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If 0<x<y, is y-x < 0.00005 [#permalink]
 05 Apr 2012, 09:26
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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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Re: If 0<x<y, is y-x < 0.00005 [#permalink]
05 Apr 2012, 16:46
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Re: If 0<x<y, is y-x < 0.00005 [#permalink]
21 Feb 2013, 23:37
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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]
22 Feb 2013, 00:20
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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)
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Re: If 0<x<y, is y-x < 0.00005 [#permalink]
22 Feb 2013, 04:29
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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
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Re: If 0<x<y, is y-x < 0.00005 [#permalink]
30 Mar 2013, 16:24
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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]
05 Apr 2012, 17:57
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]
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]
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
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Re: If 0<x<y, is y-x < 0.00005 [#permalink]
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]
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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Re: If 0<x<y, is y-x < 0.00005 [#permalink]
02 Mar 2013, 11:07
I want to follow this posting.
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Re: If 0<x<y, is y-x<0.00005? [#permalink]
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
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Re: If 0<x<y, is y-x < 0.00005 [#permalink]
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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Re: If 0<x<y, is y-x < 0.00005 [#permalink]
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^-^4ahh thank you, I was multiplying .5 by 10,000 instead of 1/10,000 and knew it wasnt possible
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If 0 < x < y , is y - x < 0.00005 ? [#permalink]
26 Apr 2013, 21:27
If 0 < x < y , is y - x < 0.00005 ?
(1) x > \frac{1}{60,000}
(2)y < \frac{1}{15000}
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Re: If 0 < x < y , is y - x < 0.00005 ? [#permalink]
27 Apr 2013, 02:58
(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}=0.00005The correct answer is C.
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Re: If 0 < x < y , is y - x < 0.00005 ? [#permalink]
27 Apr 2013, 03:44
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Re: If 0 < x < y , is y - x < 0.00005 ?
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