Last visit was: 06 Aug 2024, 00:15 It is currently 06 Aug 2024, 00:15
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# If x and y are positive integers, is x/y < (x+2)/(y+3)?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94796
Own Kudos [?]: 647095 [29]
Given Kudos: 86860
Math Expert
Joined: 02 Sep 2009
Posts: 94796
Own Kudos [?]: 647095 [12]
Given Kudos: 86860
Senior Manager
Joined: 28 Feb 2014
Posts: 269
Own Kudos [?]: 325 [10]
Given Kudos: 132
Location: United States
Concentration: Strategy, General Management
General Discussion
Manager
Joined: 14 Oct 2014
Posts: 53
Own Kudos [?]: 519 [1]
Given Kudos: 98
Location: United States
GMAT 1: 500 Q36 V23
Re: If x and y are positive integers, is x/y < (x+2)/(y+3)? [#permalink]
1
Kudos
Given: x,y >0; x,y are integers.
Question: is x/y<(x+2)/(y+3)? or if we cross-multiply (we can do this because x and y are positive) and simplify we get is 3x<2y?

(1) Insufficient. If x is small then the answer to the question will be yes, but if x is very big and y=21, then answer will be no.
(2) Insufficient. No info about y, so y can be either very small or very big which will yield two different answers.

(1)+(2) Sufficient. If y=21 and x=4, then we get 12< 42, so the answer to the question is no.

Manager
Joined: 25 Mar 2014
Posts: 108
Own Kudos [?]: 126 [1]
Given Kudos: 48
Location: India
Concentration: Operations, Finance
GMAT Date: 05-10-2015
GPA: 3.51
WE:Programming (Computer Software)
Re: If x and y are positive integers, is x/y < (x+2)/(y+3)? [#permalink]
1
Kudos
Bunuel wrote:
If x and y are positive integers, is x/y < (x+2)/(y+3)?

(1) y > 20
(2) x < 5

Kudos for a correct solution.

As i thought, this problem cannot be dependent on value of any one of the variable. I mean even if y > 20, for x = y given equation does not hold true, and conclusion varies for condition x < y and x > y. So, option A, B and D are out.
So, we need values or range for x and y both, and keep an eye on relation between x and y, since the validity of the equation varies depending on conditions: x = y, x > y and x < y.
For the given ranges combined, we get only one relation between x and y, i.e. y > x.
Retired Moderator
Joined: 26 Nov 2012
Posts: 473
Own Kudos [?]: 499 [2]
Given Kudos: 46
Re: If x and y are positive integers, is x/y < (x+2)/(y+3)? [#permalink]
2
Kudos
stonecold wrote:
1) If x and y are positive integers, is {x/y} <{{x+2}/{y+3}}?

Statement #1: y > 20
Statement #2: x < 5

HAPPY INDEPENDENCE DAY...STONY..

Given {x/y} <{{x+2}/{y+3}}

cross multiply or mulitiply individual variables we get the same equation...

x(y+3) < y(x+2)
xy + 3x < yx + 2y

3x < 2y
=> x/y < 2/3 ? we need to find this.

Stat 1: y > 20..no information about x...not sufficient...

Stat 2: x < 5..no information about y...not sufficient..

Stat 1 + Stat 2: Now take least y value and greater number from x i.e y = 21 and x = 4 ...since the value is not divisible consider 4/24 = 1/6 < 2/3.

Similarly consider some other value let x = 3 and y = 18..these values are exactly divisible, hence consider 1/6 < 2/3

or x = 4 and y = 21 we get result < 2/3....Sufficient..

Hence C is sufficient..
Intern
Joined: 01 Jan 2016
Posts: 47
Own Kudos [?]: 136 [0]
Given Kudos: 49
GPA: 3.75
WE:Engineering (Energy and Utilities)
Re: If x and y are positive integers, is x/y < (x+2)/(y+3)? [#permalink]
Option C, since the fraction gets closer to 2/3, we need to know values of x and Y to know if 2/3 is greater than or less than x/y.
Intern
Joined: 01 Jan 2017
Posts: 5
Own Kudos [?]: 1 [0]
Given Kudos: 0
Location: Indonesia
Concentration: Finance, Technology
GMAT 1: 530 Q34 V38
Re: If x and y are positive integers, is x/y < (x+2)/(y+3)? [#permalink]
msk0657 wrote:
stonecold wrote:
1) If x and y are positive integers, is {x/y} <{{x+2}/{y+3}}?

