Set B has 7 members and x and y are distinct positive integers. If x

Question

Set B = {x, x, y, 9, 10, 16, 16}

Set B has 7 members and x and y are distinct positive integers. If x is the mode of Set B and the mean of Set B is 12, which of the following is a valid value of x that would cause the standard deviation of the set to be greatest?

A. 9
B. 10
C. 12
D. 16
E. 18

rohit8865 · Answer

clearly its D

if x=18 then y =negative value ,which is not possible as y is positive 
thus if x =16 the mode is 16 and then there will be 4 extreme points from mean 12,making set more disperse

Ans D

mohshu · Answer

since mean is 12,, so total sum will be 7 * 12 = 84

9+10+16+16 = 51..

hence x, x and y should add-up to 84-51 = 33..

start from the largest option 18,, if x = 18, the y will be -ve,,, not possible

x= 16 fits the criteria given in the question..

ans D

GMATinsight · Answer

Mode = x  but since 16 has already appeared twice so x must be  equal to  an existing term of the set other than 16 or 16 itself 
Mean = 12 
=> 2x+y+51 = 12*7
=> 2x+y = 84-51 = 33

CONCEPT: STANDARD DEVIATION is MAXIMUM when new term is FARTHEST from mean

so the value of x farthest from mean which can set mode 16 must be 16 itself

Answer: Option D

RMD007 · Answer

From the given information we can deduce that 2x+ y = 33

If the value of x is 16, y=1 (the least positive integer), gives us maximum range = 15.

BrentGMATPrepNow · Answer

The mean of Set B is 12  
We can write: (x + x + y + 9 + 10 + 16 + 16)/7 = 12
So: x + x + y + 9 + 10 + 16 + 16 = 84
Simplify: 2x + y + 51 = 84
So,  2x + y = 33

x is the mode of Set B  
If x = 9, 10, or 16, the mode of Set B will equal x
So, x can have 3 possible values.

Let's test all 3 cases: 
case i: x = 9
If  2x + y = 33 , and x = 9, then y = 15
So, our two values are: x = 9 & y = 15

case ii: x = 10
If  2x + y = 33 , and x = 10, then y = 13
So, our two values are: x = 10 & y = 13

case iii: x = 16
If  2x + y = 33 , and x = 16, then y = 1
So, our two values are: x = 16 & y = 1

Which of the following is a valid value of x that would cause the standard deviation of the set to be greatest?  
To maximize the Standard Deviation, we must find the pair of values that are farthest from the mean (mean = 12)
The pair of values x = 16 and y = 1 are the farthest from the mean.

So, x = 16 will maximize the Standard Deviation
Answer: D

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harshbirsingh · Answer

Hi  BrentGMATPrepNow ,

Thank you for the solution. I had one conceptual query - I believe X need not be equal to only 9, 10 or 16. If x was 18, X could still be the mode (additionally, we would have another mode as 16.) So can we rule out 18 initially itself, without testing it?

BrentGMATPrepNow · Answer

The question tells us that there is only one mode:   "x is THE mode of Set B"  
If x = 18, then there are two modes: 16 and 18

If the question had been worded to say "x is A mode of Set B," then it would be possible for X to equal 18.

Cheers,
Brent

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Set B has 7 members and x and y are distinct positive integers. If x

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Set B has 7 members and x and y are distinct positive integers. If x

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