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On the coordinate plane is point (0, 0) closer to point (u, [#permalink]
 28 Aug 2008, 09:27
On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ?
1.v + u^2 = -1
2. v < 0
ive taken it out ....
Last edited by arjtryarjtry on 28 Aug 2008, 09:57, edited 2 times in total.
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Re: wats this mean? [#permalink]
28 Aug 2008, 09:45
arjtryarjtry wrote: On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ?
1.v + u^2 = -1
2. v < 0
OA is A. but sorry, i didnt understand this ... Boss don't post OA .. GIVE A CHANCE TO OTHERS. Distance between (0, 0) and (u, v) = sqrt {u^2+v^2 }Distance between (0, 0) and (u, v+1) = sqrt {u^2+v^2 +2v+1} 1.v + u^2 = -1 --> u^2 = -1-v ( u^2 is alwasy positive.. So.. v must be -ve and <-1) 2v+1 --> -ve sqrt {u^2+v^2 +2v+1} is alwasy less than sqrt {u^2+v^2 }
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Last edited by x2suresh on 29 Aug 2008, 06:27, edited 1 time in total.
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Re: wats this mean? [#permalink]
28 Aug 2008, 09:55
 hmmm . k .. suresh !! thanks...
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Re: wats this mean? [#permalink]
28 Aug 2008, 11:33
x2suresh wrote: arjtryarjtry wrote: On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ?
1.v + u^2 = -1
2. v < 0
OA is A. but sorry, i didnt understand this ... Boss don't post OA .. GIVE CHANCE TO OTHERS. Distance between (0, 0) and (u, v) = sqrt {u^2+v^2 }Distance between (0, 0) and (u, v+1) = sqrt {u^2+v^2 +2v+1} 1.v + u^2 = -1 --> u^2 = -1-v ( u^2 is alwasy positive.. So.. v must be -ve and <-1) 2v+1 --> -ve sqrt {u^2+v^2 +2v+1} is alwasy less than sqrt {u^2+v^2 }Why will S2 not work? What is the OA?
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Re: wats this mean? [#permalink]
28 Aug 2008, 11:50
leonidas wrote: x2suresh wrote: arjtryarjtry wrote: On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ?
1.v + u^2 = -1
2. v < 0
OA is A. but sorry, i didnt understand this ... Boss don't post OA .. GIVE CHANCE TO OTHERS. Distance between (0, 0) and (u, v) = sqrt {u^2+v^2 }Distance between (0, 0) and (u, v+1) = sqrt {u^2+v^2 +2v+1} 1.v + u^2 = -1 --> u^2 = -1-v ( u^2 is alwasy positive.. So.. v must be -ve and <-1) 2v+1 --> -ve sqrt {u^2+v^2 +2v+1} is alwasy less than sqrt {u^2+v^2 }Why will S2 not work? What is the OA? Hey Nemo, 2v+1 --> -ve or +ve. v<0 v=-1/4 2v+1>0 v=-2 2v+1<0
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Re: wats this mean? [#permalink]
28 Aug 2008, 13:26
x2suresh wrote: leonidas wrote:
Why will S2 not work? What is the OA?
Hey Nemo, 2v+1 --> -ve or +ve. v<0 v=-1/4 2v+1>0 v=-2 2v+1<0 Got it, didn't try a fraction  Thanks X2Suresh
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Re: wats this mean? [#permalink]
29 Aug 2008, 01:44
Let's consider each statement carefully: a) On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ? First of all, u does not influence on answer. Therefore, we can restate: On the coordinate line is point (0) closer to point (v) than to point (v + 1) ? Now, we can translate it to language of formulas: |v|<|v+1| Eventually, we can write: v>-0.5 b) v + u^2 = -1 --> v=-1-u^2 --> v<-1 Now, we can restate our problem as following: Does v>-0.5 ? 1. v<-1 2. v<0 Answer is obviously A.
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Re: wats this mean? [#permalink]
29 Aug 2008, 03:44
thanks , but how did u get 2 from 1?? could not quite understand... walker wrote: Let's consider each statement carefully:
a) On the coordinate plane is point (0, 0) closer to point (u, v) than to point (u, v + 1) ?
First of all, u does not influence on answer. Therefore, we can restate: On the coordinate line is point (0) closer to point (v) than to point (v + 1) ?
Now, we can translate it to language of formulas: |v|<|v+1|......(1)
Eventually, we can write: v>-0.5....(2)
b) v + u^2 = -1 --> v=-1-u^2 --> v<-1
Now, we can restate our problem as following:
Does v>-0.5 ?
1. v<-1
2. v<0
Answer is obviously A.
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Re: wats this mean? [#permalink]
29 Aug 2008, 04:13
Full solution: |v|<|v+1| 1) v<-1: -v<-v-1 --> 0<-1 --> always false 2) -1<=v<=0: -v<v+1 --> v>-0.5 --> -0.5<v<=03) v>0: --> v<v+1 --> 0<1 always true. Therefore, inequality is true when v>-0.5Fast solution: large negative v: inequality is false large positive v: inequality is true switch point v=-0.5 --> v>-0.5
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Re: wats this mean? [#permalink]
29 Aug 2008, 09:11
Duh! I went for D but after reading your solutions I realized I forgot to test fractions.
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Re: wats this mean?
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29 Aug 2008, 09:11
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