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If xy < 5, is x < 1 ? (1) | y | > 5 (2) x / y > 0

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rxs0005
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If xy < 5, is x < 1 ? (1) | y | > 5 (2) x / y > 0 [#permalink] New post   07 Feb 2012, 16:36
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If xy < 5, is x < 1 ?

(1) |y| > 5
(2) x/y > 0
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C
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Bunuel
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Re: is x < 1 ? [#permalink] New post   07 Feb 2012, 16:49
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If xy < 5, is x < 1 ?

(1) |y| > 5 --> if y=10 and x=0 then the answer is YES but if y=-10 and x=2 then the answer is NO. Not sufficient.

(2) x/y > 0 --> x and y have the same sign. Still insufficient: if y=-2 and x=-1 then the answer is YES but if y=2 and x=2 then the answer is NO.

(1)+(2) From (2) x and y have the same sign. Now, if from (1) y>5 then 0<x<1 (in order xy<5 to hold true) and if from (1) y<-5 then -1<x<0 (again in order xy<5 to hold true). So in both cases x<1. Sufficient.

Answer: C.
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Re: If xy < 5, is x < 1 ? (1) | y | > 5 (2) x / y > 0 [#permalink] New post   16 Jun 2020, 23:54
rxs0005 wrote:
If xy < 5, is x < 1 ?

(1) |y| > 5
(2) x/y > 0

(1)-> if y is +ve (y=6,7 etc.. check) x < 1 , if y is -ve x > -1 ( y= -6, -7 etc..) here it can be both less than one or greater than one
(2) -> both x and y are same sign : we still dont know (take values of y as 1 or ten , x can be both >1 or <1)
combined : if y is +ve we know x<1 , if y is -ve x>-1 but now, x is also negative that gives us 0>x>-1 so here too x<1 , thus we can say that x<1 for sure
hence, C
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If xy < 5, is x < 1 ? (1) | y | > 5 (2) x / y > 0 [#permalink] New post   17 Jun 2020, 00:16
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rxs0005 wrote:
If xy < 5, is x < 1 ?

(1) |y| > 5
(2) x/y > 0



\(xy<5\).....Is x<1?

(1) |y| > 5
Two cases
a) \(y>5......xy<5.....\)
Add both the equations....\(y+5>xy+5......xy-y<0.....y(x-1)<0\)
We know y>0, so x-1<0 or x<1....YES
b) \(y<-5......xy<5.....\)
Add both the equations....\(5-5>xy+y......xy+y<0.....y(x+1)<0\)
We know y<0, so x+1>0 or x>-1.... x could be 10, 100, or 0....... Both YES and NO possible.
Insuff

(2) \(\frac{x}{y} > 0\)
This means x and y have same sign.
(x,y) = (4,1)=(-4,-1)...So Yes and No both possible

Combined..
Both have same sign
y>5...x has to be positive, so 0<x<1....YES x<1
y<-5...x has to be negative, so -1<x<0...YES x<1.
Suff

C
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Re: If xy < 5, is x < 1 ? (1) | y | > 5 (2) x / y > 0 [#permalink] New post   17 Jun 2020, 08:01
Hi chetan2u,

Need some clarification regarding the range of x in ST1. If we are obtaining x < 1, x > -1, doesn't it imply that -1 < x < 1 ?

Or, is it because |y| > 5 gives us an OR result set (either less than -5 OR greater than 5) thus, the range for x will also be OR and not AND?
If so, what will be the range of x in ST1?

Thanks in advance!

Lipun
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Re: If xy < 5, is x < 1 ? (1) | y | > 5 (2) x / y > 0 [#permalink] New post   17 Jun 2020, 09:26
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Lipun wrote:
Hi chetan2u,

Need some clarification regarding the range of x in ST1. If we are obtaining x < 1, x > -1, doesn't it imply that -1 < x < 1 ?

Or, is it because |y| > 5 gives us an OR result set (either less than -5 OR greater than 5) thus, the range for x will also be OR and not AND?
If so, what will be the range of x in ST1?

Thanks in advance!

Lipun



Range of x is dependent on the value of y..
So we cannot take any specific range.
If y>5, it is different and if y<-5, it is different.
As the values of y is totally different in two cases, we cannot join the ranges of x.
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Re: If xy < 5, is x < 1 ? (1) | y | > 5 (2) x / y > 0 [#permalink]
17 Jun 2020, 09:26
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Bunuel
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