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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu Sep 21, 2017 12:04 am
vaibhav101 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.

Clearly insufficient.

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

Since the sum of any three numbers is 12, all numbers must equal, because if they are not equal, then we could pick a set of three numbers such that their sum is not 12. Sufficient.

The correct answer: B

Hope this helps!

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by Brent@GMATPrepNow » Thu Sep 21, 2017 5:35 am
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.
Target question: Are all 15 numbers equal?

Statement 1: The sum of all the numbers in the list is 60.
There are several possible scenarios that satisfy this statement. Here are two.
Case a: numbers are: {4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4}, in which case all of the numbers are equal
Case b: numbers are: {4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 7}, in which case all of the numbers are not equal
Statement 1 is NOT SUFFICIENT

Statement 2: The sum of any 3 numbers in the list is 12.
This is a very powerful statement, because it tells us that all of the numbers in the set are equal.
Let's let a,b,c and d be four of the 15 numbers in the set.
We know that a + b + c = 12
Notice that if I replace ANY of these three values (a,b or c) with d, the sum must still be 12.
This tells us that a, b and c must all equal d.
I can use a similar approach to show that e, f and g must also equal d.
In fact, I can show that ALL of the numbers in the set must equal d, which means all of the numbers in the set must be equal.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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