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

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Senior Manager
Joined: 10 Nov 2010
Posts: 263
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Followers: 6

Kudos [?]: 336 [0], given: 22

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

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27 Jul 2011, 09:02
00:00

Difficulty:

35% (medium)

Question Stats:

77% (01:39) correct 23% (01:15) wrong based on 31 sessions

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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.

how option 2 is sufficient
[Reveal] Spoiler: OA

_________________

The proof of understanding is the ability to explain it.

Manager
Joined: 31 May 2011
Posts: 87
Location: India
GMAT Date: 12-07-2011
GPA: 3.22
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 52 [0], given: 4

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27 Jul 2011, 09:19
GMATD11 wrote:
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.

how option 2 is sufficient

statement 1 is clearly insufficient as the some numbers could repeat and give more than one solution

Statement 2 is sufficient as it states that sum of any 3 numbers is 12.
i.e. is a1,a2,a3....a15 are the numbers then

a1+a5+a6 = a1+a3+a15= ....= 12
this is only sufficient when all the numbers are equal.

Hence B
Senior Manager
Joined: 10 Nov 2010
Posts: 263
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Followers: 6

Kudos [?]: 336 [0], given: 22

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27 Jul 2011, 10:08
I didn't get how the

a1+a3+a5 =12

it can be 1+3+8
4+4+4
3+4+5

how statement two is sufficient
_________________

The proof of understanding is the ability to explain it.

Manager
Joined: 31 May 2011
Posts: 87
Location: India
GMAT Date: 12-07-2011
GPA: 3.22
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 52 [0], given: 4

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27 Jul 2011, 11:57
GMATD11 wrote:
I didn't get how the

a1+a3+a5 =12

it can be 1+3+8
4+4+4
3+4+5

how statement two is sufficient

Its given in statement 2 that the sum of any 3 numbers is 12. In your case the numbers in the set can be 1,3,4,5,8,... as you have mentioned above. now taking any 3 numbers 4+5+8 not equal to 12 so it cannot be. The question says any 3 numbers shall add up to 12.

to be more clear think that its a matrix such that given below. Now the numbers should also add up to 12 when added vertically or diagonally.Now this will only be possible when all the numbers are same i.e. 4

a1+a2+a3 = 12
a3+a4+a5 = 12
a6+a7+a8 = 12
=============
12 12 12

Hope this clarifies.
Manager
Joined: 07 Jun 2011
Posts: 73
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Kudos [?]: 11 [0], given: 31

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29 Jul 2011, 02:56
I agree with the answer B. If the sum of any three numbers are equal, then all the numbers must be equal
Re: Number Properties   [#permalink] 29 Jul 2011, 02:56
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