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If a, b, x, and y are all positive, is a/b > x/y ?

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If a, b, x, and y are all positive, is a/b > x/y ?  [#permalink]

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New post 24 Apr 2017, 03:34
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68% (01:34) correct 32% (02:02) wrong based on 84 sessions

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If a, b, x, and y are all positive, is a/b > x/y ?  [#permalink]

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New post 24 Apr 2017, 04:20
3
As a,b,x and y are positive, it makes our life easy while playing with inequalities.

we have to find is : a/b>x/y ---> ay>bx ---> ay-bx > 0

S1.
ay+1>bx ---> ay-bx>-1

So, we cannot say whether ay-bx is always > 0 (for ex. ay-bx could be -0.5)

Insufficient!


S2.

(ay/bx)^2 > (ay/bx) ---> ay/bx > 1 ---> ay>bx ---> ay-bx>0

Sufficient.

Hence, answer should be B.
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Re: If a, b, x, and y are all positive, is a/b > x/y ?  [#permalink]

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New post 24 Apr 2017, 04:23
rewrite the question as (ay/bx)>1

statement 1
> divide the entire inequality by bx
we get
(ay/bx) + (1/bx) > 1
that is (positive number) + (positive Number) >1. This does not say anything about (ay/bx) as it can be 0.5 or 1.5 and so on

This is not sufficient as we need to know whether (ay/bx)>1

Statement 2
(ay/bx)^2 > (ay/bx)
>(ay/bx)^2 - (ay/bx)>0
>(ay/bx)*((ay/bx)-1)>0

this means that either both the boldface terms are greater than zero or both are less than zero.
as a,y,b and x are positive (ay/bx) cannot be less than zero. Hence both cannot be less than zero.
Now both are greater than zero. which means,
(ay/bx)> 0 and (ay/bx) - 1 > 0

Remember that this is an AND condition. Both have to be true.

therefore ay/bx >1
statement 2 alone is sufficient.
So answer should be B
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Re: If a, b, x, and y are all positive, is a/b > x/y ?  [#permalink]

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New post 24 Apr 2017, 04:37
simplify the given stem

ay>bx
ay-bx >0 ????
stat 1: ay-bx > -1,,not suff

stat 2 : divide the entire equation by ax/by

gives ax/by >1

ax>by
ax-by >0.. suff

ans B
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Re: If a, b, x, and y are all positive, is a/b > x/y ?  [#permalink]

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New post 24 Apr 2017, 04:37
skothaka wrote:
rewrite the question as (ay/bx)>1

statement 1
> divide the entire inequality by bx
we get
(ay/bx) + (1/bx) > 1
that is (positive number) + (positive Number) >1. This does not say anything about (ay/bx) as it can be 0.5 or 1.5 and so on

This is not sufficient as we need to know whether (ay/bx)>1

Statement 2
(ay/bx)^2 > (ay/bx)
>(ay/bx)^2 - (ay/bx)>0
>(ay/bx)*((ay/bx)-1)>0

this means that either both the boldface terms are greater than zero or both are less than zero.
as a,y,b and x are positive (ay/bx) cannot be less than zero. Hence both cannot be less than zero.
Now both are greater than zero. which means,
(ay/bx)> 0 and (ay/bx) - 1 > 0

Remember that this is an AND condition. Both have to be true.

therefore ay/bx >1
statement 2 alone is sufficient.
So answer should be B


The solution provided for S1 is not complete. We cannot conclude anything with the equation (ay/bx) + (1/bx) > 1. See the above solution for a better explanation.
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Re: If a, b, x, and y are all positive, is a/b > x/y ?  [#permalink]

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New post 24 Apr 2017, 04:42
14101992 wrote:
skothaka wrote:
rewrite the question as (ay/bx)>1

statement 1
> divide the entire inequality by bx
we get
(ay/bx) + (1/bx) > 1
that is (positive number) + (positive Number) >1. This does not say anything about (ay/bx) as it can be 0.5 or 1.5 and so on

This is not sufficient as we need to know whether (ay/bx)>1

Statement 2
(ay/bx)^2 > (ay/bx)
>(ay/bx)^2 - (ay/bx)>0
>(ay/bx)*((ay/bx)-1)>0

this means that either both the boldface terms are greater than zero or both are less than zero.
as a,y,b and x are positive (ay/bx) cannot be less than zero. Hence both cannot be less than zero.
Now both are greater than zero. which means,
(ay/bx)> 0 and (ay/bx) - 1 > 0

Remember that this is an AND condition. Both have to be true.

therefore ay/bx >1
statement 2 alone is sufficient.
So answer should be B


The solution provided for S1 is not complete. We cannot conclude anything with the equation (ay/bx) + (1/bx) > 1. See the above solution for a better explanation.



The solution for S1 says that ay/bx could be anything between 0 and infinite. So S1 is not sufficient. That is enough to rule it out. Your solution is much simpler btw.
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Re: If a, b, x, and y are all positive, is a/b > x/y ?  [#permalink]

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New post 15 May 2018, 17:52
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Re: If a, b, x, and y are all positive, is a/b > x/y ? &nbs [#permalink] 15 May 2018, 17:52
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