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A certain list consists of 3 different numbers. Does the median of the

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Re: A certain list consists of 3 different numbers. Does the median of the [#permalink] A certain list consists of 3 different numbers. Does the median of the   02 Jul 2021, 01:45
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karovd wrote:
A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median.
(2) The sum of the 3 numbers is equal to 3 times one of the numbers.


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Re: A certain list consists of 3 different numbers. Does the median of the [#permalink] A certain list consists of 3 different numbers. Does the median of the   22 Jul 2021, 04:23
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Re: A certain list consists of 3 different numbers. Does the median of the [#permalink] A certain list consists of 3 different numbers. Does the median of the   09 Nov 2021, 01:04
Bunuel wrote:

A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

Say the three numbers are x, y, and x, where x < y < z. The median would be y and the average would be (x + y + z)/3. So, the question asks whether y = (x + y + z)/3, or whether 2y = x + z.

(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median --> the range is the difference between the largest and the smallest numbers of the set, so in our case z - x. We are given that z - x = 2(z - y) --> 2y = x + z. Sufficient.

(2) The sum of the 3 numbers is equal to 3 times one of the numbers --> the sum cannot be 3 times smallest numbers or 3 times largest number, thus x + y + z = 3y --> x + z = 2y. Sufficient.

Answer: D.

Hope it's clear.


Hi Bunuel !

Thanks a lot for the explanation, it's concise and to the point - and these help a lot!

Could I ask one thing, though? In the second statement, you mention that the sum cannot be three times the smallest or largest number.
Why not? Is there a rule for series/sets that forbids this, or is this some logical deduction?

All the best,

Gil
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Re: A certain list consists of 3 different numbers. Does the median of the [#permalink] A certain list consists of 3 different numbers. Does the median of the   09 Nov 2021, 01:09
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BeepBoop wrote:
Bunuel wrote:

A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

Say the three numbers are x, y, and x, where x < y < z. The median would be y and the average would be (x + y + z)/3. So, the question asks whether y = (x + y + z)/3, or whether 2y = x + z.

(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median --> the range is the difference between the largest and the smallest numbers of the set, so in our case z - x. We are given that z - x = 2(z - y) --> 2y = x + z. Sufficient.

(2) The sum of the 3 numbers is equal to 3 times one of the numbers --> the sum cannot be 3 times smallest numbers or 3 times largest number, thus x + y + z = 3y --> x + z = 2y. Sufficient.

Answer: D.

Hope it's clear.


Hi Bunuel !

Thanks a lot for the explanation, it's concise and to the point - and these help a lot!

Could I ask one thing, though? In the second statement, you mention that the sum cannot be three times the smallest or largest number.
Why not? Is there a rule for series/sets that forbids this, or is this some logical deduction?

All the best,

Gil


We have that x < y < z.

The sum = x + y + z.

Obviously 3x < x + y + z < 3z because x < y < z (x + x + < x + y + z < z + z + z).

Does this make sense?
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Re: A certain list consists of 3 different numbers. Does the median of the [#permalink] A certain list consists of 3 different numbers. Does the median of the   09 Nov 2021, 01:14
Bunuel wrote:
BeepBoop wrote:
Bunuel wrote:

A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

Say the three numbers are x, y, and x, where x < y < z. The median would be y and the average would be (x + y + z)/3. So, the question asks whether y = (x + y + z)/3, or whether 2y = x + z.

(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median --> the range is the difference between the largest and the smallest numbers of the set, so in our case z - x. We are given that z - x = 2(z - y) --> 2y = x + z. Sufficient.

(2) The sum of the 3 numbers is equal to 3 times one of the numbers --> the sum cannot be 3 times smallest numbers or 3 times largest number, thus x + y + z = 3y --> x + z = 2y. Sufficient.

Answer: D.

Hope it's clear.


Hi Bunuel !

Thanks a lot for the explanation, it's concise and to the point - and these help a lot!

Could I ask one thing, though? In the second statement, you mention that the sum cannot be three times the smallest or largest number.
Why not? Is there a rule for series/sets that forbids this, or is this some logical deduction?

All the best,

Gil


We have that x < y < z.

The sum = x + y + z.

Obviously 3x < x + y + z < 3z because x < y < z (x + x + < x + y + z < z + z + z).

Does this make sense?


Oh wow when you put it like that it does. Thanks a lot!
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Re: A certain list consists of 3 different numbers. Does the median of the [#permalink] A certain list consists of 3 different numbers. Does the median of the   27 Dec 2022, 12:39
karovd wrote:
A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median.
(2) The sum of the 3 numbers is equal to 3 times one of the numbers.


