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What is the sum of all numbers x for which the median of the numbers 4
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15 May 2019, 03:54
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14% (01:49) correct 86% (02:44) wrong based on 22 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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What is the sum of all numbers x for which the median of the numbers 4
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15 May 2019, 04:18
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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Re: What is the sum of all numbers x for which the median of the numbers 4
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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
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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
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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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Re: What is the sum of all numbers x for which the median of the numbers 4
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15 May 2019, 22:43
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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What is the sum of all numbers x for which the median of the numbers 4
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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
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20 May 2019, 18:58
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
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