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# If the median and the average (arithmetic mean) of 4 different numbers

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Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1322
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If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

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21 Feb 2017, 16:48
2
00:00

Difficulty:

85% (hard)

Question Stats:

53% (02:20) correct 47% (02:16) wrong based on 101 sessions

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If the median and the average (arithmetic mean) of 4 different numbers are both 50, what is the smallest number?

1) The range of the 4 numbers is 50

2) The sum of the smallest and the largest of the 4 number is 100

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Re: If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

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03 Mar 2017, 03:11
can someone explain how A can be the answer ,although i am pretty sure that D can not be the answer but still unable to understand the OA

thanks
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Re: If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

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03 Mar 2017, 19:08
1
ziyuen wrote:
If the median and the average (arithmetic mean) of 4 different numbers are both 50, what is the smallest number?

1) The range of the 4 numbers is 50

2) The sum of the smallest and the largest of the 4 number is 100

Here's how I solved it -
1) Even numbered set + Average AND Median 50 -> Numbers Equidistant from 50 in either direction (50-y, 50-x, 50+x, 50+y). They're like mirror images around the number 50.

1) -> 50+y-50+y = 50. Sufficient
2) We already know sum of smallest and largest is 100! Actually, sum of 2nd largest and 2nd smallest is also 100! That's the beauty of this series.

Therefore, A.
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Re: If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

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04 Mar 2017, 03:59
1
Prompt analysis
a,b,c,d are the numbers such that a<b<c<d and (a+b+c+d)/4 = 50 and (b+c)/2 = 50 therefore a+d = 100

Super set
the answer will be a positive real number

translation
In order to find the answer, we need
1# exact value of all a
2# another equation in a and d
3# any specific property of a the restrict the valuye

statement analysis
St 1: range is 100. or d-a =100. therefore d =100 and a =0. ANSWER
St 2: a+d =100. that is already inferred from the question statement. INSUFFICIENT

Option A
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Re: If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

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04 Mar 2017, 21:08
thank you byjusclasses
i was missing that zero (0), well you made it clear now thanks
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Re: If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

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04 Mar 2017, 21:41
If the median and the average (arithmetic mean) of 4 different numbers are both 50, what is the smallest number?

1) The range of the 4 numbers is 50

2) The sum of the smallest and the largest of the 4 number is 100

Let the number be a,b,c and d ( increasing order )
as the Question
median = mean
b+c / 2 = 50
b+c = 100

mean = 50 = a+b+c+d /4
therefore a+b+c+d = 200
hence a+d = 100 ( as b+c = 100 )

(1) d-a = 50
and we know that a+d = 100
hence sufficient as we can calculate a from the two statement .

(2) no new information a+d =100 . Not sufficient

Hence the ans is A

Regards,

Press Kudos , if it helps .
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Posts: 4485
Re: If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

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05 Mar 2017, 11:24
1
ByjusClasses wrote:
Prompt analysis
a,b,c,d are the numbers such that a<b<c<d and (a+b+c+d)/4 = 50 and (b+c)/2 = 50 therefore a+d = 100

Super set
the answer will be a positive real number

translation
In order to find the answer, we need
1# exact value of all a
2# another equation in a and d
3# any specific property of a the restrict the valuye

statement analysis
St 1: range is 100. or d-a =100. therefore d =100 and a =0. ANSWER
St 2: a+d =100. that is already inferred from the question statement. INSUFFICIENT

Option A

coolnuts wrote:
The range is 50. So as per the Q S1 should be d-a=50 and not 100 as stated by you.

Dear ByjusClasses,

My colleague, a good solution. I simply want to point out, as coolnuts pointed out, that the range is 50. Of course, this doesn't change the answer to the DS question, but it would if similar information were in a PS question.

In fact, d - a = 50 and a + d = 100, so d = 75 and a = 25.

Also, coolnuts, the "report a problem" feature is really to indicate, for example, that a problem has a typo or has been miscopied from its source. Reporting a problem requires an expert to address it. If you see a problem in what another user has written, respond and tell that user yourself. Initiative and responsibility are important qualities when you are a manager, so it's good to practice them now.

Does all this make sense?
Mike
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Re: If the median and the average (arithmetic mean) of 4 different numbers  [#permalink]

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17 Apr 2018, 09:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If the median and the average (arithmetic mean) of 4 different numbers &nbs [#permalink] 17 Apr 2018, 09:53
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