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If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?
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14 Oct 2014, 05:11
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74% (02:24) correct 26% (02:50) wrong based on 221 sessions
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Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?
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14 Oct 2014, 07:38
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 = 127 =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 = 125 =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/2z/6<6 3zz<36 2z<36 z<18 thus x+y<18, i.e. sum is less than 18 hence sufficient



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Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?
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18 Oct 2014, 00:23
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?
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14 Apr 2016, 01:21
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?



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Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?
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14 Apr 2016, 10:25



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Re: If set S = {7, y, 12, 8, x, 9}, is x + y less than 18?
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16 Apr 2016, 07:00
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?
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22 Feb 2018, 06:29
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