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# What are the ages of three brothers?

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Joined: 23 Feb 2015
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What are the ages of three brothers?  [#permalink]

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10 Dec 2019, 08:09
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What are the ages of three brothers?

(1) The product of their ages is 21
(2) The sum of their ages is not divisible by 3

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Senior Manager
Joined: 16 Feb 2015
Posts: 278
Location: United States
Concentration: Finance, Operations
What are the ages of three brothers?  [#permalink]

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Updated on: 11 Dec 2019, 20:06
What are the ages of three brothers?

(1) The product of their ages is 21
(2) The sum of their ages is not divisible by 3

Explanation:
Ages of 3 Brother.
it has to be positive, & should be an integer.

St.1 Product of ages: 21
the possible values is 1,3,7.
21,1,1
Insufficient.

St.2 Sum is not divisible by 3
Multiple value are possible.
Insufficient.

Combined, Still Insuff.
IMO-E

Originally posted by rajatchopra1994 on 10 Dec 2019, 22:35.
Last edited by rajatchopra1994 on 11 Dec 2019, 20:06, edited 1 time in total.
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Re: What are the ages of three brothers?  [#permalink]

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11 Dec 2019, 13:38
There is nothing stating that the ages have to be different which then increases the possibilities of Statement 1 to
1, 3, 7 OR 21, 1, 1. Insufficient because we have 2 possibilities? rajatchopra1994

Statement 2 is insufficient on its own. Various different numbers that add up to a number that is not-divisible by three.

Taken together we know that the product of the 3 ages has to be 21 and can't be divisible by 3- which then removes the 21, 1, 1 combo. I'm guessing the answer is C ?
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Re: What are the ages of three brothers?  [#permalink]

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11 Dec 2019, 17:27
This statement on its own is clearly insufficient. As there are many combinations that can fit into it, and we were not given any number to work with.

Statement 2----->> insufficient

Let's analyse them both together

From statement 1, we already have two possible combinations, so we can check tp see if those sum is divisble by

7+3+1= 11, and
21+1+1= 23.

Both number are equally not divisible by 3, which clearly means that option C is insufficient as we cannot separate the options

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Re: What are the ages of three brothers?  [#permalink]

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11 Dec 2019, 20:09
ms1862 wrote:
There is nothing stating that the ages have to be different which then increases the possibilities of Statement 1 to
1, 3, 7 OR 21, 1, 1. Insufficient because we have 2 possibilities? rajatchopra1994

Statement 2 is insufficient on its own. Various different numbers that add up to a number that is not-divisible by three.

Taken together we know that the product of the 3 ages has to be 21 and can't be divisible by 3- which then removes the 21, 1, 1 combo. I'm guessing the answer is C ?

ms1862

I have corrected the answer. Thanks!!!

Still when we combined St1 & St2, We don't know ages of 3 brother as , 2 possibilities are there. & Both are not divisible by 3.

IMO-E
Re: What are the ages of three brothers?   [#permalink] 11 Dec 2019, 20:09
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