Are all of the terms in Set A equal?

St 1: sum of 14 term is 98. cannot say if all the term will be equal or not. INSUFFICIENT

ST 2: sum of any 3 terms is 21.let all the term be equal 7 except 1 term. there will be atleast one set of 3 for which the sum will not be equal to 21. hence all the term will be equal. ANSWER

Option B

Target question: Are all of the terms in Set A equal?

Statement 1: The sum of all 14 terms in Set A is 98
There are several possible scenarios that satisfy this statement. Here are two.
Case a: Set A = {7,7,7,7,7,7,7,7,7,7,7,7,7,7} in which case all of the numbers ARE equal
Case b: Set A = {0,0,0,0,0,0,0,0,0,0,0,0,0,98}, in which case all of the numbers are NOT equal
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The sum of any 3 terms in Set A is 21
Under most conditions this statement WOULD be sufficient.
However, if set A has only 3 terms in total, then the statement is NOT sufficient.
To see what I mean, consider these two possible scenarios that satisfy statement 2:
Case a: Set A = {7,7,7} in which case all of the numbers ARE equal
Case b: Set A = {0, 0, 21}, in which case all of the numbers are NOT equal
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
The combined statements ARE sufficient. Here's why:
Let's let a,b,c and d be four of the 14 numbers in set A.
From statement 2, we know that a + b + c = 21
Notice that if I replace ANY of these three values (a,b or c) with d, the sum must still be 21 (according to statement 2)
This tells us that a, b and c must all equal d.
I can use a similar approach to show that all of the other numbers must also equal d.
This means that all of the numbers in set A must be equal.
Since we can answer the target question with certainty, the COMBINED statements are SUFFICIENT

Answer: C

Cheers,
Brent

I must have misunderstood the question.

I picked b, because if any 3 numbers in the set always equal 21, then all terms must be the same. In this case 7.

What did I do wrong?

Oh, ofcourse! The only use we had of statement one wss the ammount of terms in the set.

Thanks

Similar question to practice from OG: are-all-of-the-numbers-in-a-certain-list-of-15-numbers-equal-144144.html

Lool I just found the same post on another forum and they had the wrond answer. Thanks for the explanantion

I am really afraid of gmat questions that ask about the properties of numbers. It is really hard to figure out all cases.

#1The sum of all 14 terms in Set A is 98.
each term can be 7 each or we can have any value of 14 terms such that their sum is 98
insufficient
#2
The sum of any 3 terms in Set A is 21
total terms are not known insufficient
from 1 &2
we can say that each term is 7
sufficient
option C

Just dropping by to note that this question is not well written—or, more accurately, not written in the same way GMAC's problems are.

If this problem were from GMAC, there would definitely be an explicit stipulation that the set contains ≥3 terms.

In the current problem, you have to conjure up the 'tricky' minimalist scenario—in which there are exactly 3 terms in the set—by something resembling pure magic, with very little help from the problem statement.
This is exactly what GMAC doesn't want to force you to do!

GMAC's style is to explicitly give you a condition stating that there are three or more terms—so that you DON'T need a lightning bolt of random inspiration to come up with the case of a three-term set.

Instead, GMAC will add a stipulation of n≥3, so that a more dour, plodding, due-diligence-intensive approach will also land on that possibility, because testing the minimum stated case is basic strategy ("test the extremes").
THAT is what GMAC WANTS to happen: Slow, steady, and logical wins the race.



More specifically, if this problem were official then it'd look like this:
Set A contains at least 3 terms. Are all of the terms in Set A equal?
(1) The sum of all 14 terms in Set A is 98.
(2) The sum of any 3 terms in Set A is 21.


Or this:
Are all of the numbers in a set of 3 or more numbers equal?
(1) The sum of all 14 numbers in the set is 98.
(2) The sum of any 3 numbers in the set is 21.



Please take a look at this official problem for comparison purposes.


(I suppose I should close by mentioning that, if the GMAT were packed with 'tricky' problems that you needed ingenious strokes of sudden insight to solve—like this one—then business schools wouldn't be interested in it!)

Posted your version of the question HERE. Thank you!