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Math Expert V
Joined: 02 Sep 2009
Posts: 56266
If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 76% (02:25) correct 24% (02:47) wrong based on 232 sessions

### HideShow timer Statistics Tough and Tricky questions: Statistics.

If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?

(1) The range of set S is less than 9.
(2) The average of x and y is less than the average of set S.

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Senior Manager  Joined: 13 Jun 2013
Posts: 271
Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?  [#permalink]

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1
Bunuel wrote:

Tough and Tricky questions: Statistics.

If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?

(1) The range of set S is less than 9.
(2) The average of x and y is less than the average of set S.

s= {7, y, 12, 8, x, 9}

st.1

{7,8,9,x,y,12} range = 12-7 =5 which satisfy the condition in statement 1

if x and y are 10 and 11 then sum x+y will be more than 18

(x,y,7,8,9,12) , now let x=5 and y =6 thus range = 12-5 =7 which satisfy the condition in statement 1

and sum of x+y = 11 which is less than 18

hence statement 1 is clearly not sufficient

st. 2

((x+y)/2)< ((x+y+7+8+9+12)/6)

let x+y=z

z/2<(36+z)/6

z/2-z/6<6

3z-z<36

2z<36
z<18

thus x+y<18, i.e. sum is less than 18 hence sufficient
Manager  S
Joined: 22 Jan 2014
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Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?  [#permalink]

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Bunuel wrote:

Tough and Tricky questions: Statistics.

If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?

(1) The range of set S is less than 9.
(2) The average of x and y is less than the average of set S.

B.

1) Range < 9
let largest number in the set be 12 and smallest be 7 ; range = 5
S = {7,8,8,8,9,12} ; x+y = 8+8 = 16 < 18
S = {7,8,8,9,11,12} ; x+y = 8+11 = 19 > 18
so inconclusive.

2) (7+y+12+8+x+9)/6 > (x+y)/2
x+y < 18
sufficient.
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Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?  [#permalink]

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In order to prove that option B is the right answer we are multiplying the inequality by the LCM (6) without knowing if x+y is positive or negative.

Is there any reason for x+y to be assumed to be positive?
Math Expert V
Joined: 02 Sep 2009
Posts: 56266
Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?  [#permalink]

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pratikshetty123 wrote:
In order to prove that option B is the right answer we are multiplying the inequality by the LCM (6) without knowing if x+y is positive or negative.

Is there any reason for x+y to be assumed to be positive?

We are multiplying by 6, which is positive. We care about the sign of the value by which we are multiplying an inequality.
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Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?  [#permalink]

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Bunuel wrote:

Tough and Tricky questions: Statistics.

If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?

(1) The range of set S is less than 9.
(2) The average of x and y is less than the average of set S.

Statement 1. If x=4 and y=5 then answer is Yes. But if x=6 and y=14 then answer is No. Insufficient
Statement 2. We have (x+y)/2<(x+y+36)/6 Multiply both sides by 6 to get 3x+3Y<x+y+36 Hence x+y<18 Sufficient
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Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?  [#permalink]

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_________________ Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?   [#permalink] 22 Feb 2018, 07:29
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