Hi BrentGMATPrepNow, question asked Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers? So it means are these numbers evenly spaced set?
Does this mean we should only assing even numbers here e.g 8 ,10 ,12 if number testing? Thought assign 1,2,3 work too but is this still correct though? Thanks Brent
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Re: A certain list consists of 3 different numbers. Does the median of the [#permalink] A certain list consists of 3 different numbers. Does the median of the   28 Dec 2022, 08:32
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Kimberly77 wrote:
karovd wrote:
A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median.
(2) The sum of the 3 numbers is equal to 3 times one of the numbers.


Hi BrentGMATPrepNow, question asked Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers? So it means are these numbers evenly spaced set?
Does this mean we should only assing even numbers here e.g 8 ,10 ,12 if number testing? Thought assign 1,2,3 work too but is this still correct though? Thanks Brent


Since we know a list consists of three different numbers, then we can reward the target question as "Are the three numbers equally spaced?"
Don't forget that, when testing numbers for each statement, the values must satisfy the information in each statement.
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Re: A certain list consists of 3 different numbers. Does the median of the [#permalink] A certain list consists of 3 different numbers. Does the median of the   01 Jan 2023, 01:53
BrentGMATPrepNow wrote:
Kimberly77 wrote:
karovd wrote:
A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median.
(2) The sum of the 3 numbers is equal to 3 times one of the numbers.


Hi BrentGMATPrepNow, question asked Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers? So it means are these numbers evenly spaced set?
Does this mean we should only assing even numbers here e.g 8 ,10 ,12 if number testing? Thought assign 1,2,3 work too but is this still correct though? Thanks Brent


Since we know a list consists of three different numbers, then we can reward the target question as "Are the three numbers equally spaced?"
Don't forget that, when testing numbers for each statement, the values must satisfy the information in each statement.


Noted thanks BrentGMATPrepNow :thumbsup: :please:
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Re: A certain list consists of 3 different numbers. Does the median of the [#permalink] A certain list consists of 3 different numbers. Does the median of the   16 Mar 2023, 21:09
Bunuel wrote:
HBSdetermined wrote:
Bunuel plz help in the second statement how is that sufficient most of the explanations above are cryptic!


A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

Say the three numbers are x, y, and x, where x < y < z. The median would be y and the average would be (x + y + z)/3. So, the question asks whether y = (x + y + z)/3, or whether 2y = x + z.

(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median --> the range is the difference between the largest and the smallest numbers of the set, so in our case z - x. We are given that z - x = 2(z - y) --> 2y = x + z. Sufficient.

(2) The sum of the 3 numbers is equal to 3 times one of the numbers --> the sum cannot be 3 times smallest numbers or 3 times largest number, thus x + y + z = 3y --> x + z = 2y. Sufficient.

Answer: D.

Hope it's clear.



Could you please go through my reasoning for the 2nd statement and let me know if it is correct?
Let the 3 nos be a,b,c where a<b<c
Say 3 times the mean = 3 times smallest no. Thus,
a+b+c=3a
Thus b+c=2a
This cannot be possible until b and c are less than or equal to a. But the qs states that these 3 numbers are distinct. Hence not possible. Same would be the case if the sum is 3 times the greatest number. a+b=2c... not possible becasue of the above mentioned reason
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Re: A certain list consists of 3 different numbers. Does the median of the [#permalink] A certain list consists of 3 different numbers. Does the median of the   16 Mar 2023, 21:18
BeepBoop wrote:
Bunuel wrote:

A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

Say the three numbers are x, y, and x, where x < y < z. The median would be y and the average would be (x + y + z)/3. So, the question asks whether y = (x + y + z)/3, or whether 2y = x + z.

(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median --> the range is the difference between the largest and the smallest numbers of the set, so in our case z - x. We are given that z - x = 2(z - y) --> 2y = x + z. Sufficient.

(2) The sum of the 3 numbers is equal to 3 times one of the numbers --> the sum cannot be 3 times smallest numbers or 3 times largest number, thus x + y + z = 3y --> x + z = 2y. Sufficient.

Answer: D.

Hope it's clear.


Hi Bunuel !

Thanks a lot for the explanation, it's concise and to the point - and these help a lot!

Could I ask one thing, though? In the second statement, you mention that the sum cannot be three times the smallest or largest number.
Why not? Is there a rule for series/sets that forbids this, or is this some logical deduction?

All the best,

Gil


We have that x < y < z.

The sum = x + y + z.

Obviously 3x < x + y + z < 3z because x < y < z (x + x + < x + y + z < z + z + z).

Does this make sense?[/quote]

Oh wow when you put it like that it does. Thanks a lot![/quote]

Hi, I tried some derivation- may be helpful thus posting it here:
For the 2nd statement, I tried solving and deriving- 3nos: a,b,c where a<b<c
Say 3 times the mean = 3 times smallest no. Thus
a+b+c=3a
Thus b+c=2a
This cannot be possible until b and c are less than or equal to a. But the qs states that these 3 numbers are distinct. Hence not possible. Same would be the case if the sum is 3 times the greatest number. a+b=2c... not possible because of the above mentioned reason
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