Set A consists of a series of unique numbers. When added together, the

Question

Set A consists of a series of unique numbers. When added together, the numbers of Set A total 140. How many of the numbers within the set are above the median?

(1) The average of the set of numbers is equal to its median.
(2) The average of the set of numbers is equal to 28.

DmitryFarberMPrep · Accepted Answer

You don't need to assume that the numbers are consecutive. If you know there are 5 numbers and they're all different ("unique"), by definition two of them will be greater than the median.

In addition to the consecutive set, we could have any of these:

0, 5, 28, 50, 57
1, 2, 3, 4, 130
-1,000,000; -100; 0, 100; 1,000,140

You get the idea . . .

Gnpth · Answer

Statement 1: We don't know much about the average. So not sufficient to solve.

Statement 2: If Average=28. Let n be the total number in the set.

We are given the sum of numbers, we know that sum divided by total number(n) will equal average.

So  \frac{140}{n}= 28  ,

Now,

\frac{140}{28}= n  =>  n=5 .

We now know the total number of numbers in the set.

let x be the median. And,

x-2, x-1, x, x+1, x+2 be the numbers.

We are given

(x-2) +(x-1)+x +(x+1) + (x+2)= 140 .--->  5x=140

x=28. So median is 28. Then the numbers above the median in 29 and 30.

So there are 2 numbers above median.

Statement 2 is sufficient.

Answer is B.

Bunuel · Answer

Comment for (2):

We have that the median of 5  distinct  numbers is 28: {a, b, 28, c, d}. Thus two numbers must be greater than the median.

Caesar · Answer

Hi Gnpth

How did you come up with the following assumption?

let x be the median. And,

x-2, x-1, x, x+1, x+2 be the numbers.

Since we are given in the question that Set A consists of a series of unique numbers, but we are not given that those unique numbers are consecutive numbers, if they are not consecutive numbers, the series might be different

r0ckst4r · Answer

Looked at this problem again and realized OA is wrong.

Please look at the following set:

27 27 27 27 32

Adds up to 140, has mean: 28 median:27.
Only 1 number is more than the median.

Same assumption (II) we can create set 26 27 28 29 30 which has median 28 and 2 numbers more than the median.

Someone please confirm and correct the OA.

DmitryFarberMPrep · Answer

Watch out for those constraints! "Set A consists of a series of unique numbers."

nerdfighter87 · Answer

Stem says Set of Unique Numbers.. so not all can be same

lenaon · Answer

hey, what if the set was 1,2,3,4,130 then 1 number above right? or im missing snth?

niks18 · Answer

Hi  lenaon

the role of statement 2 is to tell that the set has 5 elements. Once you know this fact and you also know that all the elements are unique, so median will be the middle number of the set and there will be 2 elements that will be above/below the median

KarishmaB · Answer

A has unique numbers. Sum of all numbers = 140 To get the number of numbers above the median, we need to know how many numbers there are. That is all. Once we have that, we can get how many numbers are above the median. (1) The average of the set of numbers is equal to its median. Doesn't tell us how many numbers there are. There could be 2 numbers at 69 and 71 such that mean = median = 70 and 1 number is above the median. There could be 4 numbers 32, 34, 36, 38 such that mean = median = 35 and 2 numbers are above median etc. Not sufficient alone. (2) The average of the set of numbers is equal to 28. Sum = 140 and average is 28 so we know that the number of numbers = 140/28 = 5 Hence third number will be the median and 2 numbers will be above it (since all are distinct). Sufficient alone. Answer (B) Now try out this question on mean, median and range: https://anaprep.com/sets-statistics-mea ... -question/

bumpbot · Answer

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Set A consists of a series of unique numbers. When added together, the

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