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# Are all of the numbers in a certain list of 15 numbers

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Are all of the numbers in a certain list of 15 numbers [#permalink]

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23 Sep 2010, 00:45
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25% (medium)

Question Stats:

84% (01:43) correct 16% (00:40) wrong based on 37 sessions

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Are all of the numbers in a certain list of 15 numbers equal?

(1) The sum of all the numbers in the list is 60.

(2) The sum of any 3 numbers in the list is 12.
[Reveal] Spoiler: OA

Last edited by jpr200012 on 23 Sep 2010, 10:23, edited 1 time in total.
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Re: Number properties from OG 12 DS133 [#permalink]

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23 Sep 2010, 07:53
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Atrain13gm wrote:
B is the correct answer not because it allows you to demonstrate that all numbers in the set are equal, but because it allows you to prove they are NOT equal.

If all numbers are the same, then any two numbers would have to be the same. Thus, those numbers would need to be 6 an 6. But 15x6 =90, not 60.

There is a typo in statement (2). Correct question is below:

Are all of the numbers in a certain list of 15 numbers equal?

(1) The sum of all the numbers in the list is 60 --> clearly insufficient.

(2) The sum of ANY 3 numbers in the list is 12 --> as the sum of ANY 3 numbers is 12 then ALL numbers must equal to 12/3=4, because if not all the numbers equal to 4, then we could pick certain set of 3 numbers so that their sum is not 12. Sufficient.

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Re: Number properties from OG 12 DS133 [#permalink]

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23 Sep 2010, 00:49
Argh, this happens to me about 1/2 the time I come here to post about an explanation. While I'm typing, or right after I post the light bulb comes on over my head.

I was misinterpreting statement 2. I was thinking the sum of each consecutive group of 3 numbers equals 12. Obviously if any 3 numbers sum to equal twelve, each number must be 4. Therefore, all numbers in the list are equal.
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Re: Number properties from OG 12 DS133 [#permalink]

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23 Sep 2010, 07:35
B is the correct answer not because it allows you to demonstrate that all numbers in the set are equal, but because it allows you to prove they are NOT equal.

If all numbers are the same, then any two numbers would have to be the same. Thus, those numbers would need to be 6 an 6. But 15x6 =90, not 60.
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Re: Number properties from OG 12 DS133 [#permalink]

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23 Sep 2010, 08:11
Bunuel wrote:
Atrain13gm wrote:
B is the correct answer not because it allows you to demonstrate that all numbers in the set are equal, but because it allows you to prove they are NOT equal.

If all numbers are the same, then any two numbers would have to be the same. Thus, those numbers would need to be 6 an 6. But 15x6 =90, not 60.

There is a typo in statement (2). Correct question is below:

Are all of the numbers in a certain list of 15 numbers equal?

(1) The sum of all the numbers in the list is 60 --> clearly insufficient.

(2) The sum of ANY 3 numbers in the list is 12 --> as the sum of ANY 3 numbers is 12 then ALL numbers must equal to 12/3=4, because if not all the numbers equal to 4, then we could pick certain set of 3 numbers so that their sum is not 12. Sufficient.

I was wondering what kind of weird question is this, until you corrected the typo.
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Re: Number properties from OG 12 DS133 [#permalink]

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23 Sep 2010, 10:24
Sorry, I corrected the post. I guess that is what happens when you post at like 2AM! Might also be why I was having trouble with it in the first place
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Re: Number properties from OG 12 DS133 [#permalink]

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23 Sep 2010, 11:35
jpr200012 wrote:
Sorry, I corrected the post. I guess that is what happens when you post at like 2AM! Might also be why I was having trouble with it in the first place

No problem. Take it easy !
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14 Feb 2011, 09:07
Are all of the numbers in a certain list of 15 numbers equal?

1) The sum of all the numbers in the list is 60

2) The sum of any 3 numbers in the list is 12.

whether the B is right choice?
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14 Feb 2011, 09:22
Statement 1:

The numbers can be any set of 15 numbers that add up to 60!

Not sufficient

Statement 2:
Out of 15, if we pick any 3 the sum is 12.
Suppose we pick three numbers x y and z. Given x + y + z = 12

Now we replace any of the three numbers with another number. Say 'q'

q + y + z = 12 [Given]

So q = x ... same way q = y and q = z!
This can be extended to all the numbers in the set.
Thus they're all equal!

Sufficient!

Ans: 'B'
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17 Feb 2011, 01:13
naveerayala wrote:
Are all of the numbers in a certain list of 15 numbers equal?

1) The sum of all the numbers in the list is 60

2) The sum of any 3 numbers in the list is 12.

whether the B is right choice?

B is right because it tells you that all the numbers are the same. You see, you have 15C3 choices to pick 3 numbers out of 15. If even one of the numbers is different from the others, the sum of any 1 combination of 3 different numbers may differ from a different combination. Since all the all different combinations give you the same number, you can safely assume all numbers are same.
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23 Feb 2011, 22:21
133. Are all of the numbers in a certain list of 15 numbers equal?
(1) The sum of all the numbers in the list is 60.
(2) The sum of any 3 numbers in the list is 12.
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Re: OG DS 133Arithmetic Properties [#permalink]

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24 Feb 2011, 03:34
Merging similar topics.
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Re: Number properties from OG 12 DS133 [#permalink]

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16 Apr 2011, 03:57
Quote:
Are all of the numbers in a certain list of 15 numbers equal?

(1) The sum of all the numbers in the list is 60.

(2) The sum of any 3 numbers in the list is 12.

My explanation is similar to Entwistle's explanation.

Here's my explanation.

(1)- Trivial Case: All numbers in the list are 4.
Alternative Case: All but two numbers in the list are 4; the others are 3 and 5. Please that this alternative case is only one of many alternative cases; for example, all but 3 numbers could be 4, and the remaining three numbers could be 3,4, and 5.

INSUFFICIENT
(2) implies that for numbers a,b,c,d,e,f,g,h,i,j,k,l,m,n,o, in the the list of 15 numbers,
a+b+c=a+b+d--> c=d
a+b+d=a+b+e--> d=e
a+b+e=a+b+f--> e=f
...a+b+n=a+b+o--> o=n=m=l=k=j=i=h=g=f=e=d=c
To cover a and b, note: c+d+e=b+d+e-->b=c
and a+d+e=b+d+e-->a=b
Thus all numbers in the list are equal.

SUFFICIENT.

B
Re: Number properties from OG 12 DS133   [#permalink] 16 Apr 2011, 03:57
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