It is currently 22 Nov 2017, 17:41

### 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
Your Progress

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If 0<x<y, is y-x < 0.00005

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 07 Sep 2010
Posts: 330

Kudos [?]: 1054 [6], given: 136

If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

05 Apr 2012, 09:26
6
This post received
KUDOS
22
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

72% (01:24) correct 28% (01:33) wrong based on 501 sessions

### HideShow timer Statistics

If 0<x<y, is y-x < 0.00005

(1) x>1/60,000
(2) y<1/15,000
[Reveal] Spoiler: OA

_________________

+1 Kudos me, Help me unlocking GMAT Club Tests

Kudos [?]: 1054 [6], given: 136

Math Expert
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133073 [21], given: 12403

Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

05 Apr 2012, 16:46
21
This post received
KUDOS
Expert's post
22
This post was
BOOKMARKED
If 0<x<y, is y-x < 0.00005

Notice that $$0.00005=\frac{5}{100,000}=\frac{3}{60,000}$$, and $$\frac{1}{15,000}=\frac{4}{60,000}$$.

So, we can rewrite the question as:

If 0<x<y, is y-x<3

(1) x>1 --> if $$x=2$$ and $$y=3$$ then the answer is YES but if $$x=2$$ and $$y=5$$ the answer is NO. Not sufficient.
(2) y<4 --> if $$x=2$$ and $$y=3$$ then the answer is YES but if $$x=0.5$$ and $$y=3.5$$ the answer is NO. Not sufficient.

(1)+(2) Remember we can subtract inequalities if their signs are in opposite directions --> subtract (1) from (2): $$y-x<4-1$$ --> $$y-x<3$$. Sufficient.

Answer: C.
_________________

Kudos [?]: 133073 [21], given: 12403

Current Student
Joined: 30 Apr 2011
Posts: 15

Kudos [?]: 5 [2], given: 0

Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

05 Apr 2012, 17:57
2
This post received
KUDOS
1
This post was
BOOKMARKED
imhimanshu wrote:
If 0<x<y, is y-x < 0.00005

(1) x>1/60,000
(2) y<1/15,000

1) NS - nothing about y
2) NS - nothing about x

So it's between E and C

Is y-x < 1/20,000?
LT = less than
GT = Great than
LT 1/15,000 - GT 1/60,000 < 1/20,000. Multiply by 60,000 to simplify results in LT 4 - GT 1 < 3? Test extremes - 3.9 - 1.1 = 2.8 . YES ...sufficient. C

Kudos [?]: 5 [2], given: 0

Director
Joined: 29 Nov 2012
Posts: 866

Kudos [?]: 1454 [0], given: 543

Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

17 Jan 2013, 05:42
I have one question is this step possible for this question ( I have re written the equations in this way)

1/60000 < X
Y< 4/60000

Add both equations and then subtract you reach back to the original question and can prove sufficiency.
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Kudos [?]: 1454 [0], given: 543

Retired Moderator
Joined: 05 Jul 2006
Posts: 1749

Kudos [?]: 444 [0], given: 49

Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

21 Feb 2013, 17:01
[quote="DelSingh"]If 0<x<y, is y-x < 0.00005

(1) x>1/60,000
(2) y<1/15,000

this ain't 700 or 600-700 level question , it is way sub 600

anyways

the question is asking whether the difference between both +ve numbers x,y is very small ie. 5/100,000 = 1/20,000

obviously each alone is not suff

both

subtract 2 from 1

x-y >-1/20,000... i.e. y-x<1/20,000.....an then answer is a definite yes ...c

Kudos [?]: 444 [0], given: 49

Manager
Joined: 25 Jul 2012
Posts: 73

Kudos [?]: 121 [0], given: 137

Location: United States
Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

21 Feb 2013, 17:53
yezz wrote:
DelSingh wrote:
If 0<x<y, is y-x < 0.00005

(1) x>1/60,000
(2) y<1/15,000

this ain't 700 or 600-700 level question , it is way sub 600

anyways

the question is asking whether the difference between both +ve numbers x,y is very small ie. 5/100,000 = 1/20,000

obviously each alone is not suff

both

subtract 2 from 1

x-y >-1/20,000... i.e. y-x<1/20,000.....an then answer is a definite yes ...c

I took off the difficulty, but GMAT Prep did rate this medium level.

