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

Question

(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.

manpreetsingh86 · Answer

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

thefibonacci · Answer

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.

pratikshetty123 · Answer

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?

Bunuel · Answer

We are multiplying by 6, which is positive. We care about the sign of the value by which we are multiplying an inequality.

Konstantin1983 · Answer

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

MarmikUpadhyay · Answer

S = {7, y, 12, 8, x, 9}. Is x + y < 18? Statement 1: Range < 9 Case 1: Let x = y = 4 Range = 12 - 4 = 8 < 9 x + y = 8 < 18 Case 2: Let x = y = 15 Range = 15 - 7 = 8 < 9 x + y = 30 > 18 Statement 1 is Not Sufficient. Statement 2: \frac{x + y}{2} < \frac{7 + y + 12 + 8 + 9 + x}{6} => 3 * (x + y) < 36 + x + y => 2 * (x + y) < 36 => x + y < 18 Statement 2 is Sufficient. So, correct answer is option B .

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

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

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