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by anirudhbhalotia » Thu Jan 13, 2011 10:33 pm
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.


OA - B
Last edited by anirudhbhalotia on Sun Jan 16, 2011 3:03 am, edited 1 time in total.
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Source: — Data Sufficiency |

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by Anurag@Gurome » Thu Jan 13, 2011 11:22 pm
anirudhbhalotia 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.
Statement 1: The sum of all the numbers in the list is 60.
We can have different set of 15 numbers such that their sum is 60.

Not sufficient

Statement 2: The sum of any 3 numbers in the list is 12.
This is only possible when all the numbers in the set are equal. Consider the case when we have a single different number, say a and other are equal, say b. Now the selection of any three numbers may result (a, b, b) and (b, b, b). Now according to the question, (a + b + b) and (b + b + b) both must be equal to 12. Which is only possible when a = b = 4.

This can shown for other combinations too. (Like 2 different, others equal etc)

Sufficient

The correct answer is B.
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by GMATGuruNY » Fri Jan 14, 2011 4:45 am
anirudhbhalotia 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.


OA - B

Plug in numbers in order to see the situation more clearly.

Statement 1: sum = 60
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 works because the sum = 15*4 = 60. All the numbers are equal.
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 3 works because 13*4 + 5 + 3 = 60. All the numbers are not equal.
Insufficient.

Statement 2: sum of any 3 numbers in the list is 12

Let's start by seeing whether all the numbers in the list can be equal:

4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 works because no matter which 3 we choose, the sum will be 4 + 4 + 4 = 12.

Now let's see whether we can change one of the numbers:

4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1? Doesn't work, because we could pick out 4 + 4 + 1 = 9, and the sum of any 3 numbers must be 12.
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2? Doesn't work, because we could pick out 4 + 4 + 2 = 10, and the sum of any 3 numbers must be 12.
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3? Doesn't work, because we could pick out 4 + 4 + 3 = 11, and the sum of any 3 numbers must be 12.

Do you see the situation? If we change any of the numbers, we can't satisfy statement 2. The only way to satisfy statement 2 is if each number is 4. So all the numbers must be equal.
Sufficient.

The correct answer is B.
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by anirudhbhalotia » Sun Jan 16, 2011 2:02 am
Anurag@Gurome wrote:
anirudhbhalotia 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.
Statement 1: The sum of all the numbers in the list is 60.
We can have different set of 15 numbers such that their sum is 60.

Not sufficient

Statement 2: The sum of any 3 numbers in the list is 12.
This is only possible when all the numbers in the set are equal. Consider the case when we have a single different number, say a and other are equal, say b. Now the selection of any three numbers may result (a, b, b) and (b, b, b). Now according to the question, (a + b + b) and (b + b + b) both must be equal to 12. Which is only possible when a = b = 4.

This can shown for other combinations too. (Like 2 different, others equal etc)

Sufficient

The correct answer is B.

Nice!

If I remember correctly in OG-12, the 2nd statement is explained in a way too complicated form!

Thanks for simplifying!
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by anirudhbhalotia » Sun Jan 16, 2011 2:03 am
GMATGuruNY wrote:
anirudhbhalotia 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.


OA - B

Plug in numbers in order to see the situation more clearly.

Statement 1: sum = 60
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 works because the sum = 15*4 = 60. All the numbers are equal.
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 3 works because 13*4 + 5 + 3 = 60. All the numbers are not equal.
Insufficient.

Statement 2: sum of any 3 numbers in the list is 12

Let's start by seeing whether all the numbers in the list can be equal:

4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4 works because no matter which 3 we choose, the sum will be 4 + 4 + 4 = 12.

Now let's see whether we can change one of the numbers:

4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1? Doesn't work, because we could pick out 4 + 4 + 1 = 9, and the sum of any 3 numbers must be 12.
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2? Doesn't work, because we could pick out 4 + 4 + 2 = 10, and the sum of any 3 numbers must be 12.
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3? Doesn't work, because we could pick out 4 + 4 + 3 = 11, and the sum of any 3 numbers must be 12.

Do you see the situation? If we change any of the numbers, we can't satisfy statement 2. The only way to satisfy statement 2 is if each number is 4. So all the numbers must be equal.
Sufficient.

The correct answer is B.
Gotcha!

After these explanations I feel like a dork not being able to solve it!
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by ankur.agrawal » Sun Jan 16, 2011 3:01 am
anirudhbhalotia 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.


OA - B
Pls use the spoiler for OA.
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by anirudhbhalotia » Sun Jan 16, 2011 3:03 am
ankur.agrawal wrote:
anirudhbhalotia 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.


OA - B
Pls use the spoiler for OA.
My bad!

Error rectified!
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