Anyway, I understand why the both statements are insufficient but I do not know how you combines them? What did you when you 'subtracted 2 from 1'?
_________________

If my post has contributed to your learning or teaching in any way, feel free to hit the kudos button ^_^

Kudos [?]: 121 [0], given: 137

Manager
Joined: 24 Sep 2012
Posts: 90

Kudos [?]: 171 [0], given: 3

Location: United States
Concentration: Entrepreneurship, International Business
GMAT 1: 730 Q50 V39
GPA: 3.2
WE: Education (Education)
Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

21 Feb 2013, 23:26
When you subtract 1 from 2, you get the value of y-x. However, since we know only one sided limits of these values, let's consider those values.

y-x=(1/15000)-(1/60,000)

Taking L.CM. y-x=1/20,000

y-x=0.00005

However, this just gives us the limit of the difference. Since y<1/15,000 and x>1/60,000, a bigger number on the L.H.S is being subtracted from a smaller number and hence, the actual difference will be less than 1/20,000. This is by applying concept. Let us test values for better understanding.

For e.g. the value of y could be y=1/20,000(the greater the denominator, the smaller the number and hence y>1/15000) and x=1/40,000(by similar idea)

y-x=1/20,000-1/40,000=1/40,000
1/40,000<1/20,000. Hence proved.

Hope that helps!

DelSingh wrote:
yezz wrote:
DelSingh wrote:
If 0<x<y, is y-x < 0.00005

(1) x>1/60,000
(2) y<1/15,000

this ain't 700 or 600-700 level question , it is way sub 600

anyways

the question is asking whether the difference between both +ve numbers x,y is very small ie. 5/100,000 = 1/20,000

obviously each alone is not suff

both

subtract 2 from 1

x-y >-1/20,000... i.e. y-x<1/20,000.....an then answer is a definite yes ...c

I took off the difficulty, but GMAT Prep did rate this medium level.

Anyway, I understand why the both statements are insufficient but I do not know how you combines them? What did you when you 'subtracted 2 from 1'?

Kudos [?]: 171 [0], given: 3

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7745

Kudos [?]: 17853 [15], given: 235

Location: Pune, India
Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

21 Feb 2013, 23:37
15
This post received
KUDOS
Expert's post
8
This post was
BOOKMARKED
DelSingh wrote:
If 0<x<y, is y-x < 0.00005

(1) x>1/60,000
(2) y<1/15,000

Source: GMAT Prep question pack 1

There are two ways to deal with it.

Method 1:

Is y-x < 0.00005?

We can see that both statements alone are not sufficient.

(1) x>1/60,000
(2) y<1/15,000

We know that we can add inequalities when they have the same sign ie.
a < b
c < d
then, a+c < b+d

Also, when we multiply an inequality by -1, the inequality sign flips.
x>1/60,000 implies -x < -1/60,000

You can add these two inequalities: -x < -1/60,000 and y<1/15,000 to get y-x < 1/15000 - 1/60,000
which is y-x < 1/20,000 i.e. y-x < 0.00005

Another method is to see this on the number line. Draw a number line to understand this.

0<x<y implies that x and y are both positive and x is to the left of y on the number line.
Is y-x < 0.00005 means is the distance between x and y less than .00005?

(1) x>1/60,000
means x lies to the right of 1/60,000

(2) y<1/15,000
means y lies to the left of 4/60,000

So the distance between them must be less than 4/60,000 - 1/60,000 = 3/60,000 = .00005
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17853 [15], given: 235

Intern
Joined: 20 Feb 2013
Posts: 20

Kudos [?]: 9 [1], given: 2

Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

22 Feb 2013, 00:20
1
This post received
KUDOS
If 0<x<y, is y-x < 0.00005

(1) x>1/60,000
(2) y<1/15,000

Solution: (Answer is C)

What do we know?

X is positive and Y is greater than X.

What do we need to know?

Is Y is less than 0.00005 + X?

Whenever you face a Data Sufficiency question asking Yes, No. Simply substitute and try to disprove the statement.

