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What is the sum of all numbers x for which the median of the numbers 4

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Bunuel
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What is the sum of all numbers x for which the median of the numbers 4 [#permalink] New post   15 May 2019, 03:54
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27% (02:34) correct 73% (02:28) wrong based on 51 sessions
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What is the sum of all numbers x for which the median of the numbers 4, 6, 8, 17, and x is equal to the mean of those five numbers?

A. -5
B. 0
C. 5
D. 15/4
E. 35/4
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A
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LeoN88
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What is the sum of all numbers x for which the median of the numbers 4 [#permalink] New post   15 May 2019, 04:18
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Bunuel wrote:
What is the sum of all numbers x for which the median of the numbers 4, 6, 8, 17, and x is equal to the mean of those five numbers?

A. -5
B. 0
C. 5
D. 15/4
E. 35/4


Possible list:- (Medians marked in red)
1. 4 6 8 17 x
2. 4 6 8 x 17

3. 4 6 x 8 17

4. 4 x 6 8 17
5. x 4 6 8 17


Mean in all the above 6 cases= (35+x)/5. Equating Mean=Median


Case A, let's see if 8 can be a median:-
8 = (35+x)/5
5=x (Not possible for case# 1 and 2)

Case B Next, let's see when x is median
x= (35+x)/5
x=(35/4)= 8.something (Not possible for case#3)

Case C Finally let's see if 6 can be median
6=(35+x)/5
-5=x (Possible for case#5)

So Sum of all possible values of x= -5.


<Waiting for OA>
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nick1816
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Re: What is the sum of all numbers x for which the median of the numbers 4 [#permalink] New post   15 May 2019, 04:56
When x<6
(35+x)/5 =6
x= -5

When 6<x<8
(35+x)/5 =x
x= 8.75( not in our range)

When x>8
(35+x)/5 =8
x= 5( again not in our range)

Only value of x possible is -5
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Re: What is the sum of all numbers x for which the median of the numbers 4 [#permalink] New post   15 May 2019, 21:30
Bunuel wrote:
What is the sum of all numbers x for which the median of the numbers 4, 6, 8, 17, and x is equal to the mean of those five numbers?

A. -5
B. 0
C. 5
D. 15/4
E. 35/4

mean= (sum of numbers)/5 = (35+x)/5
test no if x= -5 then Mean= 6 set = -5,4,6,8,17
median= 6

if x=0 then mean= 7 set = 0,4,6,8,17
median= 6 (not possible bcoz mean=median)
test rest of numbers but A will only fulfill the condition. So OA will be A
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Re: What is the sum of all numbers x for which the median of the numbers 4 [#permalink] New post   15 May 2019, 22:11
'0' or any other option is not the value of x. It's actually the sum of all possible values of x. You can't substitute it for x.

rahul12988 wrote:
Bunuel wrote:
What is the sum of all numbers x for which the median of the numbers 4, 6, 8, 17, and x is equal to the mean of those five numbers?

A. -5
B. 0
C. 5
D. 15/4
E. 35/4

mean= (sum of numbers)/5 = (35+x)/5
test no if x= -5 then Mean= 6 set = -5,4,6,8,17
median= 6

if x=0 then mean= 7 set = 0,4,6,8,17
median= 6 (not possible bcoz mean=median)
test rest of numbers but A will only fulfill the condition. So OA will be A
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KarishmaB
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Re: What is the sum of all numbers x for which the median of the numbers 4 [#permalink] New post   15 May 2019, 22:43
Expert Reply
Bunuel wrote:
What is the sum of all numbers x for which the median of the numbers 4, 6, 8, 17, and x is equal to the mean of those five numbers?

A. -5
B. 0
C. 5
D. 15/4
E. 35/4


The median of 4, 6, 8, 17 and x will be 6 or 8 or x (if x is between 6 and 8)

Assuming median is 6,
6 = (4 + 6 + 8 + 17 + x)/5
x = -5

Assuming median is 8,
8 = (4 + 6 + 8 + 17 + x)/5
x = 5
But x cannot be 5 because median must be 6 in the case.

Assuming median is x (between 6 and 8),
x = (4 + 6 + 8 + 17 + x)/5
x = 35/4
x is not between 6 and 8.

So x can be only -5.
Answer (A)
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georgethomps
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What is the sum of all numbers x for which the median of the numbers 4 [#permalink] New post   16 May 2019, 10:08
I found this question to be poorly written. The question asks "What is the sum of all numbers x". The answer is not the sum of all 5 numbers. I also was very confused because I initially thought "x" was supposed to represent the sum of the 5 numbers.
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Re: What is the sum of all numbers x for which the median of the numbers 4 [#permalink] New post   20 May 2019, 18:58
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Bunuel wrote:
What is the sum of all numbers x for which the median of the numbers 4, 6, 8, 17, and x is equal to the mean of those five numbers?

A. -5
B. 0
C. 5
D. 15/4
E. 35/4


We can have 3 scenarios: 1) If x ≤ 6, then the median is 6; 2) if 6 < x < 8, then the median is x; and 3) if x ≥ 8, then the median is 8.

Scenario 1:

If the median is 6, we have:

(35 + x)/5 = 6

35 + x = 30

x = -5

Since -5 ≤ 6, x can be -5.

Scenario 2:

If the median is x, we have:

(35 + x)/5 = x

35 + x = 5x

35 = 4x

x = 35/4

Since 35/4 is not between 6 and 8, x can’t be 35/4.

Scenario 3:

If the median is 8, we have:

(35 + x)/5 = 8

35 + x = 40

x = 5

Since 5 is not greater than or equal to 8, x can’t be 5.

So x can only be -5.

Answer: A
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Re: What is the sum of all numbers x for which the median of the numbers 4 [#permalink]
20 May 2019, 18:58
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