Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 07 Sep 2010
Posts: 289

If 0<x<y, is yx < 0.00005
[#permalink]
Show Tags
05 Apr 2012, 09:26
Question Stats:
70% (01:24) correct 30% (01:27) wrong based on 624 sessions
HideShow timer Statistics
If 0<x<y, is yx < 0.00005 (1) x>1/60,000 (2) y<1/15,000
Official Answer and Stats are available only to registered users. Register/ Login.




GMAT Club Legend
Joined: 16 Oct 2010
Posts: 8128
Location: Pune, India

Re: If 0<x<y, is yx < 0.00005
[#permalink]
Show Tags
21 Feb 2013, 23:37
DelSingh wrote: If 0<x<y, is yx < 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 yx < 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 yx < 1/15000  1/60,000 which is yx < 1/20,000 i.e. yx < 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 yx < 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 Private Tutor for GMAT Contact: bansal.karishma@gmail.com




Tutor
Joined: 20 Apr 2012
Posts: 99
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
(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: \(yx<\frac{1}{15,000}\frac{1}{60,000}=\frac{1}{20,000}=0.00005\) The correct answer is C.
_________________
I'm happy, if I make math for you slightly clearer And yes, I like kudos:)




Math Expert
Joined: 02 Sep 2009
Posts: 47112

Re: If 0<x<y, is yx < 0.00005
[#permalink]
Show Tags
05 Apr 2012, 16:46
If 0<x<y, is yx < 0.00005Notice 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 yx<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): \(yx<41\) > \(yx<3\). Sufficient. Answer: C.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 30 Apr 2011
Posts: 15

Re: If 0<x<y, is yx < 0.00005
[#permalink]
Show Tags
05 Apr 2012, 17:57
imhimanshu wrote: If 0<x<y, is yx < 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 yx < 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



Director
Joined: 29 Nov 2012
Posts: 818

Re: If 0<x<y, is yx < 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/gmatprepsoftwareanalysisandwhatifscenarios146146.html



Manager
Joined: 25 Jul 2012
Posts: 70
Location: United States

Re: If 0<x<y, is yx < 0.00005
[#permalink]
Show Tags
21 Feb 2013, 17:53
yezz wrote: DelSingh wrote: If 0<x<y, is yx < 0.00005
(1) x>1/60,000 (2) y<1/15,000
this ain't 700 or 600700 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
xy >1/20,000... i.e. yx<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 ^_^



Manager
Joined: 24 Sep 2012
Posts: 85
Location: United States
Concentration: Entrepreneurship, International Business
GPA: 3.2
WE: Education (Education)

Re: If 0<x<y, is yx < 0.00005
[#permalink]
Show Tags
21 Feb 2013, 23:26
When you subtract 1 from 2, you get the value of yx. However, since we know only one sided limits of these values, let's consider those values. yx=(1/15000)(1/60,000) Taking L.CM. yx=1/20,000 yx=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) yx=1/20,0001/40,000=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 yx < 0.00005
(1) x>1/60,000 (2) y<1/15,000
this ain't 700 or 600700 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
xy >1/20,000... i.e. yx<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'?



Intern
Joined: 20 Feb 2013
Posts: 20

Re: If 0<x<y, is yx < 0.00005
[#permalink]
Show Tags
22 Feb 2013, 00:20
If 0<x<y, is yx < 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 yx<0.00005, to try to disprove that we need to maximize yx 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 yx will always be less than 0.000048. Hence answer is (C)
_________________
Pushpinder Gill



Retired Moderator
Joined: 05 Jul 2006
Posts: 1734

Re: If 0<x<y, is yx < 0.00005
[#permalink]
Show Tags
22 Feb 2013, 04:29
DelSingh wrote: yezz wrote: DelSingh wrote: If 0<x<y, is yx < 0.00005
(1) x>1/60,000 (2) y<1/15,000
this ain't 700 or 600700 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
xy >1/20,000... i.e. yx<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 yx > 1/20,000



Manager
Joined: 21 Jul 2012
Posts: 66

Re: If 0<x<y, is yx < 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?



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1098
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

If 0<x<y, is yx < 0.00005
[#permalink]
Show Tags
30 Mar 2013, 16:24
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 III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Manager
Joined: 21 Jul 2012
Posts: 66

Re: If 0<x<y, is yx < 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



Intern
Joined: 03 May 2014
Posts: 14

Re: If 0<x<y, is yx < 0.00005
[#permalink]
Show Tags
30 Oct 2017, 04:33
Bunuel wrote: If 0<x<y, is yx < 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 yx<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): \(yx<41\) > \(yx<3\). Sufficient.
Answer: C. How do you know what sign the combined inequality takes when combining two inequalities with different signs?



Math Expert
Joined: 02 Sep 2009
Posts: 47112

Re: If 0<x<y, is yx < 0.00005
[#permalink]
Show Tags
30 Oct 2017, 04:38
Edofarmer wrote: Bunuel wrote: If 0<x<y, is yx < 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 yx<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): \(yx<41\) > \(yx<3\). Sufficient.
Answer: C. How do you know what sign the combined inequality takes when combining two inequalities with different signs? ADDING/SUBTRACTING INEQUALITIES1. 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 \(<\)) > \(ac>bd\) ( take the sign of the inequality you subtract from). Example: \(3<4\) and \(5>1\) > \(35<41\). Check for more the links below: Inequalities Made Easy!
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 01 Oct 2017
Posts: 3

Re: If 0<x<y, is yx < 0.00005
[#permalink]
Show Tags
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



Intern
Joined: 15 Dec 2016
Posts: 8
Location: India
GPA: 3.5
WE: Marketing (Real Estate)

Re: If 0<x<y, is yx < 0.00005
[#permalink]
Show Tags
24 Jun 2018, 00:11
VeritasPrepKarishma wrote: DelSingh wrote: If 0<x<y, is yx < 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 yx < 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 yx < 1/15000  1/60,000 which is yx < 1/20,000 i.e. yx < 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 yx < 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 yx=0.00005 That gives answer as NO
_________________
GEARING UP FOR THE GMAT RETAKE.




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