Statement(1):

X is greater than 1/60,000 = 0.00001666

Which does not tell any relation between X and Y

Hence it is insufficient.

Statement (2) is also insufficient as it only tells that Y is less than 0.000066
(It is very important to know the importance of converting fractions to percentage)

If we combine both the statements, we get that X is greater than 0.000016 and Y is less than 0.000066

Now the question is asking us that y-x<0.00005, to try to disprove that we need to maximize y-x and for that let us get the maximum value of y and minimum value of x.
Let us say y = 0.000065 and x = 0.000017
So the maximum difference is = 0.000065 - 0.000017 = 0.000048

Hence combining both the statements we can say that y-x will always be less than 0.000048. Hence answer is (C)
_________________

Pushpinder Gill

Kudos [?]: 9 [1], given: 2

Retired Moderator
Joined: 05 Jul 2006
Posts: 1749

Kudos [?]: 444 [1], given: 49

Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

22 Feb 2013, 04:29
1
This post received
KUDOS
DelSingh wrote:
yezz wrote:
DelSingh wrote:
If 0<x<y, is y-x < 0.00005

(1) x>1/60,000
(2) y<1/15,000

this ain't 700 or 600-700 level question , it is way sub 600

anyways

the question is asking whether the difference between both +ve numbers x,y is very small ie. 5/100,000 = 1/20,000

obviously each alone is not suff

both

subtract 2 from 1

x-y >-1/20,000... i.e. y-x<1/20,000.....an then answer is a definite yes ...c

I took off the difficulty, but GMAT Prep did rate this medium level.

Anyway, I understand why the both statements are insufficient but I do not know how you combines them? What did you when you 'subtracted 2 from 1'?

for 2 ineq to subtract they have to be with opposit direction , one of them is bigger than and 2nd is smaller than and what u do is keep the sign ( direction in terms of bigger than or smaller than) of the ineq from which u subtract the 2nd ....

Another way of seeing it is as follows

if we subtract 1 from 2

is like flipping the sign of 1 and adding it to the 2nd , thus

x>1/60,000 becomes -x<-1/60,000...............1 after changing direction ( flipping the sign)

now add 2 to 1

y>1/15,000........2

y+ (-x) > 1/15,000 + (-1/60,000).................. simplify

y-x > 1/20,000

Kudos [?]: 444 [1], given: 49

Current Student
Joined: 02 May 2012
Posts: 8

Kudos [?]: 5 [0], given: 61

Location: Argentina
Concentration: General Management, Strategy
GMAT 1: 700 Q47 V42
WE: Corporate Finance (Manufacturing)
Re: If 0<x<y, is y-x<0.00005? [#permalink]

### Show Tags

26 Mar 2013, 07:11
Since they are asking if "y-x<0.00005"; first I will try if the statement 2 is enough : Is y<0.00005 or y<1/20000 ?

y = 1/15000 (bigger that 1/20000) ; therefore it´s not enough,

I will resolve both sides of the equation now:

y-x = 1/15000 - 1/60000 = 3/60000 = 1/20000
0.00005 = 5/100000 = 1 /20000

Therefore you need both statements. Answer C

Kudos [?]: 5 [0], given: 61

Manager
Joined: 21 Jul 2012
Posts: 68

Kudos [?]: 8 [0], given: 32

Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

30 Mar 2013, 16:02
In relation to this question, I have a basic scientific notation question, how would you write the sci notation of 1 / 20,000?

Kudos [?]: 8 [0], given: 32

VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1120

Kudos [?]: 2380 [1], given: 219

Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

30 Mar 2013, 16:24
1
This post received
KUDOS
jmuduke08 wrote:
In relation to this question, I have a basic scientific notation question, how would you write the sci notation of 1 / 20,000?

$$\frac{1}{20000}=\frac{1}{2}*\frac{1}{10000}=0.5*10^{-4}=5*10^{-5}$$
_________________

It is beyond a doubt that all our knowledge that begins with experience.

Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]

Kudos [?]: 2380 [1], given: 219

Manager
Joined: 21 Jul 2012
Posts: 68

Kudos [?]: 8 [0], given: 32

Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

30 Mar 2013, 16:26
Zarrolou wrote:
jmuduke08 wrote:
In relation to this question, I have a basic scientific notation question, how would you write the sci notation of 1 / 20,000?

$$\frac{1}{20000}=\frac{1}{2}*\frac{1}{10000}=0.5*10^-^4$$

ahh thank you, I was multiplying .5 by 10,000 instead of 1/10,000 and knew it wasnt possible

Kudos [?]: 8 [0], given: 32

Tutor
Joined: 20 Apr 2012
Posts: 100

Kudos [?]: 340 [4], given: 36

Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE: Education (Education)
Re: If 0 < x < y , is y - x < 0.00005 ? [#permalink]

### Show Tags

27 Apr 2013, 02:58
4
This post received
KUDOS
1
This post was
BOOKMARKED
(1) Insufficient. We know nothing about $$y$$.
(2) Insufficient. We know nothing about $$x$$.

(1)+(2) Sufficient.
We know that $$y<\frac{1}{15,000}$$ and $$-x<-\frac{1}{60,000}$$. If we add this two inequalities we will get:
$$y-x<\frac{1}{15,000}-\frac{1}{60,000}=\frac{1}{20,000}=0.00005$$

The correct answer is C.
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos:)

Kudos [?]: 340 [4], given: 36

Senior Manager
Joined: 15 Aug 2013
Posts: 301

Kudos [?]: 83 [0], given: 23

Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

05 Dec 2014, 17:45
Bunuel wrote:
If 0<x<y, is y-x < 0.00005

Notice that $$0.00005=\frac{5}{100,000}=\frac{3}{60,000}$$, and $$\frac{1}{15,000}=\frac{4}{60,000}$$.

So, we can rewrite the question as:

If 0<x<y, is y-x<3

(1) x>1 --> if $$x=2$$ and $$y=3$$ then the answer is YES but if $$x=2$$ and $$y=5$$ the answer is NO. Not sufficient.
(2) y<4 --> if $$x=2$$ and $$y=3$$ then the answer is YES but if $$x=0.5$$ and $$y=3.5$$ the answer is NO. Not sufficient.

(1)+(2) Remember we can subtract inequalities if their signs are in opposite directions --> subtract (1) from (2): $$y-x<4-1$$ --> $$y-x<3$$. Sufficient.

Answer: C.

Hi Bunuel,

This is great. I actually went the long division route and it took quite some time.

Can you suggest similar problems where we manipulate fractions/decimals as such?

I clicked on the tab on the top right but it just let me to regular inequalities problems.

Thanks,

Kudos [?]: 83 [0], given: 23

Intern
Joined: 30 Mar 2016
Posts: 1

Kudos [?]: [0], given: 0

Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

03 May 2016, 18:27
After viewing the responses, I think there's one potential twist where the GMAT creators could make this question harder.

Many posters have been saying that both (1) and (2) are obviously insufficient because they say nothing about the other variable. However, we do know that both x and y are greater than 0 and that y is greater than x. Were y to be less than 3/60,000, then (2) would be sufficient as x still has to be greater than 0 and therefore y-x would be greater than 3/60,000.

Please let me know if I'm thinking about this right!

Kudos [?]: [0], given: 0

Intern
Joined: 03 May 2014
Posts: 14

Kudos [?]: [0], given: 3

Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

30 Oct 2017, 04:33
Bunuel wrote:
If 0<x<y, is y-x < 0.00005

Notice that $$0.00005=\frac{5}{100,000}=\frac{3}{60,000}$$, and $$\frac{1}{15,000}=\frac{4}{60,000}$$.

So, we can rewrite the question as:

If 0<x<y, is y-x<3

(1) x>1 --> if $$x=2$$ and $$y=3$$ then the answer is YES but if $$x=2$$ and $$y=5$$ the answer is NO. Not sufficient.
(2) y<4 --> if $$x=2$$ and $$y=3$$ then the answer is YES but if $$x=0.5$$ and $$y=3.5$$ the answer is NO. Not sufficient.

(1)+(2) Remember we can subtract inequalities if their signs are in opposite directions --> subtract (1) from (2): $$y-x<4-1$$ --> $$y-x<3$$. Sufficient.

Answer: C.

