A box contains bags of marbles. All of the bags hold the same number of marbles except one bag, which holds one marble more than each of the other bags hold. If the box contains a total of 2001 marbles, how many bags are in the box?
(1) The number of bags is between 13 and 23 inclusive
(2) There is an even number of bags, and there is an even number of marbles in the bag containing the extra marble.
OA - Later
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Box, Bags, and Marbles!!
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anshumishra
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n - number of bags of marblesgig92 wrote:A box contains bags of marbles. All of the bags hold the same number of marbles except one bag, which holds one marble more than each of the other bags hold. If the box contains a total of 2001 marbles, how many bags are in the box?
(1) The number of bags is between 13 and 23 inclusive
(2) There is an even number of bags, and there is an even number of marbles in the bag containing the extra marble.
OA - Later
m - number of marbles (which are same in all but one bag)
n*m + 1 = 2001
=> n*m = 2000 = 2*2*2*2*5*5*5
n = ?
Statement 1:
13 <= n <=23
Since; n*m = 2*2*2*2*5*5*5 = ( 2*2*2*2) *(5*5*5) = 16*125; n can be 16
Also; n*m = 2*2*2*2*5*5*5 = (2*2*5) * (2*2*5*5) = 20*100 ; n can be 20 --- Insufficient
Statement 2:
There is an even number of bags, and there is an even number of marbles in the bag containing the extra marble.
=> n = even, m+1 = even => m = odd
n*m = 2000 = ( 2*2*2*2) *(5*5*5) => n = 16, m = 125
n*m = 2000 = ( 2*2*2*2*5) *(5*5) => n=80, m = 25
Insufficient
Combining 1 and 2 :
13 <= n <=23 ; n = even and m=odd
Only n = 16 is the solution, as shown above .
So, C
Thanks
Anshu
(Every mistake is a lesson learned )
Anshu
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Rahul@gurome
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Let the number of bags be n and the number of marbles in each bag except one be x.
So one bag has x+1 marble.
Or (n-1)*x + (x+1) = 2001.
Or nx + 1 = 2001.
Or nx = 2000.
Note that both n and x are positive integers and are factors of 2000.
First consider (1) alone .
The factors of 2000 between 13 and 23 are 16 and 20.
So n can be 16 or 20.
Or (1) alone is not sufficient.
Next consider (2) alone.
This means n is even and x+1 is even.
Or x is odd.
Now 2000 = 16*125 = 80*25
So if n = 16 and x is 125, n is even and x is odd.
Also if n = 80 and x is 25, n is even and x is odd.
Again we are not getting any unique value of n.
Or (2) alone is not sufficient.
Next combine both the statements together and check.
On combining, the only possible value of n is n = 16.
Or both statements together are sufficient.
The correct answer is (C).
So one bag has x+1 marble.
Or (n-1)*x + (x+1) = 2001.
Or nx + 1 = 2001.
Or nx = 2000.
Note that both n and x are positive integers and are factors of 2000.
First consider (1) alone .
The factors of 2000 between 13 and 23 are 16 and 20.
So n can be 16 or 20.
Or (1) alone is not sufficient.
Next consider (2) alone.
This means n is even and x+1 is even.
Or x is odd.
Now 2000 = 16*125 = 80*25
So if n = 16 and x is 125, n is even and x is odd.
Also if n = 80 and x is 25, n is even and x is odd.
Again we are not getting any unique value of n.
Or (2) alone is not sufficient.
Next combine both the statements together and check.
On combining, the only possible value of n is n = 16.
Or both statements together are sufficient.
The correct answer is (C).
Rahul Lakhani
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Quant Expert
Gurome, Inc.
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On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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+91-99201 32411 (India)
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gig92
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OA - CRahul@gurome wrote:Let the number of bags be n and the number of marbles in each bag except one be x.
So one bag has x+1 marble.
Or (n-1)*x + (x+1) = 2001.
Or nx + 1 = 2001.
Or nx = 2000.
Note that both n and x are positive integers and are factors of 2000.
First consider (1) alone .
The factors of 2000 between 13 and 23 are 16 and 20.
So n can be 16 or 20.
Or (1) alone is not sufficient.
Next consider (2) alone.
This means n is even and x+1 is even.
Or x is odd.
Now 2000 = 16*125 = 80*25
So if n = 16 and x is 125, n is even and x is odd.
Also if n = 80 and x is 25, n is even and x is odd.
Again we are not getting any unique value of n.
Or (2) alone is not sufficient.
Next combine both the statements together and check.
On combining, the only possible value of n is n = 16.
Or both statements together are sufficient.
The correct answer is (C).
gig92
