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Intern  Joined: 05 Jan 2011
Posts: 47
Are all of the terms in Set A equal?  [#permalink]

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Question Stats: 35% (01:23) correct 65% (01:05) wrong based on 183 sessions

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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.
Intern  Joined: 20 Dec 2012
Posts: 17
Re: Are all of the terms in Set A equal?  [#permalink]

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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?
Intern  Joined: 05 Jan 2011
Posts: 47
Re: Are all of the terms in Set A equal?  [#permalink]

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Hiho wrote:
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?

There could be only three elements in set e.g {18,2,1}
Intern  Joined: 20 Dec 2012
Posts: 17
Re: Are all of the terms in Set A equal?  [#permalink]

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vishu1414 wrote:
Hiho wrote:
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?

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

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

Thanks
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Re: Are all of the terms in Set A equal?  [#permalink]

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vishu1414 wrote:
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.

Similar question to practice from OG: are-all-of-the-numbers-in-a-certain-list-of-15-numbers-equal-144144.html
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Re: Are all of the terms in Set A equal?  [#permalink]

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Lool I just found the same post on another forum and they had the wrond answer. Thanks for the explanantion
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Re: Are all of the terms in Set A equal?  [#permalink]

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vishu1414 wrote:
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.

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.
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Re: Are all of the terms in Set A equal?  [#permalink]

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vishu1414 wrote:
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.

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
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Re: Are all of the terms in Set A equal?  [#permalink]

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I am really afraid of gmat questions that ask about the properties of numbers. It is really hard to figure out all cases.
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Re: Are all of the terms in Set A equal?  [#permalink]

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vishu1414 wrote:
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.

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

Cheers,
Brent
_________________ Re: Are all of the terms in Set A equal?   [#permalink] 12 Aug 2018, 06:23
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