A set S={10,1,5,a,b,6,c} where a,b&c are different positive integers,

Question

A set S={10,1,5,a,b,6,c} where a,b&c are different positive integers, represents the different score of 7 teams in a match. What is the mean score of the 7 teams in the match?

I. a, b, c are 3 distinct prime numbers less than 9.
II. a=b+c, where b&c are consecutive integers less than 5.

WizakoBaskar · Accepted Answer

Information from the question stem 
1. a, b, and c are different positive integers.
2. I am interpreting "represents different score of 7 teams in a match" to mean that the elements of set S are distinct.

What is to be found?  
Mean score of the 7 teams.

When is the data sufficient? 
If we can find a unique value for a + b + c or for a, b, and c independently the data is sufficient.

Evaluate statement 1 alone 
a, b, c are 3 distinct prime numbers less than 9.

Prime numbers less than 9 are 2, 3, 5, and 7.
Set S already includes 5 in it. Therefore, the values that a, b, and c can take are 2, 3, and 7 - not necessarily in that order. 
Even though we do not know which of a, b, and c corresponds to the 3 values, we can find the sum, a + b + c and hence the mean of set S with this information.

Statement 1 alone is sufficient. Answer options narrow down to A or D.

Evaluate statement 2 alone 
a=b+c, where b&c are consecutive integers less than 5

Possible values for b and c
1. (1, 2)
2. (2, 3)
3. (3, 4)

Set S already includes 1. So, possibility 1 can be eliminated.
Set S already includes 5. So, possibility 2 can be eliminated. If b and c take values 2 and 3, the value of 'a' will be 5. That is not possible.

So, possibility 3 is the only one that is valid.
From statement 2, we can find a + b + c and hence the average of set S.

Statement 2 alone is also sufficient.

Choice D is the answer

Kezia9 · Answer

Can someone explain?? I chose C as statement 1 gave me different values for the mean.

sghoshgt · Answer

How each statement is sufficient?

m1033512 · Answer

Hi ,

statement one : possible values are 2,3,5,7

If you put any combination in the set and arrange them in ascending order.

you always get 4th value as 5 which is the median.

sufficient

statement 2 .

it gives only option, b=1,c=2 and a=3

it again gives one value .

sufficient

IMO D

Award kudos if helpf

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thyagi · Answer

OA is wrong...

Take values of a,b,c as 2,3 and 5 
The average score will be 4.57

Take values of a,b,c as 3,5 and 7
The average will be 5.28 .. statement 1 is clearly not sufficient

Statement 2 - 
A= b + c where b and c are consecutive integers less than 5

This is clearly not sufficient because if a,b,c take values as 3,2,1
The average will be 4

A,b,c as 7,3,4
The average will be 5.14

Combining both statements..

The only possibility is a=5
B=3 and c=2.. 
Thus the mean being 4.57..

The right answer has to be C. Not D..

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m1033512 · Answer

Mine is totally wrong , I solved to find the median not mean

:(

thyagi · Answer

My bad, I didn't realize that a,b,c are distinct numbers....

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nileshm · Answer

We are asked to find the Mean (not Median) which will diffee depending on the values chosen by this approach.

However, you can rule 5 out as a possible value since the question mentions that the set contains all 'different positive integers'. Hence you are left with 2,3 & 7!

medic19 · Answer

For statement 1, this is the key phrase: ''....different positive integers, represents the different score....''

So for 1 you can pick from 2,3,5,7 - but 5 is already included. Bet if this question was not labelled a 700 you would not have looked closer. I didn't....

For statement 2: luckily we are dealing with positive integers only and there are not many combinations of numbers 1,2,3,4 (i.e. numbers less than 5) which then produce another one of the numbers from this small set.

Edit: also, is there a typo in the phrase (and therefore the question)? Should it not be "scores"?

GMATBusters · Answer

chetan2u ,  Bunuel

A set S={10,1,5,a,b,6,c} where a,b&c are different positive integers:
Can we assume all elements of the set are distinct or only a, b and c are distinct?

chetan2u · Answer

a, b and c distinct means only these three integers are distinct from each other, it has got nothing to do with the other elements of the set.

Also, the line "represents the different score of 7 teams in a match" cannot be interpreted as all the elements are different from each other.
It just means these elements represent the different scores 7 teams scored.

Either the OA is wrong or if the OA is correct, it is a poorly worded question and should have read

GMATBusters · Answer

Thanks  chetan2u  Sir, We can change the OA to C without changing the question.

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A set S={10,1,5,a,b,6,c} where a,b&c are different positive integers,

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A set S={10,1,5,a,b,6,c} where a,b&c are different positive integers,

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