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Re: DS: Are all the numbers in a certain list integers/ [#permalink]
29 Nov 2009, 10:52

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. _________________

Re: Are all the numbers in a certain list of 20 numbers equal? [#permalink]
11 Jul 2013, 21:10

1

This post received KUDOS

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 _________________

Did you find this post helpful?... Please let me know through the Kudos button.

Re: Are all the numbers in a certain list of 20 numbers equal? [#permalink]
11 Jul 2013, 22:18

1

This post received KUDOS

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.

Re: Are all the numbers in a certain list of 20 numbers equal? [#permalink]
26 Mar 2015, 17:16

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Are all the numbers in a certain list of 20 numbers equal? [#permalink]
26 Mar 2015, 18:06

Expert's post

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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