GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 09 Apr 2020, 18:12

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 x and y are positive integers, is x/y < (x+5)/(y+5)?

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62676
If x and y are positive integers, is x/y < (x+5)/(y+5)?  [#permalink]

Show Tags

02 Mar 2015, 07:21
4
10
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:14) correct 27% (01:40) wrong based on 376 sessions

HideShow timer Statistics

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.

_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10263
Location: Pune, India
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)?  [#permalink]

Show Tags

02 Mar 2015, 20:54
8
2
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.

Concept: When the same positive number is added to the numerator as well as denominator of a positive fraction, the fraction tends toward 1. If the original fraction is smaller than 1, it increases in value. If the original fraction is greater than 1, it decreases in value. Try a few values say 2/3. Add 1 to both to get 3/4 which is closer to 1 than 2/3. Another value say 5/4. Add 1 to both to get 6/5 which is less than 5/4.

Discussed here: http://www.veritasprep.com/blog/2011/06 ... round-one/

We want to know that when we add 5 to both x and y of the fraction x/y, do we get a smaller fraction or a larger fraction. This depends on whether x/y is less than 1 or greater than 1.

(1) y = 5
Doesn't tell us whether x/y is greater than 1 or less than 1.

(2) x > y
This tells us that x/y > 1. So when we add 5 to both numerator and denominator, the fraction will decrease in value. This gives us that x/y > x+5/y+5.
Sufficient alone.

_________________
Karishma
Veritas Prep GMAT Instructor

General Discussion
Intern
Joined: 26 Mar 2010
Posts: 9
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)?  [#permalink]

Show Tags

02 Mar 2015, 10:47
1
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: 62676
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)?  [#permalink]

Show Tags

08 Mar 2015, 14:48
2
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: 40
Re: ) If x and y are positive integers, is {x/y} <{{x+5}/{y+5}}?  [#permalink]

Show Tags

15 Aug 2016, 01:12
according to the solution
x>y
lets take x=2 y=1
2<7/6
its not valid
Can someone give the solution?
Current Student
Joined: 12 Aug 2015
Posts: 2536
Schools: Boston U '20 (M)
GRE 1: Q169 V154
If x and y are positive integers, is x/y < (x+5)/(y+5)?  [#permalink]

Show Tags

Updated on: 15 Aug 2016, 02:33
1
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 => http://magoosh.com/gmat/2012/gmat-short ... nominator/
_________________

Originally posted by stonecold on 15 Aug 2016, 01:20.
Last edited by stonecold on 15 Aug 2016, 02:33, edited 1 time in total.
Intern
Joined: 16 Nov 2016
Posts: 5
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)?  [#permalink]

Show Tags

29 Nov 2016, 11:07
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!
RSM Erasmus Moderator
Joined: 26 Mar 2013
Posts: 2373
Concentration: Operations, Strategy
Schools: Erasmus RSM "22
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)?  [#permalink]

Show Tags

03 Feb 2017, 19:49
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
Status: Preparing for GMAT!!
Joined: 11 Oct 2015
Posts: 125
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]

Show Tags

04 Feb 2017, 05:59
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.
_________________
Yours,
Siva Rama Krishna Meka
Manager
Joined: 01 Jan 2016
Posts: 52
GPA: 3.75
WE: Engineering (Energy and Utilities)
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)?  [#permalink]

Show Tags

28 Aug 2017, 23:36
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
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4605
GMAT 1: 770 Q49 V46
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)?  [#permalink]

Show Tags

12 Jan 2018, 06:33
5
Top Contributor
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.

Target question: Is x/y < (x+5)/(y+5)?

This is a great candidate for REPHRASING the target question.
Aside: We have a free video with tips on rephrasing the target question (below)

If y is a positive integer, then we can be certain that y and (y+5) are both POSITIVE. This allows us to safely multiply both sides of our inequality by y and (y+5).

Take x/y < (x+5)/(y+5) and multiply both sides by y to get: Is x < (y)(x+5)/(y+5)?
Then take x < (y)(x+5)/(y+5) and multiply both sides by (y+5) to get: Is x(y+5) < (y)(x+5)?
Expand to get: Is xy + 5x < xy + 5y?
Subtract xy from both sides to get: Is 5x < 5y?
Divide both sides by 5 to get: Is x < y?

We now have a very simple, REPHRASED target question.....
REPHRASED target question: Is x < y?

Now onto the statements!

Statement 1: y = 5
Since we have no information about x, there's no way to tell whether or not x < y.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x > y
Perfect!
If x > y then we can answer our REPHRASED target question with certainty: NO, x is definitely not less than y.
So, statement 2 is SUFFICIENT

RELATED VIDEO

_________________
Test confidently with gmatprepnow.com
Non-Human User
Joined: 09 Sep 2013
Posts: 14506
Re: If x and y are positive integers, is x/y < (x+5)/(y+5)?  [#permalink]

Show Tags

26 Mar 2020, 19:28
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] 26 Mar 2020, 19:28
Display posts from previous: Sort by