Set A consists of 5 different integers. If 1 is the least number in th

Given, Set has 5 different integers, and 1 is the least number in the set. Therefore, 1 is also present in the set.
We need to find whether Median < 4?

(1) The range of the Set A is 4
i.e. max - min = 4
Thus, max = 4 + 1 = 5
Thus the only possible elements in set A are: [1 2 3 4 5]
Therefore in set A, Median < 4

Sufficient

(2) 5 is the greatest number in the Set A
Given, max = 5
We know min = 1
Thus the only possible elements in set A are: [1 2 3 4 5]
Therefore in set A, Median < 4

Sufficient

Answer D

Set A consists of 5 different integers. If 1 is the least number in the set, is the median of the set less than 4?
Given: 1<=x1<x2<x3<x4<x5 (all xs are integer & >=1)
x1=1
Median = x3 < 4?

(1) The range of the Set A is 4 --> sufficient: x5-x1 = 4 => x5 =5, x1=1, so only only possible values of the set A = {1, 2, 3, 4 & 5} i.e. median = x3 = 3 <4
(2) 5 is the greatest number in the Set A --> sufficient: x5 =5, x1=1, so only only possible values of the set A = {1, 2, 3, 4 & 5} i.e. median = x3 = 3 <4

So the answer is D

Set A consists of 5 different integers. If 1 is the least number in the set, is the median of the set less than 4?

5 DIFFERENT INTEGERS - so no repeating numbers in the set

1 is the least, so all other numbers are 2 or above,


(1) The range of the Set A is 4
Range is 4, so Highest-1 = 4, Highest = 5
Since all integers are different, the set has to be 1, 2, 3, 4, 5 in ascending order

3 is median, which is less than 4

(1) IS SUFFICIENT

(2) 5 is the greatest number in the Set A
5 is the greatest number, this is the same situation as (1)

So, set is 1, 2, 3, 4, 5 and median is 3 (less than 4)

(2) IS SUFFICIENT


ANSWER: D - Each is Sufficient

What we know right out of the box is that all five numbers in set \(A\) are different integers. The least number is \(1\). Is \(median < 4\) ?

ST1. The range \(= 4\).

So the largest number – the least number is = 4. Let the largest be \(x\). So \(x-1=4\) or \(x=5\). So set A will look as follows \(A\) {\(1, x, y, z, 5\)}. If all numbers are different integers and we have five numbers in total, then the numbers in between \(1\) and \(5\) must be \(2\), \(3\), and \(4\). Yes median \(3\) is less than \(4\).

Sufficient

ST2. The greatest number in \(A = 5\).

We have already figured out that if set \(A\) looks as {\(1, x, y, z, 5\)}, then considering that all number are different integers, the set has no choice but be {\(1, 2, 3, 4, 5\)}. Yes median \(3\) is less than \(4\).

Sufficient

Hence D

Known: Set A consists of 5 different integers and 1 is the least number in the set
--> Set A must comprise of five different positive integers that are greater than or equal to 1, e.g. {1,2,3,4,5}, {1,2,3,4,6}, {1,3,4,5,6},etc

Question: is the median of the set less than 4?

(1) The range of the Set A is 4
The maximum integer in Set A = 1 + 4 = 5 --> the only possible solution of set A is {1,2,3,4,5} and thus, the median of the set is 3, which is clearly less than 4.
SUFFICIENT

(2) 5 is the greatest number in the Set A
The maximum integer in Set A = 5 --> the only possible solution of set A is {1,2,3,4,5} and thus, the median of the set is 3, which is clearly less than 4.
SUFFICIENT


Answer is (D)

Set A consists of 5 different integers. If 1 is the least number in the set, is the median of the set less than 4?

(1) The range of the Set A is 4
(2) 5 is the greatest number in the Set A

Solution:

Given:
Set A ={1,a,b,c,d}.We nee to find whether median is less than 4 or not.
Since it a set of 5 different integers ,so median would be the moiddle value i.e "b" when the elements of the set are arranged either in the ascendin or decending order.
1 is the least value of set.

