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SVP  Joined: 29 Aug 2007
Posts: 1912
Are all the numbers in a certain list of 20 numbers equal?  [#permalink]

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2 00:00

Difficulty:   25% (medium)

Question Stats: 71% (00:50) correct 29% (00:54) wrong based on 229 sessions

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Are all the numbers in a certain list of 20 numbers equal?

(1) The sum of any 2 numbers in the list is an integer.
(2) The sum of any 2 numbers in the list is 10.

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Originally posted by GMAT TIGER on 28 Nov 2009, 23:08.
Last edited by Bunuel on 11 Jul 2013, 23:10, edited 1 time in total.
Manager  Joined: 24 Sep 2009
Posts: 58
Re: DS: Are all the numbers in a certain list integers/  [#permalink]

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B.
(1) says nothing.
(2) the list incluses a,b,c...n (n=20) numbers.
a+b=b+c=> a=c.
a+c=c+d=> a=d
Similarly, a=b=c=....=n.
Hence all the numbers are equal.
B.
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SVP  Joined: 29 Aug 2007
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Re: DS: Are all the numbers in a certain list integers/  [#permalink]

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1
Thats a simple one.

B is the answer.

GMAT TIGER wrote:
Are all the numbers in a certain list of 20 numbers equal?

1) The sum of any 2 numbers in the list is an integer.
2) The sum of any 2 numbers in the list is 10.

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Manager  Joined: 11 Sep 2009
Posts: 57
Re: DS: Are all the numbers in a certain list integers/  [#permalink]

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B

(1) 2+2 = 4 --> Yes
2+3 = 5 --> No

(2) only 5 + 5 is valid
Thus, B
Manager  B
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Re: Are all the numbers in a certain list of 20 numbers equal?  [#permalink]

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GMAT TIGER wrote:
Are all the numbers in a certain list of 20 numbers equal?

1) The sum of any 2 numbers in the list is an integer.
2) The sum of any 2 numbers in the list is 10.

Hi All,

Though its an old post, but I am unable to understand why B is the answer....

From Stm#2 - ( 2, 4,5,5,6....)

4+6 = 10
5+5=10 ...

So, how can be prove the numbers are equal?? VP  Joined: 02 Jul 2012
Posts: 1103
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42 GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: Are all the numbers in a certain list of 20 numbers equal?  [#permalink]

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1
Mountain14 wrote:
GMAT TIGER wrote:
Are all the numbers in a certain list of 20 numbers equal?

1) The sum of any 2 numbers in the list is an integer.
2) The sum of any 2 numbers in the list is 10.

Hi All,

Though its an old post, but I am unable to understand why B is the answer....

From Stm#2 - ( 2, 4,5,5,6....)

4+6 = 10
5+5=10 ...

So, how can be prove the numbers are equal?? If the list is as you say ( 2, 4,5,5,6....), then the sum of ANY two numbers wont be 10.. eg :2+4 = 6, 2+6 = 8, 2+5=7, 4+4 = 8, 6+6 = 12
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Joined: 02 Sep 2009
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Re: Are all the numbers in a certain list of 20 numbers equal?  [#permalink]

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2
Mountain14 wrote:
GMAT TIGER wrote:
Are all the numbers in a certain list of 20 numbers equal?

1) The sum of any 2 numbers in the list is an integer.
2) The sum of any 2 numbers in the list is 10.

Hi All,

Though its an old post, but I am unable to understand why B is the answer....

From Stm#2 - ( 2, 4,5,5,6....)

4+6 = 10
5+5=10 ...

So, how can be prove the numbers are equal?? Are all the numbers in a certain list of 20 numbers equal?

(1) The sum of any 2 numbers in the list is an integer. Clearly insufficient. For example, consider {0.5, 0.5, 0.5, ..., 0.5, 1.5} or {1, 1, 1, ...}

(2) The sum of any 2 numbers in the list is 10. Since the sum of ANY 2 numbers is 10, then ALL numbers must equal to 10/2=5, because if not all the numbers equal to 5, then we could pick certain set of 2 numbers so that their sum is not 10. Sufficient.

Hope it's clear.

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new-set-number-properties-149775-60.html#p1205373
the-discreet-charm-of-the-ds-126962-40.html#p1039655
if-there-are-more-than-two-numbers-in-a-certain-list-is-128114.html

Hope it helps.
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Re: Are all the numbers in a certain list of 20 numbers equal?  [#permalink]

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Got it... So stupid of me... Thanks MacFauz and Bunuel....
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Re: Are all the numbers in a certain list of 20 numbers equal?  [#permalink]

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Can someone please advise why it cant be 10 & 0; 10+0=10 or 5+5=10..Why the answer is not E?
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Re: Are all the numbers in a certain list of 20 numbers equal?  [#permalink]

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dragster88 wrote:
Can someone please advise why it cant be 10 & 0; 10+0=10 or 5+5=10..Why the answer is not E?

It cannot be {10, 0} because we are told that the list contains 20 numbers not 2.

Hope it helps.
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Are all the numbers in a certain list of 20 numbers equal?  [#permalink]

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Hi All,

We're told that there are 20 numbers in a list. We're asked if all of the numbers are EQUAL. This is a YES/NO question.

Fact 1: The sum of ANY 2 numbers in the list is an integer.

This Fact tells us that ALL of the numbers are either integers OR ALL of the numbers end in .5

IF.....
The list is twenty 1/2s, then taking the sum of ANY 2 will give you an integer.
The answer to the question is YES.

IF....
The list is the twenty integers from 1 to 20 inclusive, then taking the sum of ANY 2 will give you an integer.
The answer to the question is NO.
Fact 1 is INSUFFICIENT.

Fact 2: The sum of ANY 2 numbers in the list is 10.

You have to think about what this means conceptually....

The 'easy' way to think about this is if ALL twenty numbers are 5s. In this way, taking the sum of ANY 2 of these numbers will give a sum of 10.
The answer to the question is YES.

You might also consider a list that is made up of ten 0s and ten 10s. HOWEVER, taking the sum of 2 numbers from this list does NOT NECESSARILY give us a sum of 10. If you take two 0s, then the sum is 0. If you take two 10s, then the sum is 20. This example PROVES that the list CANNOT have different values in it (and by extension, ALL 20 terms MUST be 5).
Fact 2 is SUFFICIENT

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Re: Are all the numbers in a certain list of 20 numbers equal?  [#permalink]

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_________________ Re: Are all the numbers in a certain list of 20 numbers equal?   [#permalink] 19 Feb 2018, 09:37
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