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

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

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28 Nov 2009, 23:08
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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.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 11 Jul 2013, 23:10, edited 1 time in total.

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Re: DS: Are all the numbers in a certain list integers/ [#permalink]

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29 Nov 2009, 11:52
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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Re: DS: Are all the numbers in a certain list integers/ [#permalink]

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05 Dec 2009, 10:00
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Thats a simple one.

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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Re: DS: Are all the numbers in a certain list integers/ [#permalink]

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20 Dec 2009, 08:24
B

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

(2) only 5 + 5 is valid
Thus, B

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

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11 Jul 2013, 19:17
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??
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Re: Are all the numbers in a certain list of 20 numbers equal? [#permalink]

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11 Jul 2013, 22:10
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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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Re: Are all the numbers in a certain list of 20 numbers equal? [#permalink]

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11 Jul 2013, 23:18
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Expert's post
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.

Similar question to practice:
are-all-of-the-numbers-in-a-certain-list-of-15-numbers-equal-144144.html
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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12 Jul 2013, 00:57
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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14 Jul 2013, 22:53
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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14 Jul 2013, 22:58
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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Re: Are all the numbers in a certain list of 20 numbers equal? [#permalink]

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26 Mar 2015, 18:16
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Re: Are all the numbers in a certain list of 20 numbers equal? [#permalink]

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26 Mar 2015, 19:06
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

[Reveal] Spoiler:
B

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

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29 Jul 2016, 11:26
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Re: Are all the numbers in a certain list of 20 numbers equal?   [#permalink] 29 Jul 2016, 11:26
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