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Is 1/(x-y) < (y - x) ?

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Is 1/(x-y) < (y - x) ? [#permalink] New post 15 Jan 2012, 05:26
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Is 1/(x-y) < (y - x) ?

(1) y is positive.
(2) x is negative.
[Reveal] Spoiler: OA
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Re: Inequality...involving reciprocals [#permalink] New post 15 Jan 2012, 05:35
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Apoorva81 wrote:
Is 1/x-y < y - x ?

(1) y is positive.
(2) x is negative.

can you please provide detailed explanation..??


Is \(\frac{1}{x-y}<y - x\)?

(1) \(y\) is positive, clearly insufficient, as no info about \(x\);
(2) \(x\) is negative, also insufficient, as no info about \(y\);

(1)+(2) We have \(y=positive\) and \(x=negative\), thus \(y>x\) (this can be rewritten as \(y-x>0\) or \(0>x-y\)). Now: \(LHS=\frac{1}{x-y}=\frac{1}{negative}=negative\), and \(RHS=y-x=positive\) thus \(\frac{1}{x-y}=negative<y-x=positive\). Sufficient.

Answer: C.
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Re: Is 1/x-y<y-x? (1) y is positive (2) x is negative [#permalink] New post 15 Jan 2012, 09:07
Is 1/(x-y) < y - x ?

1
______ - (y-x) < 0
(x-y)


(1) y is positive.
(2) x is negative.

From 1 and 2 -

(x-y) is always negative.
(y-x) will be positive
-(y-x) will be negative

Adding 2 negatives = -ve

If it were 1/(x-y) < x - y then answer would have been E
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Re: Is 1/x-y<y-x? (1) y is positive (2) x is negative [#permalink] New post 09 May 2012, 16:18
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Slightly different approach, I hope everyone can see the attached images with solutions.

Dabral


Apoorva81 wrote:
Is 1/x-y < y - x ?

(1) y is positive.
(2) x is negative.

can you please provide detailed explanation..??

Attachments

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image1.png [ 57.59 KiB | Viewed 1916 times ]

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image2.png [ 44.46 KiB | Viewed 1916 times ]


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Re: Inequalities [#permalink] New post 02 Apr 2013, 19:52
In order to separate your x's and y's from each other, you need to know which term is larger. This is because you need to know whether x-y or y-x is negative (one of them will be, unless they are equal). Taking both statements together, you know that the two variables are not equal, and you can manipulate the inequality, keeping in mind that you need to flip the sign when multiplying or dividing by a negative number.
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Re: Inequalities [#permalink] New post 02 Apr 2013, 19:53
I explained it in kind of a backwards way. The first thing you need to know in that problem is whether x and y are equal. No single statement tells you that.

Sorry for the double post, but it seems I can't edit my previous post while viewing the forum with Tapatalk.

Sent from my HTC Glacier using Tapatalk 2
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Re: Is 1/(x-y) < (y - x) ? [#permalink] New post 22 Feb 2014, 13:15
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Re: Inequality...involving reciprocals [#permalink] New post 09 May 2014, 07:38
Bunuel wrote:
Apoorva81 wrote:
Is 1/x-y < y - x ?

(1) y is positive.
(2) x is negative.

can you please provide detailed explanation..??


Is \(\frac{1}{x-y}<y - x\)?

(1) \(y\) is positive, clearly insufficient, as no info about \(x\);
(2) \(x\) is negative, also insufficient, as no info about \(y\);

(1)+(2) We have \(y=positive\) and \(x=negative\), thus \(y>x\) (this can be rewritten as \(y-x>0\) or \(0>x-y\)). Now: \(LHS=\frac{1}{x-y}=\frac{1}{negative}=negative\), and \(RHS=y-x=positive\) thus \(\frac{1}{x-y}=negative<y-x=positive\). Sufficient.

Answer: C.



Why can't we do the following rephrase?

1/(x-y) < (y-x)

-1/(y-x) < (y-x)

-1 < (y-x)^2

since the RHS is a square, irrespective of x and y values the equation is satisfied.
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Re: Inequality...involving reciprocals [#permalink] New post 09 May 2014, 08:25
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rishiroadster wrote:
Bunuel wrote:
Apoorva81 wrote:
Is 1/x-y < y - x ?

(1) y is positive.
(2) x is negative.

can you please provide detailed explanation..??


Is \(\frac{1}{x-y}<y - x\)?

(1) \(y\) is positive, clearly insufficient, as no info about \(x\);
(2) \(x\) is negative, also insufficient, as no info about \(y\);

(1)+(2) We have \(y=positive\) and \(x=negative\), thus \(y>x\) (this can be rewritten as \(y-x>0\) or \(0>x-y\)). Now: \(LHS=\frac{1}{x-y}=\frac{1}{negative}=negative\), and \(RHS=y-x=positive\) thus \(\frac{1}{x-y}=negative<y-x=positive\). Sufficient.

Answer: C.



Why can't we do the following rephrase?

1/(x-y) < (y-x)

-1/(y-x) < (y-x)

-1 < (y-x)^2

since the RHS is a square, irrespective of x and y values the equation is satisfied.


The point is that we don't know whether y-x is positive or negative. If it's positive, then yes we'd have -1 < (y-x)^2 but if it's negative, then we'd have -1 > (y-x)^2 (flip the sign when multiplying by negative value).

