GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2018, 00:39

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50001
If a, b, x, and y are all positive, is a/b > x/y ?  [#permalink]

### Show Tags

24 Apr 2017, 03:34
3
2
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:34) correct 32% (02:02) wrong based on 84 sessions

### HideShow timer Statistics

If a, b, x, and y are all positive, is $$\frac{a}{b} > \frac{x}{y}$$ ?

(1) $$ay + 1 > bx$$

(2) $$(\frac{ay}{bx})^2 > \frac{ay}{bx}$$

_________________
Manager
Joined: 22 Jun 2016
Posts: 246
If a, b, x, and y are all positive, is a/b > x/y ?  [#permalink]

### Show Tags

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.

_________________

P.S. Don't forget to give Kudos

Intern
Joined: 18 Jul 2016
Posts: 16
Re: If a, b, x, and y are all positive, is a/b > x/y ?  [#permalink]

### Show Tags

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.
_________________

Engineer, Quant score 53 First attempt.

Director
Joined: 21 Mar 2016
Posts: 526
Re: If a, b, x, and y are all positive, is a/b > x/y ?  [#permalink]

### Show Tags

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
Manager
Joined: 22 Jun 2016
Posts: 246
Re: If a, b, x, and y are all positive, is a/b > x/y ?  [#permalink]

### Show Tags

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.

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.
_________________

P.S. Don't forget to give Kudos

Intern
Joined: 18 Jul 2016
Posts: 16
Re: If a, b, x, and y are all positive, is a/b > x/y ?  [#permalink]

### Show Tags

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.

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.
_________________

Engineer, Quant score 53 First attempt.

Non-Human User
Joined: 09 Sep 2013
Posts: 8459
Re: If a, b, x, and y are all positive, is a/b > x/y ?  [#permalink]

### Show Tags

15 May 2018, 17:52
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If a, b, x, and y are all positive, is a/b > x/y ? &nbs [#permalink] 15 May 2018, 17:52
Display posts from previous: Sort by