Are all of the terms in Set A equal?

Question

(1) The sum of all 14 terms in Set A is 98.
(2) The sum of any 3 terms in Set A is 21.

Hiho · Answer

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?

vishu1414 · Answer

There could be only three elements in set e.g {18,2,1}

Hiho · Answer

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

Thanks

Bunuel · Answer

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

Ross2018 · Answer

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

BillyZ · Answer

OFFICIAL SOLUTION

C. Statement 1 gives us the number of terms and the sum of those terms. Since 98/14 = 7, the set certainly could contain 14 instances of 7, but it could also contain 4 7’s, 5 8’s, and 5 6’s. Insufficient. Statement 2 tells us that any 3 terms add to 21. This again is not sufficient on its own - but it might be closer than you think. If Set A only had three terms, then the terms could be any set that adds to 21 (for example, 18, 2, and 1). But if Set A has more than three terms, the only way for any three of them to add to 21 would be if they were all 7. Otherwise, consider the set: 7, 7, 3, 11. The sum of 7, 3, and 11 is 21, but the sum of 7, 7, and 3 is not, nor is 7 + 7 + 11. So the two statements together are sufficient - statement 1 guarantees that the set has more than 3 terms, and statement 2 then guarantees that they all must be the same.

KrishnakumarKA1 · Answer

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

chesstitans · Answer

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

BrentGMATPrepNow · Answer

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

Archit3110 · Answer

#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

RonTargetTestPrep · Answer

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!)

Bunuel · Answer

Posted your version of the question  HERE . Thank you!

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Are all of the terms in Set A equal?

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