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

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Senior Manager
Joined: 07 Sep 2010
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If 0<x<y, is y-x < 0.00005  [#permalink]

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05 Apr 2012, 09:26
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35% (medium)

Question Stats:

70% (01:24) correct 30% (01:27) wrong based on 624 sessions

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

(1) x>1/60,000
(2) y<1/15,000
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Joined: 16 Oct 2010
Posts: 8128
Location: Pune, India
Re: If 0<x<y, is y-x < 0.00005  [#permalink]

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21 Feb 2013, 23:37
17
8
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
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Re: If 0 < x < y , is y - x < 0.00005 ?  [#permalink]

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27 Apr 2013, 02:58
6
(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:
$$y-x<\frac{1}{15,000}-\frac{1}{60,000}=\frac{1}{20,000}=0.00005$$

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Posts: 47112
Re: If 0<x<y, is y-x < 0.00005  [#permalink]

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05 Apr 2012, 16:46
25
23
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.

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

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05 Apr 2012, 17:57
3
1
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
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Re: If 0<x<y, is y-x < 0.00005  [#permalink]

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

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

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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'?
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Joined: 20 Feb 2013
Posts: 20
Re: If 0<x<y, is y-x < 0.00005  [#permalink]

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

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

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

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22 Feb 2013, 04:29
1
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)

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

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

y-x > 1/20,000
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Re: If 0<x<y, is y-x < 0.00005  [#permalink]

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

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30 Mar 2013, 16:24
1
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?

$$\frac{1}{20000}=\frac{1}{2}*\frac{1}{10000}=0.5*10^{-4}=5*10^{-5}$$
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Re: If 0<x<y, is y-x < 0.00005  [#permalink]

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

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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.

How do you know what sign the combined inequality takes when combining two inequalities with different signs?
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Posts: 47112
Re: If 0<x<y, is y-x < 0.00005  [#permalink]

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30 Oct 2017, 04:38
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.

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

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

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22 May 2018, 04:48
This question deals with advanced knowledge of decimals and fractions.

X < Y → First Condition

Statement 1 - X is greater than 1/60000 → 1/6 = 0.16
1/60 → 0.016
1/600 → 0.0016
1/6000 → 0.00016
1/60000 → 0.000016

But we don’t have the value of “y”

Statement 2 - y < 1/15000

1/15 = ½ of 1/7 → 0.07
1/150 → 0.007
1/1500 → 0.00007
1/15000 → 0.000007

If the value of Y is to be greater than 0.007 then the value can be 0.7, 0.1, 1 upto infinitely positive numbers

But we still don’t have the value of “x”

Combining 1 + 2 we can easily conclude that the difference will be greater/lesser
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Re: If 0<x<y, is y-x < 0.00005  [#permalink]

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24 Jun 2018, 00:11
VeritasPrepKarishma wrote:
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

WHAT IF . . .
y= 0.000067 and x= 0.000017
y-x=0.00005

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Re: If 0<x<y, is y-x < 0.00005 &nbs [#permalink] 24 Jun 2018, 00:11
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