 Aug 2010, 02:45
For information of mods: I think this one is also posted in the PS. Eager to see the reply
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Re: Hard DS: Two russian mathematicians [#permalink]

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05 Sep 2010, 09:37
Finally, I have posted the solution in spoiler.
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Re: Hard DS: Two russian mathematicians [#permalink]

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06 Sep 2010, 11:08
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.[/spoiler]

Please explain....did not understand the colored part clearly..
Re: Hard DS: Two russian mathematicians   [#permalink] 06 Sep 2010, 11:08
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