If x - y 10, is x - y x + y ? (1) x = 8 (2) y = -20

Question

If x - y > 10, is x - y > x + y ? (1) x = 8 (2) y = -20 1.JPG

Bunuel · Accepted Answer

If x - y > 10, is x - y > x + y ?

Given: \(x-y>10\).

Question: is \(x-y>x+y\)?
Is \(2y<0\)?
Is \(y<0\)?

(1) \(x=8\). Plug into \(x - y > 10\):
\(8-y>10\);
\(y<-2\), hence \(y<0\). Sufficient.

(2) \(y=-20\), hence \(y<0\). Sufficient.

Answer: D.

jamifahad · Answer

To prove: x-y>x+y or x-y-x-y>0 or -2y>0 or y<0 ? Stmt1: x=8 x-y > 10 8-y>10 -2-y>0 2+y<0 y<-2 Hence y < 0. Sufficient. Stmt2: y=-20 Hence y <0. Sufficient. OA D.

dcummins · Answer

So we can do the arithmetic, but we can't divide?

Bunuel · Answer

Yes, we can add/subtract a number to both sides of an inequality but we cannot multiply/divide unless we know the sign.

750Barrier · Answer

perfect , no doubt ! but can u pl help me with the following approach? it happened to strike in exam.. lets say i rephrase the question to 'Is X+Y<10 ? ' since i know X-Y>10 . Now (i) sufficient but (ii) is not. For example - when I substitute y=-20 in x-y >10 , I get X>-10. and then I use this range in X+Y<10.. i get both Y and N. need urgent help in this. Thanks Bunuel

Bunuel · Answer

How did you re-phrased the question as "is x + y < 10?" ? That's not correct. x - y > 10 and y < 0 (actual re-phrased question) can be true even if x + y > 10 is not. For example, x = 100 and y = -1.

750Barrier · Answer

i did the following way. it's given X-Y> 10 and the question asked is -- is x - y > x + y ? then, i can say Is X+Y

Bunuel · Answer

So, we have that x - y > 10 and the question asks whether x + y < x - y ?

10 < x - y and x + y < x - y does not mean that x + y < 10 < x - y, we could also have that 10 < x + y < x - y.

bumpbot · Answer

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If x - y > 10, is x - y > x + y ? (1) x = 8 (2) y = -20

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