Last visit was: 14 Aug 2024, 07:38 It is currently 14 Aug 2024, 07:38
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+5)/(y+5)?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94941
Own Kudos [?]: 649531 [26]
Given Kudos: 86938
Tutor
Joined: 16 Oct 2010
Posts: 15221
Own Kudos [?]: 67335 [18]
Given Kudos: 437
Location: Pune, India
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 31011 [9]
Given Kudos: 799
General Discussion
Intern
Joined: 26 Mar 2010
Posts: 9
Own Kudos [?]: 13 [2]
Given Kudos: 3
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)? [#permalink]
2
Kudos
Simplify (we can cross multiply, since x and y are positive)

xy+5x<xy+5y
5x<5Y
So basically the question asks if x<y

Math Expert
Joined: 02 Sep 2009
Posts: 94941
Own Kudos [?]: 649531 [3]
Given Kudos: 86938
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)? [#permalink]
2
Kudos
1
Bookmarks
Bunuel wrote:
If x and y are positive integers, is x/y < (x+5)/(y+5)?

(1) y = 5
(2) x > y

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

We are adding the same number, 5, to both the numerator and the denominator, so the value of x/y will move closer to 1. All we need to determine is whether x/y is greater than 1 or less than 1.

Statement #1: y = 5. Here, we have a definite value for y, but zero information about x. If y = 5, some fractions (1/5) can be less than one, while others (7/5) will be greater than one. Either is possible. Since both are possible, we can’t give a definitive answer to the prompt. This statement, alone, by itself, is insufficient.

Statement #2: x>y. Dividing both sides of this inequality by y, we get (x/y) > 1. This means x/y must be a fraction greater than 1, which means the resultant fraction (x + 5)/(y + 5) must be closer to one, which means the resultant fraction must be smaller. Therefore, we can definitively say: the answer to the prompt question is, “No.” Because we can give a definite answer to the prompt, we have sufficient information. This statement, alone, by itself, is sufficient.
Statement #1 is insufficient and Statement #2 is sufficient.

Intern
Joined: 29 Jun 2016
Posts: 37
Own Kudos [?]: 26 [0]
Given Kudos: 5
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)? [#permalink]
according to the solution
x>y
lets take x=2 y=1
2<7/6
its not valid
Can someone give the solution?
Alum
Joined: 12 Aug 2015
Posts: 2270
Own Kudos [?]: 3211 [2]
Given Kudos: 893
GRE 1: Q169 V154
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)? [#permalink]
2
Kudos
See here the question is asking us whether x/y<x+5/y+5
There are two ways to solve this
First one => Using the concept of Fractions and decimals => Adding the same thing number to the numerator and the denominator just bring the number closer to one. Hence the question is really asking us if x/y is a proper fraction or an improper one.
Here if x>y => x/y will be an improper fraction
Hence x+5/y+5 will be less than the x/y so the answer is always a NO.
Second using the concept of inequality we can cross multiply to change the sides and the stem of the question reduces to is x/y<1

AS per your query you are absolutely right
The reason B is the answer is that no matter what be the values of x and y ; if x>y => x/y>1
so if x=2 y=1 => the answer is a NO
The answer to the question is always a NO

Refer to this to learn this concept => https://magoosh.com/gmat/2012/gmat-short ... nominator/

Originally posted by stonecold on 15 Aug 2016, 02:20.
Last edited by stonecold on 15 Aug 2016, 03:33, edited 1 time in total.
Intern
Joined: 16 Nov 2016
Posts: 5
Own Kudos [?]: [0]
Given Kudos: 2
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)? [#permalink]
Hello!

I understand this concept, however, when I first went through this question, I answered D.

The reason is that for (1), I substituted y=5 into the equation, which lead me to x<5. And if x<5 then this statement is sufficient as that would make x<y.

Could someone please explain the flaw in my reasoning?

Thank you!
SVP
Joined: 26 Mar 2013
Posts: 2455
Own Kudos [?]: 1376 [0]
Given Kudos: 641
Concentration: Operations, Strategy
Schools: Erasmus (II)
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)? [#permalink]
If x and y are positive integers, is x/y < (x+5)/(y+5)?

x/y < (x+5)/(y+5)

0 < (x+5)/(y+5) - x/y

0 < y(x+5) - [x(y+5)]/ y(y+5)....looks ugly but simplifying we get

0 < (5y-5x) / y(y+5)

0 < 5(y-x) / y(y+5)

As y & x are positive integers, the denominator is always positive.

teh question repharsed to be

is y-x> 0?? or is y>x

(1) y = 5

No info about x. We do not know sign of (y-x)

Insufficient

(2) x > y

Directly we can say: y-x<0 means it is ALWAYS negative. Answer is ALWAYS No

Sufficient

Current Student
Joined: 11 Oct 2015
Status:Preparing for GMAT!!
Posts: 112
Own Kudos [?]: 55 [0]
Given Kudos: 109
Location: India
GMAT 1: 660 Q47 V34
GMAT 2: 700 Q48 V38
GPA: 3.1
WE:General Management (Entertainment and Sports)
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)? [#permalink]
Bunuel wrote:
If x and y are positive integers, is x/y < (x+5)/(y+5)?

(1) y = 5
(2) x > y

Kudos for a correct solution.

$$\frac{x}{y}<\frac{x+5}{y+5}$$
=> $$x<y?$$

1. y=5, no information about x. -> INSUFFICIENT.
2. x>y -> SUFFICIENT.

B.
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+5)/(y+5)? [#permalink]
1) Insufficient since we need the value of both x and y to determine x/y. So we can know if x/y is less than 1 or more than one.
2) sufficient
Non-Human User
Joined: 09 Sep 2013
Posts: 34422
Own Kudos [?]: 865 [0]
Given Kudos: 0
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)? [#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+5)/(y+5)? [#permalink]