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Re: If x - y > 10, is x - y > x + y ? (1) x = 8 (2) y = -20 [#permalink]
Bunuel wrote:
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 --> \(8-y>10\) --> \(y<-2\), hence \(y<0\). Sufficient.
(2) y = -20, hence \(y<0\). Sufficient.

Answer: D.


So we can do the arithmetic, but we can't divide?
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Re: If x - y > 10, is x - y > x + y ? (1) x = 8 (2) y = -20 [#permalink]
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dcummins wrote:
Bunuel wrote:
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 --> \(8-y>10\) --> \(y<-2\), hence \(y<0\). Sufficient.
(2) y = -20, hence \(y<0\). Sufficient.

Answer: D.


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


Yes, we can add/subtract a number to both sides of an inequality but we cannot multiply/divide unless we know the sign.
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Re: If x - y > 10, is x - y > x + y ? (1) x = 8 (2) y = -20 [#permalink]
Bunuel wrote:
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.


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
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Re: If x - y > 10, is x - y > x + y ? (1) x = 8 (2) y = -20 [#permalink]
Expert Reply
750Barrier wrote:
Bunuel wrote:
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.


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


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.
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Re: If x - y > 10, is x - y > x + y ? (1) x = 8 (2) y = -20 [#permalink]
Bunuel wrote:
750Barrier wrote:
Bunuel wrote:
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.


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


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.


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<X-Y? since i know X-Y is greater than 10 so, i can say Is X+Y<10? <- rephrased version/ new version of question.

Thank you for taking up my doubt.


aaaaaahh, i got it where my approach was wrong.. Thank you bunuel
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Re: If x - y > 10, is x - y > x + y ? (1) x = 8 (2) y = -20 [#permalink]
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750Barrier wrote:
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<X-Y? since i know X-Y is greater than 10 so, i can say Is X+Y<10? <- rephrased version/ new version of question.

Thank you for taking up my doubt.


aaaaaahh, i got it where my approach was wrong.. Thank you bunuel


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.
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Re: If x - y > 10, is x - y > x + y ? (1) x = 8 (2) y = -20 [#permalink]
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Re: If x - y > 10, is x - y > x + y ? (1) x = 8 (2) y = -20 [#permalink]
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