From statement 1:
Range=Highest Value of the element in the set -Lowest value of the element in set.
4=Highest Value of the element in the set-1
Highest Value of the element in set=5
Therefore elements of the set would be ={1,a,b,c,5}
Now it given in the question that all the element of the set are different integers and 1 being the lowest.Also we calculated the highest element being 5.So the values of a,b,c would be 2,3,4 respectivlely for sure.No other options can be posible.
Hence Set A={1,2,3,4,5}
Median=3 which is less than 4.Hence sufficient.


From Statement 2:
Highest value of the element in the set =5.

Least value of thr element in the set=1

Set A={1,A,B,C,D,5}
Now it given in the question that all the element of the set are different integers and 1 being the lowest.Also we are the highest element being 5.So the values of a,b,c would be 2,3,4 respectivlely for sure.No other options can be posible.

Hence Set A={1,2,3,4,5}
Median=3 which is less than 4.Hence sufficient.

Therefore. D IMO

Set A consists of 5 different integers.
If 1 is the least number in the set, is the median of the set less than 4?

STATEMENT (1) The range of the Set A is 4
there are 5 different integers
the least number in the set = 1

range = highest number - least number
4 = highest number - 1
highest number = 5
since all the numbers are integer
1,2,3,4,5 are the 5 different integers
median = 3 which is less than 4
yes this statement is SUFFICIENT

STATEMENT (2) 5 is the greatest number in the Set A
least number in the set = 1
highest number in the set= 5
so the numbers are 1,2,3,4,5---(since all are different integers and between 1 and 5 (1,5)inclusive)

median of the set =3 which is less than 4
yes this statement is SUFFICIENT

D is the answer

Set A consists of 5 different integers. If 1 is the least number in the set, is the median of the set less than 4?

(1) The range of the Set A is 4
This means difference between highest and lowest value of a data set is 4
---> least number is set 1
so, x-1=4 x=5 ---> Set A is: 1,2,3,4,5 - median is 3 ---> 3<4
Sufficient


(2) 5 is the greatest number in the Set A
and all numbers integers --->
Set A: 1,,2,3,4,5, median is 3 ---> 3<4
Sufficient

D is the answer.

Set A consists of 5 different integers. If 1 is the least number in the set, is the median of the set less than 4?

(1) The range of the Set A is 4
(2) 5 is the greatest number in the Set A

Solution:

Question Stem Analysis:

We can assume the 5 numbers to be a,b,c,d,e. in a median sequence that is in ascending order And we know that value of least number 1, i.e a = 1
We have to figure out the median, which is C is less than 4.

Statement one Alone
Range of the set is e - a = 4,We know that a is 1, hence e = 5. and since we know that the least number is 1 and the numbers in the set are different integers, we cannot assume any negative integers or fractions. We can straight away say that the set consists of 1,2,3,4,5 , 3 being the median is lower than 4.
Hence statement one alone is sufficient . Eliminate C & E

Statement two alone:
Since 5 is the greatest number, and 1 is the least number, we cannot assume any negative integers or fractions. We can straight away say that the set consists of 1,2,3,4,5 , 3 being the median is lower than 4.
Statement two is sufficient.

Hence the answer must be D

Hi Bunuel, Other Math experts, and all members,

I have a question related to this..

Would the answer change, if the word 'DIFFERENT integers' was not used?

If it said ONLY integers, can we assume that A SET ALWAYS HAS UNIQUE members??

From doing some google search, it seems that a set is not allowed to have duplicate elements, BUT, Is this true for GMAT questions?


Have you come across any questions questions where this fact would be relevant?

Thanks

Yes, technically a set is a collection of different items. Usually official questions use term LIST instead, which can have repeated elements in it. So, if the question used a list instead of a set, then the answer would have been E. For example, consider {1, 1, 1, 1, 5} and {1, 5, 5, 5, 5}.