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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.

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

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)

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
_________________

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)

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

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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:)

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.

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!

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?

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 \(5>1\) --> \(3-5<4-1\).

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 \(5>1\) --> \(3-5<4-1\).