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This problem has been recently posted by halle i believe, I [#permalink]
 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]>=[x-y]+[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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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]>=[x-y]+[y], is y>x?
1. x>0
2. y>0
explain your solution
From |x| >= |x-y| + |y| we get that |x| = |x-y| + |y|, because actually for every x and y it is true that |x| <= |x-y| + |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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You may ask, why from |x| = |x-y| + |y| => x, x-y and y have the same sign?
It follows from:
(|x|-|y|)^2 = |x-y|^2 => -2*|x|*|y| = -2*x*y => x*y >= 0. And if x > 0, then y >= 0.
etc.
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Senior Manager
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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]>=[x-y]+[y], is y>x?
1. x>0
2. y>0
explain your solution From |x| >= |x-y| + |y| we get that |x| = |x-y| + |y|, because actually for every x and y it is true that |x| <= |x-y| + |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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Senior Manager
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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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Manager
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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]>=[x-y]+[y], is y>x?
1. x>0
2. y>0
explain your solution From |x| >= |x-y| + |y| we get that |x| = |x-y| + |y|, because actually for every x and y it is true that |x| <= |x-y| + |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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Senior Manager
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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| >= |x-y| + |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| >= |x-y| + |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| >= |x-y| + |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. _________________
We can crack the exam together
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