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

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

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24 Jul 2019, 08:00
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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

 This question was provided by Math Revolution for the Game of Timers Competition

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Re: Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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24 Jul 2019, 08:08
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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

Sol- 1) range= max-min
4= max-1
max=5
median =3 <4 (suff)

2)least no= 1
greatest= 5
1,2,3,4,5 (contains different int)
median <4 (suff)
(D)
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Re: Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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24 Jul 2019, 08:09
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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?

Let Set A = {1,x,y,z,w}

(1) The range of the Set A is 4
Range = Max - min = 4 => Max = 5=w
Only possible set A= {1,2,3,4,5} since all elements are different integers
Median = 3 <4
SUFFICIENT

(2) 5 is the greatest number in the Set A
Only possible set A={1,2,3,4,5} since all elements are different integers
Median = 3<4
SUFFICIENT

IMO D
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Re: Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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24 Jul 2019, 08:10
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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
Range = 4
—> Maximum value = 5
—> Possible set = {1, 2, 3, 4, 5} ONLY
—> Median = 3 (<4)

Sufficient

(2) 5 is the greatest number in the Set A
—> Possible Set = {1, 2, 3, 4, 5} ONLY
—> Median = 3 (<4)

Sufficient

IMO Option D

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

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Updated on: 24 Jul 2019, 09:31
1
Quote:
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

given: set has 5 DIFFERENT integers, least is 1 = set {1bcde}
rule: range = greatest-least;
rule: median is the middle term in an ordered set or the average of 2 middle terms if the set has an even number of integers;

(1) The range of the Set A is 4: range=4… greatest-1=4, greatest=5,… set {1bcd5} since {bcd} must be different then, they must be {2,3,4}, sufficient.
(2) 5 is the greatest number in the Set A: set {1bcd5} since {bcd} must be different then, they must be {2,3,4}, sufficient.

Originally posted by exc4libur on 24 Jul 2019, 08:12.
Last edited by exc4libur on 24 Jul 2019, 09:31, edited 1 time in total.
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Re: Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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24 Jul 2019, 08:13
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-------- set could be 1 2 3 4 5 , 1 2 4 5 6 ... we will get a Yes and a No.... Not sufficient.
(2) 5 is the greatest number in the Set A--------- The set has to be 1 2 3 4 5 ..... we will get a definite answer.

B has to be the answer.
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Re: Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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24 Jul 2019, 08:16
1
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

In this question, given 5 different integers. 1 is the least number, so all other integers are positive.

1 2 3 4 10 -- YES
1 10 15 18 24 -- NO

1) Given range is 5, so highest integer is 5. So
1 _ _ _ 5
2 3 4 must be the rest, since its all different. 2 2 2 not possible
and only three integers between 1 and 5.
2) Highest integer as 5 --> implies same meaning as 1)

So IMO D
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Re: Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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24 Jul 2019, 08:17
1
(1) The range of the Set A is 4
range is 4 .1 is minimum
numbers can be 1 ,2,3,4,5.
sufficient

(2) 5 is the greatest number in the Set A
5 is the greatest
1 is least all integers different.
1,2,3,4,5
sufficient
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Re: Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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24 Jul 2019, 08:18
1
IMO D

We know that the 5 integers are unique and the least number is 1

Statement 1 -> Range is 4, and hence, the greatest number is 5. The other 3 numbers will be 2, 3 and 4. Thus, the median is 3 and < 4 ---> Sufficient
Statement 2 -> The greatest number is 5. The same solution as statement 1 ---> Sufficient
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Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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Updated on: 24 Jul 2019, 08:37
1
Quote:
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

Least no is 1
1. Range is 4. So max no is 1+4=5

As all number are different integers, we know median is 3<4
Sufficient

2. max no is 5

As all number are different integers, we know median is 3<4
Sufficient
Hence D
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Originally posted by kitipriyanka on 24 Jul 2019, 08:19.
Last edited by kitipriyanka on 24 Jul 2019, 08:37, edited 1 time in total.
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Re: Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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24 Jul 2019, 08:20
1
D

There are 5 different integers in a set, with 1 being least. We need to check if median is less than 4.

(1) The range of the Set A is 4
Range is 4 and smallest no is 1, so greatest has to be 5. Between 1 and 5, we need 3 more places to fill, those integers have to be 2, 3 and 4 since all integers are different. Therefore, median is 3. Sufficient

(2) 5 is the greatest number in the Set A
Least is 1 and greatest is 5. Again, three other integers have to be 2, 3 and 4. So, median is 3. Sufficient.
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Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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Updated on: 24 Jul 2019, 20:31
1
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

Originally posted by Sayon on 24 Jul 2019, 08:20.
Last edited by Sayon on 24 Jul 2019, 20:31, edited 1 time in total.
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Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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Updated on: 24 Jul 2019, 18:24
1
From the statement we have that the set contain different integers and the least integer is 1, so set A must consist on the following numbers:

1 X Y Z T

From (1) The range of the Set A is 4, we have that:

Since all numbers are different integers T-1 =4, so T =5, and the only combination, since all are different numbers, must be:

1 2 3 4 5

So, sufficient.

