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

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

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03 Aug 2010, 13:36
00:00

Difficulty:

35% (medium)

Question Stats:

82% (01:36) correct 18% (02:05) wrong based on 11 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
Manager
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03 Aug 2010, 13:36
Can someone explain this.
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03 Aug 2010, 13:47
zest4mba 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.

I think I've posted different solutions to this question elsewhere, but one way to look at Statement 2:

let a, b, c and d be four random numbers from the list. From Statement 2, since the sum of *any* three numbers is 12, we know

a + b + c = 12
d + b + c = 12

and if you subtract the second equation from the first, you find that a - d = 0, so a = d. Since a and d are just randomly chosen numbers from the list, we could do the same thing for any of the numbers in our list, and so they all need to be equal. Since Statement 1 is not sufficient, the answer is B.
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03 Aug 2010, 15:42
This was my approach

You have 15 numbers that add up to 60. Factoring 60 you get that the only combination of two factors that have 15 must have 4 on them. There is no other number than 4 that repeated 15 times add up to 60

1) You know that you need a 4 for the statement to be sufficient, but as it can be any other number or fraction is not sufficient.

2) Any combination of 3 numbers of the list add 12. You can see that 4 is your lucky number, therefore answer is B.

Hope Im right!
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04 Aug 2010, 20:09
IanStewart wrote:
zest4mba 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.

I think I've posted different solutions to this question elsewhere, but one way to look at Statement 2:

let a, b, c and d be four random numbers from the list. From Statement 2, since the sum of *any* three numbers is 12, we know

a + b + c = 12
d + b + c = 12

and if you subtract the second equation from the first, you find that a - d = 0, so a = d. Since a and d are just randomly chosen numbers from the list, we could do the same thing for any of the numbers in our list, and so they all need to be equal. Since Statement 1 is not sufficient, the answer is B.

I still didn't get you....

There are 15 different numbers, but we took only 4 for our example.

what if a + b+ c = 12
and d + e+ f = 12
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04 Aug 2010, 22:28
onedayill wrote:
IanStewart wrote:
zest4mba 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.

I think I've posted different solutions to this question elsewhere, but one way to look at Statement 2:

let a, b, c and d be four random numbers from the list. From Statement 2, since the sum of *any* three numbers is 12, we know

a + b + c = 12
d + b + c = 12

and if you subtract the second equation from the first, you find that a - d = 0, so a = d. Since a and d are just randomly chosen numbers from the list, we could do the same thing for any of the numbers in our list, and so they all need to be equal. Since Statement 1 is not sufficient, the answer is B.

I still didn't get you....

There are 15 different numbers, but we took only 4 for our example.

what if a + b+ c = 12
and d + e+ f = 12

Say our list is:

a, b, c, d, e, f, g, h, i, j, k, l, m, n, o

I just took the first four numbers and proved a=d. There's nothing special about the first four numbers in the list; I can use the same logic to prove that any two numbers are equal here. For example, if I want to prove that b=d, we have

b + c + a = 12
d + c + a = 12

Subtract the second equation from the first:

b - d = 0
b = d

So now we know that b = d. Since we saw that a=d as well, a, b and d are all equal. We can do this for all the letters in the list, so they all must be equal.
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05 Aug 2010, 10:23
Question type : yes/no

Given to us that a list contains 15 numbers

statement 1) sum of all numbers is 15.

The statement does not answer the question whether the all numbers are the same as all numbers can be zero except
one which might be 60.

INSUFFICIENT

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

so this basically mean x1+x2+x10 = 12
x3+x4+x15 = 12 ... so on

so for the sum to be twelve for any numbers in the List, the numbers must be 4 each.
This answers our original question of if all the numbers are equal or not.
SUFFICIENT
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07 Aug 2010, 01:07
zest4mba 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.

Choice A ...

0 0 0 0 0 0 0....60 (14 zeros)
4 4 4 4 4 4 4 (fifteen 4's)

Insufficient...

Choice B...

only posibility is fifteen 4s to add upto 12 on selecting 3 numbers

So choice B is the answer....
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Re: DS QUESTION-DIFFICULT   [#permalink] 07 Aug 2010, 01:07
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