1. Is 0<x<1?
a) 1/x > [x]
b) [x]<1
OA is A
a) I don't know how to think this. At first I try to solve like this:
1/x>x so x could be -2 or - (1/x)<x so x could be 1/2, 1 or 2.
b) this clearly means that x is between -1 and 1 so insufficient
Tksvm
Absolute Value (lost in a)
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1. Is 0<x<1?
a) 1/x > [x]
b) [x]<1
Stmt 1:
1/x > |x|
ie 1/x - |x| > 0
The LHS (left hand side) can be >0 ONLY if x is a +ve fraction
U can try the following smart numbers to prove the above.
-2, -1/2, 0, 1/2, 1, 2
So sufficient.
stmt 2:
|x| < 1
|x| is always >= 0.
So here |x| < 1.
But -1 < x < 1 so it is insufficient.
Hence A.
Ht Helps
a) 1/x > [x]
b) [x]<1
Stmt 1:
1/x > |x|
ie 1/x - |x| > 0
The LHS (left hand side) can be >0 ONLY if x is a +ve fraction
U can try the following smart numbers to prove the above.
-2, -1/2, 0, 1/2, 1, 2
So sufficient.
stmt 2:
|x| < 1
|x| is always >= 0.
So here |x| < 1.
But -1 < x < 1 so it is insufficient.
Hence A.
Ht Helps
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1. Is 0<x<1?
a) 1/x > [x]
-1/x<x<1/x
by looking at this you should be able to determine two things
1) x is positive becuse if x were negative -1/-#<-# would be violated because the two negatives make a positive.
2) x must be <1 because an integer such as 2 would yield 2<1/2 which wouldn't make sense but 1/2<2 does make sense.
These two things make A sufficient
b) [x]<1
-1<x<1
This alone is not sufficent
a) 1/x > [x]
-1/x<x<1/x
by looking at this you should be able to determine two things
1) x is positive becuse if x were negative -1/-#<-# would be violated because the two negatives make a positive.
2) x must be <1 because an integer such as 2 would yield 2<1/2 which wouldn't make sense but 1/2<2 does make sense.
These two things make A sufficient
b) [x]<1
-1<x<1
This alone is not sufficent
now 1/x > |x|
Part 1 :- since |x| is always +ve and 1/x is greater than tht +ve value, 1/x shud definitely be +ve.
Part 2 :- From statement 1 we also get 1>x*|x|.
So x>0 since x is +ve and less than 1 since x*|x|<1
Hence A
Part 1 :- since |x| is always +ve and 1/x is greater than tht +ve value, 1/x shud definitely be +ve.
Part 2 :- From statement 1 we also get 1>x*|x|.
So x>0 since x is +ve and less than 1 since x*|x|<1
Hence A
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First of All, let me make it clear:
[x] and |x| are different
[x] means greatest integer function, this function rounds off the number to nearest smallest integer value.
eg : [8.3] = 8
and [-9.2] =-10
|x| = gives a positive value,no matter x is negative or positive
so |-4| = 4
and |-4.5| = 4.5
we use greatest integer function
Everyone has misinterpreted the [x] as |x|
(I) this statement means
0< x < 1
because if we take x = 0.5
1/0.5 = 2
and [x] = [0.5] =0
so 1/x > [x]
And if we take -1<x< 0
because x has to be negative fraction lets say: -0.5
1/-0.5 = -2
and [-0.5] = -1
so 1/x not greater than [x]
rest other options where x>1 or x<-1 also cannot satisfy this inequation
So A is Suff
I looks big but it is very easy.
Although one can get an answer correct but I believe it is much more important to learn the correct method, that is what learning is.
https://www.beatthegmat.com/is-x-y-t10389.html#141440
Hope this Helps
Karan
[x] and |x| are different
[x] means greatest integer function, this function rounds off the number to nearest smallest integer value.
eg : [8.3] = 8
and [-9.2] =-10
|x| = gives a positive value,no matter x is negative or positive
so |-4| = 4
and |-4.5| = 4.5
In the original questiona) 1/x > [x]
we use greatest integer function
Everyone has misinterpreted the [x] as |x|
(I) this statement means
0< x < 1
because if we take x = 0.5
1/0.5 = 2
and [x] = [0.5] =0
so 1/x > [x]
And if we take -1<x< 0
because x has to be negative fraction lets say: -0.5
1/-0.5 = -2
and [-0.5] = -1
so 1/x not greater than [x]
rest other options where x>1 or x<-1 also cannot satisfy this inequation
So A is Suff
I looks big but it is very easy.
Although one can get an answer correct but I believe it is much more important to learn the correct method, that is what learning is.
https://www.beatthegmat.com/is-x-y-t10389.html#141440
Hope this Helps
Karan
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Oops
I have never seen that notation [] before. I suppose the question should have a explanation of []. Since this was absent, I assumed it to be | |.
I have never seen that notation [] before. I suppose the question should have a explanation of []. Since this was absent, I assumed it to be | |.
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IMO Cgmat740 wrote:First of All, let me make it clear:
[x] and |x| are different
[x] means greatest integer function, this function rounds off the number to nearest smallest integer value.
eg : [8.3] = 8
and [-9.2] =-10
|x| = gives a positive value,no matter x is negative or positive
so |-4| = 4
and |-4.5| = 4.5
In the original questiona) 1/x > [x]
we use greatest integer function
Everyone has misinterpreted the [x] as |x|
(I) this statement means
0< x < 1
because if we take x = 0.5
1/0.5 = 2
and [x] = [0.5] =0
so 1/x > [x]
And if we take -1<x< 0
because x has to be negative fraction lets say: -0.5
1/-0.5 = -2
and [-0.5] = -1
so 1/x not greater than [x]
rest other options where x>1 or x<-1 also cannot satisfy this inequation
So A is Suff
I looks big but it is very easy.
Although one can get an answer correct but I believe it is much more important to learn the correct method, that is what learning is.
https://www.beatthegmat.com/is-x-y-t10389.html#141440
Hope this Helps
Karan
Karan , what if the value of x = 1?