From (2) 5 is the greatest number in the Set A, we have that:

T = 5, and since all numbers are different, the only possible combination is:

1 2 3 4 5

So, sufficient.

Originally posted by Mizar18 on 24 Jul 2019, 08:26.
Last edited by Mizar18 on 24 Jul 2019, 18:24, edited 1 time in total.
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Re: Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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24 Jul 2019, 08:28
1
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?

a = {1, a, b, c, d}
is b<4?

(1) The range of the Set A is 4

d-1=4
d=5
Hence, the maximum value that c can take is 4.
And hence, b has to be less than 3.
Sufficient.

(2) 5 is the greatest number in the Set A
d=5 is given.
Same info that statement 1 gives.
Sufficient.

Ans should be (D)
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Re: Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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24 Jul 2019, 08:29
1
Things to note:
1) Set A has 5 different Integers (positive or negative)
2) Least number in the set is 1,therefore all the numbers must be positive.

Rephrasing equation 1) Set A has 5 different positve Integers

To Find: Median<4?

1) The range of the Set A is 4

The range is the difference between the highest and lowest values in the set. --- (3)
Let a) Highest value in Set A is H.V
b) Lowest Value in Set A is L.V

Range=H.V - L.V (according to 3)
4 = H.V- 1 ( L.V =1 (acc. to 2)
Upon solving, H.V = 5 --- (4)

Now, Set A= (1,2,3,4,5) ---- because highest value is 5, lowest value is 1, all the integers must be different and must be positive. So, we can have the definite answer for the median. Sufficient statement

(2) 5 is the greatest number in the Set A

It is saying the same thing as in equation 4. Therefore, sufficient.

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Re: Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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24 Jul 2019, 08:32
1
Quote:
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?

This is Data Sufficiency (DS) question, and we have a set A with 5 distinct numbers. The smallest number is 1. It means that all other numbers are positive and greater than 1.
We need to identify if the median i.e. the third smallest or third greatest number in this set is less than 4.
Median < 4?

Let us analyze statements 1 by 1 and check if it can be identified:
Statement 1:
(1) The range of the Set A is 4

If range of set A is 4, it means that $$the$$ $$greatest$$ $$value - lowest$$ $$value = 4$$
In this case, as all numbers in the set are different, the greatest value is $$1+4=5$$ and the third value is $$1+2=3$$ which is less than 4
$$median<4$$
Statement 1 alone is sufficient.
Sufficient.

(2) 5 is the greatest number in the Set A
If number 5 is the greatest number in the set A, we can continue with the solution as per statement 1.
Statement 2 is Sufficient.

As both statements are sufficient on their own, the answer is D.

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Re: Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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24 Jul 2019, 08:36
1
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

given
A ; ( 1,b,c,d,e)
find c<4
#1The range of the Set A is 4
so e or say max value is 5
since given all values are different so c= 3 <4
sufficient
#2
5 is the greatest number in the Set A
same info as #1
sufficeint
IMO D
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Re: Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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24 Jul 2019, 08:37
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Lets us say 5 different integers are 1,a,b,c,d in ascending order.
To determine: is b<4?

(1) d=5, so the integers are 1,2,3,4,5. Sufficient.

(2) again d=5. Sufficient.

D is correct.
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Re: Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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24 Jul 2019, 08:38
1
Both statements tell us the same information.

(1) The range of the Set A is 4
If the range is 4 then the highest number is 5.
Since all integers are different we have the only possible solution
These integers are 1, 2, 3, 4, and 5.
And we can answer the question.

Sufficient.

(2) 5 is the greatest number in the Set A
If 5 is the greatest number, 1 is the least number and all 5 integers are different we have only one solution
These integers are 1, 2, 3, 4, and 5.
And we can answer the question.

Sufficient.

IMO D
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Re: Set A consists of 5 different integers. If 1 is the least number in th  [#permalink]

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24 Jul 2019, 08:38
1
Let the numbers be x1,x2,x3,x4 and x5. Let x1<x2<x3<x4<x5 and x1=1. Question is is x3<4.

1) Range =4; implies x2=2,x3=3,x4=4 and x5=5; Hence x3=3 <4. Sufficient
2) x5=5; implies x2=2,x3=3 and x4=4, x3<4. Sufficient

Re: Set A consists of 5 different integers. If 1 is the least number in th   [#permalink] 24 Jul 2019, 08:38

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