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The following set of six numbers is in order from least to greatest.

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Bunuel
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The following set of six numbers is in order from least to greatest. [#permalink] New post  02 Sep 2021, 01:30
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The following set of six numbers is in order from least to greatest.
{x − 3, 5, 7, 8, 11, 2x + y}
If the mean of the set is 8 and its range is 11, then what is the value of x − y ?

A. -4
B. 4
C. 6
D. 28
E. 48



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lalaland1234545
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Re: The following set of six numbers is in order from least to greatest. [#permalink] New post  02 Sep 2021, 01:44
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Kudos
{x − 3, 5, 7, 8, 11, 2x + y}
Range : x + y + 3 = 11

x + y = 8

Mean is 8 :

28 + 3x + y = 48
3x + y = 20
x = 6
y = 2

x - y = 4

OA : B

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sj296
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Re: The following set of six numbers is in order from least to greatest. [#permalink] New post  02 Sep 2021, 01:51
Numbers are: {x − 3, 5, 7, 8, 11, 2x + y}

Mean = \(\frac{(x-3)+5+7+8+11+(2x+y)}{6} = 48\)

=> 3x+y = 20

Range = 2x+y - x+3 = 11

=> x+y = 8

Two equations, two variables. Solve for x & y

=> x = 6; y = 2

x-y = 6-2 = 4

OA should be B
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v12345
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Re: The following set of six numbers is in order from least to greatest. [#permalink] New post  02 Sep 2021, 01:55
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Kudos
{x − 3, 5, 7, 8, 11, 2x + y}

Mean \(= \frac{x-3 + 5 + 7 + 8 + 11 + 2x+y}{6} = \frac{3x + y + 28}{6} = 8\)
3x + y = 48-28 = 20

Range = 2x+y - x + 3 = 11
x + y = 8

Solving the two equations, we get
x = 6 and y = 2
x-y = 4
Hence, OA is (B).
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Re: The following set of six numbers is in order from least to greatest. [#permalink] New post  02 Sep 2021, 03:08
1
Kudos
{x − 3, 5, 7, 8, 11, 2x + y}
The above set is in the ascending order
Given, mean = 8
Range = 11

Sum of all the terms = 3x+y+28 = 48
3x + y =20 (1)

Range = 2x + y - x + 3 = 11
x + y = 8 (2)
Putting 2 in equation 1
2x = 12
x = 6
y = 8-6=2

x - y= 4

IMO B
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mendax
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Re: The following set of six numbers is in order from least to greatest. [#permalink] New post  02 Sep 2021, 09:48
1
Kudos
The following set of six numbers is in order from least to greatest.
{x − 3, 5, 7, 8, 11, 2x + y}
If the mean of the set is 8 and its range is 11, then what is the value of x − y ?

Mean= \((x-3+5+7+8+11+2x+y)/6\)
=> \((28+3x+y)/6 = 8\)

=> 28+3x+y=48

=> 3x+y= 20 (Eq-1)

Range= Maximum-Minimum
2x+y-(x-3)=11
2x+y-x+3=11
x+y=8. (Eq-2)


Solving Eq-1 and Eq-2
x=6,y=2
Difference x-y=> 4
the correct option should be B
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manish1708
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Re: The following set of six numbers is in order from least to greatest. [#permalink] New post  02 Sep 2021, 20:27
1
Kudos
Answer: B

Mean = 8
=> x-3 + 5 + 7 + 8 + 11 + 2x + y = 8*6
=> 3x + y = 48 - 28 = 20

Range = 11
=> 2x + y - x + 3 = 11
=> x + y = 8

Solving two equations,
x = 6
y = 2

Hence, x - y = 6-2 = 4
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Re: The following set of six numbers is in order from least to greatest. [#permalink] New post  02 Sep 2021, 21:55
1
Kudos
IMO B

from given condition of mean, we can come up with 3x+y=20
and from range, we can come up with x+y=8

solving two equation we get x = 6 & y=2

Hence, x-y = 4
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CrackverbalGMAT
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Re: The following set of six numbers is in order from least to greatest. [#permalink] New post  03 Sep 2021, 02:01
1
Kudos
Top Contributor
Range is the difference b/w the highest and the lowest numbers.

Since the numbers are arranged in ascending order, x-3 is the smallest number and 2x + y is the largest number.

So range = 2x+y - (x-3)

=x + y -3 =11

Mean =8

=>28 + 3x + y = 48

=>3x + y =20

Solving the two equations
x = 6 & y = 2

=>x-y = 6-2= 4

(option b)

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Re: The following set of six numbers is in order from least to greatest. [#permalink]
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