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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.

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 _________________

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

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27 Apr 2013, 02:58

2

This post received KUDOS

(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:)

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

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) _________________

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)

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 ^_^

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)

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. _________________

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.

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.

In the beginning of your explanation, how do you get 1/15,000 and 4/60,000 ?

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

well explained. You got KUDO for this. _________________

Discipline does not mean control. Discipline means having the sense to do exactly what is needed.

gmatclubot

Re: If 0<x<y, is y-x < 0.00005
[#permalink]
21 Dec 2015, 10:14

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