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If -2x > 3y, is x negative? (1) y > 0 (2) 2x + 5y - 20 = 0

Hi, -2x > 3y... (a)If y<0, x can be both +ive and -ive.. (b)if y>0, x will have to be +ive as 3y is positive and -2x , to be positive, has to have x as -ive..

now lets see the choices..

(1) y > 0 If y>0, x is -ive as proved in (b) above... suff

(2) 2x + 5y - 20 = 0.. this can be written as 2x+3y + 2y -20=0.. now 2x+3y<0, so 2y>20... or y is +ive and therefore x is -ive.... suff

Statement 1: y > 0 In other words, y is POSITIVE This means that 3y is POSITIVE It is given that -2x > 3y Since 3y is POSITIVE, we can write: -2x > SOME POSITIVE # If -2x is greater than SOME POSITIVE #, we know that -2x is POSITIVE If -2x is POSITIVE, then x must be negative Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 2x + 5y - 20 = 0 IMPORTANT: It is given that -2x > 3y So, let's take 2x + 5y - 20 = 0 and rewrite it as 5y - 20 = -2x [I have isolated -2x, just like we have in the GIVEN information] Now, we'll take -2x > 3y, and replace -2x with 5y - 20 to get: 5y - 20 > 3y Subtract 3y from both sides: 2y - 20 > 0 Add 20 to both sides: 2y > 20 Solve: y > 10 This means that y is POSITIVE We already saw in statement 1, that when y is positive, x must be negative Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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