Statement #1: y > 20
Statement #2: x < 5

HAPPY INDEPENDENCE DAY...STONY..

Given {x/y} <{{x+2}/{y+3}}

cross multiply or mulitiply individual variables we get the same equation...

x(y+3) < y(x+2)
xy + 3x < yx + 2y

3x < 2y
=> x/y < 2/3 ? we need to find this.

Stat 1: y > 20..no information about x...not sufficient...

Stat 2: x < 5..no information about y...not sufficient..

Stat 1 + Stat 2: Now take least y value and greater number from x i.e y = 21 and x = 4 ...since the value is not divisible consider 4/24 = 1/6 < 2/3.

Similarly consider some other value let x = 3 and y = 18..these values are exactly divisible, hence consider 1/6 < 2/3

or x = 4 and y = 21 we get result < 2/3....Sufficient..

Hence C is sufficient..

sorry can you explain why we need to simplify the x/y < (x+2)/(y+3) to become 3x < 2y, does if we just put the number directly we could get the answear.
Thanks
Retired Moderator
Joined: 22 Aug 2013
Posts: 1181
Own Kudos [?]: 2559 [0]
Given Kudos: 459
Location: India
Re: If x and y are positive integers, is x/y < (x+2)/(y+3)? [#permalink]
ryanpri wrote:
msk0657 wrote:
stonecold wrote:
1) If x and y are positive integers, is {x/y} <{{x+2}/{y+3}}?

Statement #1: y > 20
Statement #2: x < 5

HAPPY INDEPENDENCE DAY...STONY..

Given {x/y} <{{x+2}/{y+3}}

cross multiply or mulitiply individual variables we get the same equation...

x(y+3) < y(x+2)
xy + 3x < yx + 2y

3x < 2y
=> x/y < 2/3 ? we need to find this.

Stat 1: y > 20..no information about x...not sufficient...

Stat 2: x < 5..no information about y...not sufficient..

Stat 1 + Stat 2: Now take least y value and greater number from x i.e y = 21 and x = 4 ...since the value is not divisible consider 4/24 = 1/6 < 2/3.

Similarly consider some other value let x = 3 and y = 18..these values are exactly divisible, hence consider 1/6 < 2/3

or x = 4 and y = 21 we get result < 2/3....Sufficient..

Hence C is sufficient..

sorry can you explain why we need to simplify the x/y < (x+2)/(y+3) to become 3x < 2y, does if we just put the number directly we could get the answear.
Thanks

Hi

The word simplification in almost every task does what its supposed to do: - it 'simplifies' the question or makes our task 'simple'.

Eg, if here we look at statement 1, and try to plug in the values straightaway, we will have to put a value of y>20 in the question. So we will write: LHS = x/21. RHS = (x+2)/24
We can see that this on its own doesnt tell us anything unless we know something about x. Or we will have to cross multiply to get 24x on LHS and 21x+42 on RHS.

From statement 2, similarly we will take a value of x less than 5, say 4. So we will substitute x=4 and then again this statement will become insufficient unless we know something about y.

But as you can see, this method of substituting numbers is slightly complicated. Instead if we can just simplify the question stem (as explained by others), all we have to then find is whether x/y < 2/3. And for this we need to know something about both x as well as y. So individual statements are not sufficient on their own.
Intern
Joined: 01 Jan 2017
Posts: 5
Own Kudos [?]: 1 [0]
Given Kudos: 0
Location: Indonesia
Concentration: Finance, Technology
GMAT 1: 530 Q34 V38
Re: If x and y are positive integers, is x/y < (x+2)/(y+3)? [#permalink]
Hi

The word simplification in almost every task does what its supposed to do: - it 'simplifies' the question or makes our task 'simple'.

Eg, if here we look at statement 1, and try to plug in the values straightaway, we will have to put a value of y>20 in the question. So we will write: LHS = x/21. RHS = (x+2)/24
We can see that this on its own doesnt tell us anything unless we know something about x. Or we will have to cross multiply to get 24x on LHS and 21x+42 on RHS.

From statement 2, similarly we will take a value of x less than 5, say 4. So we will substitute x=4 and then again this statement will become insufficient unless we know something about y.

