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.
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Are all numbers equal?
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LulaBrazilia
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Patrick_GMATFix
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Statement 1 only tells us the average (60/15) but numbers could differ. Statement 2 on the other hand guarantees that all numbers are equal; if any two numbers were different, swapping one for the other from a group of 3 would change the sum of the 3.
The answer is B. I go through the question in detail in the full solution below (taken from the GMATFix App).
-Patrick
The answer is B. I go through the question in detail in the full solution below (taken from the GMATFix App).
-Patrick
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Brent@GMATPrepNow
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Target question: Are all 15 numbers equal?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.
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