How do you know what sign the combined inequality takes when combining two inequalities with different signs?

Kudos [?]: [0], given: 3

Math Expert
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133073 [0], given: 12403

Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

30 Oct 2017, 04:38
Expert's post
1
This post was
BOOKMARKED
Edofarmer wrote:
Bunuel wrote:
If 0<x<y, is y-x < 0.00005

Notice that $$0.00005=\frac{5}{100,000}=\frac{3}{60,000}$$, and $$\frac{1}{15,000}=\frac{4}{60,000}$$.

So, we can rewrite the question as:

If 0<x<y, is y-x<3

(1) x>1 --> if $$x=2$$ and $$y=3$$ then the answer is YES but if $$x=2$$ and $$y=5$$ the answer is NO. Not sufficient.
(2) y<4 --> if $$x=2$$ and $$y=3$$ then the answer is YES but if $$x=0.5$$ and $$y=3.5$$ the answer is NO. Not sufficient.

(1)+(2) Remember we can subtract inequalities if their signs are in opposite directions --> subtract (1) from (2): $$y-x<4-1$$ --> $$y-x<3$$. Sufficient.

Answer: C.

How do you know what sign the combined inequality takes when combining two inequalities with different signs?

ADDING/SUBTRACTING INEQUALITIES

1. You can only add inequalities when their signs are in the same direction:

If $$a>b$$ and $$c>d$$ (signs in same direction: $$>$$ and $$>$$) --> $$a+c>b+d$$.
Example: $$3<4$$ and $$2<5$$ --> $$3+2<4+5$$.

2. You can only apply subtraction when their signs are in the opposite directions:

If $$a>b$$ and $$c<d$$ (signs in opposite direction: $$>$$ and $$<$$) --> $$a-c>b-d$$ (take the sign of the inequality you subtract from).
Example: $$3<4$$ and $$5>1$$ --> $$3-5<4-1$$.

Check for more the links below:
Inequalities Made Easy!
_________________

Kudos [?]: 133073 [0], given: 12403

Intern
Joined: 03 May 2014
Posts: 14

Kudos [?]: [0], given: 3

Re: If 0<x<y, is y-x < 0.00005 [#permalink]

### Show Tags

30 Oct 2017, 09:56
Bunuel wrote:
Edofarmer wrote:
Bunuel wrote:
If 0<x<y, is y-x < 0.00005

Notice that $$0.00005=\frac{5}{100,000}=\frac{3}{60,000}$$, and $$\frac{1}{15,000}=\frac{4}{60,000}$$.

So, we can rewrite the question as:

If 0<x<y, is y-x<3

(1) x>1 --> if $$x=2$$ and $$y=3$$ then the answer is YES but if $$x=2$$ and $$y=5$$ the answer is NO. Not sufficient.
(2) y<4 --> if $$x=2$$ and $$y=3$$ then the answer is YES but if $$x=0.5$$ and $$y=3.5$$ the answer is NO. Not sufficient.

(1)+(2) Remember we can subtract inequalities if their signs are in opposite directions --> subtract (1) from (2): $$y-x<4-1$$ --> $$y-x<3$$. Sufficient.

Answer: C.

How do you know what sign the combined inequality takes when combining two inequalities with different signs?

ADDING/SUBTRACTING INEQUALITIES

1. You can only add inequalities when their signs are in the same direction:

If $$a>b$$ and $$c>d$$ (signs in same direction: $$>$$ and $$>$$) --> $$a+c>b+d$$.
Example: $$3<4$$ and $$2<5$$ --> $$3+2<4+5$$.

2. You can only apply subtraction when their signs are in the opposite directions:

If $$a>b$$ and $$c<d$$ (signs in opposite direction: $$>$$ and $$<$$) --> $$a-c>b-d$$ (take the sign of the inequality you subtract from).
Example: $$3<4$$ and $$5>1$$ --> $$3-5<4-1$$.

Check for more the links below:
Inequalities Made Easy!

Thanks for the clarification

Kudos [?]: [0], given: 3

Re: If 0<x<y, is y-x < 0.00005   [#permalink] 30 Oct 2017, 09:56
Display posts from previous: Sort by

# If 0<x<y, is y-x < 0.00005

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.