But as you can see, this method of substituting numbers is slightly complicated. Instead if we can just simplify the question stem (as explained by others), all we have to then find is whether x/y < 2/3. And for this we need to know something about both x as well as y. So individual statements are not sufficient on their own.[/quote]

Thanks for the explanation,
btw if we crop multiply we can get
Y=21
24x>21x+42

can i move the "21x" like this:
24x-21x>42
x=42/3

Retired Moderator
Joined: 22 Aug 2013
Posts: 1181
Own Kudos [?]: 2559 [0]
Given Kudos: 459
Location: India
Re: If x and y are positive integers, is x/y < (x+2)/(y+3)? [#permalink]
ryanpri wrote:
Hi

The word simplification in almost every task does what its supposed to do: - it 'simplifies' the question or makes our task 'simple'.

Eg, if here we look at statement 1, and try to plug in the values straightaway, we will have to put a value of y>20 in the question. So we will write: LHS = x/21. RHS = (x+2)/24
We can see that this on its own doesnt tell us anything unless we know something about x. Or we will have to cross multiply to get 24x on LHS and 21x+42 on RHS.

From statement 2, similarly we will take a value of x less than 5, say 4. So we will substitute x=4 and then again this statement will become insufficient unless we know something about y.

But as you can see, this method of substituting numbers is slightly complicated. Instead if we can just simplify the question stem (as explained by others), all we have to then find is whether x/y < 2/3. And for this we need to know something about both x as well as y. So individual statements are not sufficient on their own.

Thanks for the explanation,
btw if we crop multiply we can get
Y=21
24x>21x+42

can i move the "21x" like this:
24x-21x>42
x=42/3

Hi Ryan

In this particular question, you are being asked Whether x/y < (x+2)/(y+3) . We are not given this already.

But suppose we are already given that x/y < (x+2)/(y+3) and then we decide to play around with this by substituting the value of y as 21. Then we will write:

x/21 < (x+2)/24. Then cross multiplying 24x < 21x + 42. After that Yes we can do as you did. We will write:
24x-21x < 42 or 3x < 42 or x < 42/3 or x < 14 (you have written x=42/3, its not equal it will be x < 42/3)

I suggest you first go through the basics of algebra and inequalities.

You can go to the following thread by Bunuel and go through the topics of your choice.

https://gmatclub.com/forum/ultimate-gma ... 44512.html

In this particular case, I was talking about Topic no 7 (algebra) and Topic no 9 (Inequalities)
Intern
Joined: 04 Jun 2021
Posts: 42
Own Kudos [?]: 5 [0]
Given Kudos: 936
Location: India
Schools: Alberta '23
GMAT 1: 610 Q49 V25
GPA: 3.33
Re: If x and y are positive integers, is x/y < (x+2)/(y+3)? [#permalink]
can someone provide with the expalnation brunel talked abbout as I am not aware of the concept sed by brunel... can anyone please elobrate on that
Intern
Joined: 04 Feb 2022
Posts: 12
Own Kudos [?]: 1 [0]
Given Kudos: 16
Re: If x and y are positive integers, is x/y < (x+2)/(y+3)? [#permalink]
CAN SOMEONE HELP ME TO KNOW WHEN CAN WE CROSS FACTOR AND WHEN CAN WE NOT?
Intern
Joined: 04 Jun 2021
Posts: 42
Own Kudos [?]: 5 [1]
Given Kudos: 936
Location: India
Schools: Alberta '23
GMAT 1: 610 Q49 V25
GPA: 3.33
Re: If x and y are positive integers, is x/y < (x+2)/(y+3)? [#permalink]
1
Kudos
mehtasahil56 wrote:
CAN SOMEONE HELP ME TO KNOW WHEN CAN WE CROSS FACTOR AND WHEN CAN WE NOT?

when numbers involved are positive then we can do cross multipication..... here in this question we are specifically mentioned that x and y are positive so we can do cross multipication ........if satisfied with answer give kudos
Non-Human User
Joined: 09 Sep 2013
Posts: 34247
Own Kudos [?]: 859 [0]
Given Kudos: 0
Re: If x and y are positive integers, is x/y < (x+2)/(y+3)? [#permalink]
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 x and y are positive integers, is x/y < (x+2)/(y+3)? [#permalink]
Moderator:
Math Expert
94796 posts