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This problem has been recently posted by halle i believe, I [#permalink]
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26 Jun 2004, 18:33
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This problem has been recently posted by halle i believe, I couldn't trace the orginal post, so I'm reposting it in effort to clarify an issue:
[x]>=[xy]+[y], is y>x?
1. x>0
2. y>0
explain your solution



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Is this a greatest integer function problem or a mod problem ?
for mod problems I would just take appropriate values and use. However not all times we can use only values.......we might have to use a trick here and there.
 let me know b4 i can give it a try
 ash
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Re: DS101 [#permalink]
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28 Jun 2004, 00:15
lastochka wrote: This problem has been recently posted by halle i believe, I couldn't trace the orginal post, so I'm reposting it in effort to clarify an issue:
[x]>=[xy]+[y], is y>x?
1. x>0 2. y>0
explain your solution
From x >= xy + y we get that x = xy + y, because actually for every x and y it is true that x <= xy + y(this can be proven...)!
Then x, y, and x  y have the same sign (from =).
1 is sufficient: if x > 0, then x  y >= 0, then y < x is not true.
2 is sufficient too because the same is true for x  y >= 0.
C.



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Re: DS101 [#permalink]
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28 Jun 2004, 00:22
You may ask, why from x = xy + y => x, xy and y have the same sign?
It follows from:
(xy)^2 = xy^2 => 2*x*y = 2*x*y => x*y >= 0. And if x > 0, then y >= 0.
etc.



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Re: DS101 [#permalink]
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28 Jun 2004, 06:31
Emmanuel wrote: lastochka wrote: This problem has been recently posted by halle i believe, I couldn't trace the orginal post, so I'm reposting it in effort to clarify an issue:
[x]>=[xy]+[y], is y>x?
1. x>0 2. y>0
explain your solution From x >= xy + y we get that x = xy + y, because actually for every x and y it is true that x <= xy + y(this can be proven...)! Then x, y, and x  y have the same sign (from =). 1 is sufficient: if x > 0, then x  y >= 0, then y < x is not true. 2 is sufficient too because the same is true for x  y >= 0. C.
since both are sufficient you mean the answer is D
other than that, I agree with your solution



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ashkg wrote: Is this a greatest integer function problem or a mod problem ?
for mod problems I would just take appropriate values and use. However not all times we can use only values.......we might have to use a trick here and there.
 let me know b4 i can give it a try
 ash
not sure I understand the difference in your question ash. This is an absolute values problem.



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Re: DS101 [#permalink]
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28 Jun 2004, 06:39
lastochka wrote: Emmanuel wrote: lastochka wrote: This problem has been recently posted by halle i believe, I couldn't trace the orginal post, so I'm reposting it in effort to clarify an issue:
[x]>=[xy]+[y], is y>x?
1. x>0 2. y>0
explain your solution From x >= xy + y we get that x = xy + y, because actually for every x and y it is true that x <= xy + y(this can be proven...)! Then x, y, and x  y have the same sign (from =). 1 is sufficient: if x > 0, then x  y >= 0, then y < x is not true. 2 is sufficient too because the same is true for x  y >= 0. C. since both are sufficient you mean the answer is D other than that, I agree with your solution
Yes, lastochka, I don't remember exact definitions for A,B,C,D,E, but I know the solution...



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lastochka wrote: not sure I understand the difference in your question ash. This is an absolute values problem.
lastochka, ashkg want to say that [x] nay mean greatest integer, which is less than x.



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lastochka wrote: ashkg wrote: Is this a greatest integer function problem or a mod problem ?
for mod problems I would just take appropriate values and use. However not all times we can use only values.......we might have to use a trick here and there.
 let me know b4 i can give it a try
 ash not sure I understand the difference in your question ash. This is an absolute values problem.
The notation used for absolute values(modulus func) is x
The notation used for greatest integer value of x is [x]
Thats my understanding which I hope is correct. I didnt want to solve the problem before knowing that
Here's my attempt to solve the problem.
Let E => x >= xy + y
1. given x > 0
for all values of y>x, E will not hold true.
So y>x cannot be true.
So A is sufficient.
2. given y > 0
for all x, where x<y E wont hold true because x<y always.
for x>y, E will hold true.
Sor for E to hold true, x>y must be true. So y>x is not true. B is sufficient.
MY ans is D.
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ashkg wrote: lastochka wrote: ashkg wrote: Is this a greatest integer function problem or a mod problem ?
for mod problems I would just take appropriate values and use. However not all times we can use only values.......we might have to use a trick here and there.
 let me know b4 i can give it a try
 ash not sure I understand the difference in your question ash. This is an absolute values problem. The notation used for absolute values(modulus func) is x The notation used for greatest integer value of x is [x] Thats my understanding which I hope is correct. I didnt want to solve the problem before knowing that Here's my attempt to solve the problem. Let E => x >= xy + y 1. given x > 0 for all values of y>x, E will not hold true. So y>x cannot be true. So A is sufficient. 2. given y > 0 for all x, where x<y E wont hold true because x<y always. for x>y, E will hold true. Sor for E to hold true, x>y must be true. So y>x is not true. B is sufficient. MY ans is D.
I couldn't figure out what key will produce "" symbol (absolute value symbol). Which key is it on a keyboard? Thanks in advance.



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lastochka wrote: I couldn't figure out what key will produce "" symbol (absolute value symbol). Which key is it on a keyboard? Thanks in advance.
lastochka, this symbol appears when you press Shift and backslash (it is to the right from "backspace" key).



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Ash,
I have a question based on your explaination.Why do you presume for (2) that x<y will not hold true because x<y always?What is the relationship b/w both sets of inequality?How did you draw the // that x>y will hold in this case?Tx.
Anna
ashkg wrote: lastochka wrote: ashkg wrote: Is this a greatest integer function problem or a mod problem ?
for mod problems I would just take appropriate values and use. However not all times we can use only values.......we might have to use a trick here and there.
 let me know b4 i can give it a try
 ash not sure I understand the difference in your question ash. This is an absolute values problem. The notation used for absolute values(modulus func) is x The notation used for greatest integer value of x is [x] Thats my understanding which I hope is correct. I didnt want to solve the problem before knowing that Here's my attempt to solve the problem. Let E => x >= xy + y 1. given x > 0 for all values of y>x, E will not hold true. So y>x cannot be true. So A is sufficient. 2. given y > 0 for all x, where x<y E wont hold true because x<y always. for x>y, E will hold true. Sor for E to hold true, x>y must be true. So y>x is not true. B is sufficient. MY ans is D.
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