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Chicks problem

by Princess23 » Sun Jun 20, 2010 9:55 am
Please Solve this:

The Pandavas won a hen and it gave birth to 7 children. These 7 in turn gave birth to 7 children each. considering that none of them die and everyday the same process goes on for 365 days, what will be the remainder if pandavas divide the children equally among themselves.
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by Patrick_GMATFix » Sun Jun 20, 2010 10:09 am
Hi Princess,

This is not written like an actual GMAT question. Specifically, (1) it doesn't tell us how many Pandavas there are, who will share the children. (2) It doesn't give answer choices, so it cannot even be considered a proper GMAT practice question

I bring this up not to criticize you, but only to caution you against using your source to prepare for the test. Ok, on to the question:


If we assume there are 2 people who will share the children, the question is asking "what is the remainder when the number of children is divided by 2?" Good news is that any integer divided by 2 will have a remainder of 0 (if the integer is even) or a remainder of 1 (if the integer is odd). In other words, the question is really "Is the total number of children even or odd?"

Since there are 7 children who each give birth to 7 children, the number of children after 2 generations will be 7*7. After 3 generations, will be 7*7*7 After 365 generations, there will be 7*7*7.... children (365 times over).

The product of two odd integers is odd, so the number of children will be odd (the result of a product of odds). Thus the remainder when this odd number is divided by 2 (the assumed number of Panvadas) will be 1. The remainder is 1.

Please consider using a different resource to get your GMAT practice.

-Patrick
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by Princess23 » Sun Jun 20, 2010 10:18 am
Thanks for your concern but i really want to know a solution for this problem. For your verification, the pandavas are 5 in number. and i want to know if the remainder we have to find is the sum of the GP/5 or the 365th term divided by 5.
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by Patrick_GMATFix » Sun Jun 20, 2010 10:27 am
My understanding is that we want the sum of all children (not just those born on the last day). i think we want the remainder when this sum is divided by 5. What was your understanding?
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by amising6 » Sun Jun 20, 2010 11:13 am
Princess23 wrote:Please Solve this:

The Pandavas won a hen and it gave birth to 7 children. These 7 in turn gave birth to 7 children each. considering that none of them die and everyday the same process goes on for 365 days, what will be the remainder if pandavas divide the children equally among themselves.
dude if you see the pattern for few days

1 day 1 hen gave birth to 7 children
2 nd day 7 children will give birth to 7 seven children each i.e 7*7=49
3 rday this 49 children will give birth to 7 each i.e 49*7=343
so basically this will be gp series where total number of terms will be 365 days
first term 1 and ratio 7
s(365)=a[r� -1 ]/ (r-1)
=1((7^365)-1)/(7-1)
=1((7^365)-1)/6
7^365 unit digit would be be 7 -1=6 so when this is going to be divided by 5 you will get remainder as 1
Ideation without execution is delusion
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by hardik.jadeja » Sun Jun 20, 2010 6:34 pm
Here's my solution...

Day 0 = The Pandavas won a hen = 1
Hens born on Day 1 = 1 hen gave birth to 7 children = 7
Hens born on Day 2 = 7 hen in turn gave birth to 7 children each = 49
Hens born on Day 3 = 49 in turn gave birth to 7 children each = 343
Hens born on Day 4 = 343 in turn gave birth to 7 children each = 2401
.....

This goes on for 365 days.

At the end of 365 days, pandavas (5 brothers) sum up all the available hens and then divide hens among themselves.

We have to observe a pattern here. Unit's digit of number of hens born on a given day will in the pattern of 7,9,3,1,7,9,3,1,... Observe that there are 4 distinct numbers here: 7,9,3 and 1

So if we divide 365 by 4 we get 1 as reminder (4*91 = 364).

So when we add up hens born on each of the 365 days, the units digit of the sum will be 92 times 7(because of the reminder 1 we get when we divide 365 by 4), 91 times 9, 91 times 3 and 91 times 1.

92*7 = 644
91*9 = 819
91*3 = 273
91*1 = 91

to this, we also have to add the mother hen who started the whole population blast.

So units digit of number of hens available to pandavas to divide among themselves is the units digit of 1828 [644 + 819+ 273+ 91 + 1 (mother hen) = 1828]

The number of hens available to pandavas to divide among themselves will be something like xxxxxxxxxxx8. Now if we divide xxxxxxxxxxx8 by 5, the reminder is going to be 3.

So I feel the answer should be 3.

Let me know if I am doing something wrong.
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