Set S has six numbers and their average (arithmetic mean) is 32. What

Question

Set S has six numbers and their average (arithmetic mean) is 32. What is the median of the numbers?

1) The six numbers are greater than or equal to 31 
2) There is “37” in set S

chetan2u · Answer

Hi...

There are 6 numbers, so total is 6*32=192...
Median=?

Let's see the statements..
1) Six numbers are > or =31..
All numbers are 32..... Median is 32
5 numbers are 31 and 6 is 37.... Median is 31..
Different answers possible..
Insufficient

2) 37 is in set ..
Various combinations possible..
The lowest can be ALL four 0, 5th can be 37 and then 6th will be 192-37=155.... Median=0..
Five of them 31 and 6th 37.... Median 31
Insufficient

Combined..
One is 37...
So TOTAL of remaining 5 is 192-37=155...
Only possibility is 155=31*5..
As nine can be lesser than 31 as per statement I..
Median is 31..
Sufficient

C

MathRevolution · Answer

==> In the original condition, there are 6 variables and 1 equation. In order to match the number of variables to the number of equations, there must be 5 more equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), you get
31, 31, 31, 31, 31, 37, and so the median=31+310/2=31, hence it is unique and sufficient.

The answer is C.
Answer: C

bobby200 · Answer

You didn't specify that the numbers are integers!!!
With current wording I would answer E.

leanhdung · Answer

the stem does not specify these numbers are integers and, in your calculation, you only use integer numbers!

Please check!

SatvikVedala · Answer

Can anyone help

I am concerned about the word SET S

The first Instant My understanding was SET doesn't contain repeated elements

Hence
(i) a,b,c,d,e,f (Numbers but not just Integers)]
 a+b+c+d+e+f = 6*32 => sum(a,b,c,d,e,f) = 192
 
 Case 1: 6*32 -->   -- Not possible since it is a Set (32 is repeating)
   -- Not Possible since it is a Set (32 is repeating)
   -- average not equals 32
 Case2: since it is a set and all numbers are >=31
 a can be 31,31.5,32,32.5 (considering a as lowest number)
 if a = 31
 (6/2)*  = 192
 (3)*  = 192
   = 64
 L = 33 ----> limitation this is considering series in AP (but condition of AP among numbers is missing) 
 hence first option is insufficient
(ii) set has 37
 sum = 192
 element in set = 37
 rest sum = 192 - 37 => 155

-- median = 63/2
   -- median = 64/2
 Not sufficient

Combining Both
  -- But S is set
Hence Answer is E

8Harshitsharma · Answer

You don't need to assume integers, even if you take the elements as numbers you'll get the same answer by combining the statements 31.

anirchat · Answer

How on earth can a set have repeated (non-unique) numbers ? The answer should be E.

Set S has six numbers and their average (arithmetic mean) is 32. What

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GMAT Data Sufficiency (DS) Questions

Set S has six numbers and their average (arithmetic mean) is 32. What

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