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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 15 May 2019, 03:54
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

35% (02:31) correct 65% (02:25) wrong based on 78 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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What is the sum of all numbers x for which the median of the numbers 4 15 May 2019, 04:18
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Bunuel
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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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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What is the sum of all numbers x for which the median of the numbers 4 15 May 2019, 04:56
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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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What is the sum of all numbers x for which the median of the numbers 4 15 May 2019, 21:30
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Bunuel
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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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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What is the sum of all numbers x for which the median of the numbers 4 15 May 2019, 22:11
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'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
Bunuel
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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What is the sum of all numbers x for which the median of the numbers 4 15 May 2019, 22:43
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Bunuel
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
Show more

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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What is the sum of all numbers x for which the median of the numbers 4 16 May 2019, 10:08
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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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What is the sum of all numbers x for which the median of the numbers 4 20 May 2019, 18:58
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Bunuel
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
Show more

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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