Never multiply (or reduce) an inequality by variable (or by an expression with variable) if you don't know the sign of it or are not certain that variable (or expression with variable) doesn't equal to zero.
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Is 1/(x-y) < (y-x) ? [#permalink] New post 09 Aug 2014, 00:53
Is 1/(x-y) < (y-x) ?


1) x is +ve
2) y is -ve



I took a very long time to solve this :(

Does anyone know a shortcut? or a simpler method?
:|

Source: 4gmat
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Re: Is 1/(x-y) < (y-x) ? [#permalink] New post 09 Aug 2014, 01:15
alphonsa wrote:
Is 1/(x-y) < (y-x) ?


1) x is +ve
2) y is -ve



I took a very long time to solve this :(

Does anyone know a shortcut? or a simpler method?
:|

Source: 4gmat


The question can be re written as

\(\frac{1}{(x-y)} +( x-y )<0\)

Or
\(\frac{1+ (x-y)^2}{(x-y)} <0\)
For the expression to be less than zero,numerator and denominator should be of opp sign
Now\((x-y)^2\geq{0}\)

So numerator is positive ,therefore if denominator is negative then answer to the question is yes or else no

st 1 x is positive let x=1 and y=-10 then x-y=9answer is no
But if x=1 and y=3 then answer to the question is yes

St 1 not sufficient .. Option A and D ruled out

St 2 y is negative
If y= -3 and x =-8 then ans to the question is yes
If y=-3 and x =8 then answer to the q. Is no

St 2 alone not sufficient

Combining we see that x-y=+ve

So ans is C
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Re: Is 1/(x-y) < (y-x) ? [#permalink] New post 09 Aug 2014, 01:54
With the way you put it, this question seemed like a below 500 question :\

I don't know why I took so long to decipher it was option C .
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Re: Is 1/(x-y) < (y-x) ? [#permalink] New post 09 Aug 2014, 02:05
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WoundedTiger wrote:

The question can be re written as

\(\frac{1}{(x-y)} +( x-y )<0\)

Or
\(\frac{1+ (x-y)^2}{(x-y)} <0\)
For the expression to be less than zero,numerator and denominator should be of opp sign
Now\((x-y)^2\geq{0}\)

So numerator is positive ,therefore if denominator is negative then answer to the question is yes or else no

st 1 x is positive let x=1 and y=-10 then x-y=9answer is no
But if x=1 and y=3 then answer to the question is yes

St 1 not sufficient .. Option A and D ruled out

St 2 y is negative
If y= -3 and x =-8 then ans to the question is yes
If y=-3 and x =8 then answer to the q. Is no

St 2 alone not sufficient

Combining we see that x-y=+ve

So ans is C


WoundedTiger, it's better to do one step more. In data sufficiency if you have very simple statements you need to understand what you are looking for.

So, a little bit different solution:

The question can be re written as

\(\frac{1}{(x-y)} +( x-y )<0\)

Or
\(\frac{1+ (x-y)^2}{(x-y)} <0\)

Since \(1+(x-y)^2>0\), denominator must be negative: \(x-y<0\) or \(x<y\). Hence, we need to find: is \(x\) less than \(y\)?

(1) Don't know anything about \(y\). Insufficient
(2) Don't know anything about \(x\). Insufficient

(1)+(2) Since \(x>0\) and \(y<0\), we have \(x>y\). Sufficient

The correct answer is C.
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Re: Is 1/(x-y) < (y-x) ? [#permalink] New post 09 Aug 2014, 02:31
alphonsa wrote:
With the way you put it, this question seemed like a below 500 question :\

I don't know why I took so long to decipher it was option C .



It happens to the best of people especially if the question is done during exam time....
One more thing..I think you need to look at these links for books for your preparation

best-gmat-math-prep-books-reviews-recommendations-77291-180.html
gmat-prep-software-analysis-and-what-if-scenarios-146146.html#p1171760
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Re: Is 1/(x-y) < (y-x) ? [#permalink] New post 09 Aug 2014, 03:43
smyarga wrote:
WoundedTiger wrote:

The question can be re written as

\(\frac{1}{(x-y)} +( x-y )<0\)

Or
\(\frac{1+ (x-y)^2}{(x-y)} <0\)
For the expression to be less than zero,numerator and denominator should be of opp sign
Now\((x-y)^2\geq{0}\)

So numerator is positive ,therefore if denominator is negative then answer to the question is yes or else no

st 1 x is positive let x=1 and y=-10 then x-y=9answer is no
But if x=1 and y=3 then answer to the question is yes

St 1 not sufficient .. Option A and D ruled out

St 2 y is negative
If y= -3 and x =-8 then ans to the question is yes
If y=-3 and x =8 then answer to the q. Is no

St 2 alone not sufficient

Combining we see that x-y=+ve

So ans is C


WoundedTiger, it's better to do one step more. In data sufficiency if you have very simple statements you need to understand what you are looking for.

So, a little bit different solution:

The question can be re written as

\(\frac{1}{(x-y)} +( x-y )<0\)

Or
\(\frac{1+ (x-y)^2}{(x-y)} <0\)

Since \(1+(x-y)^2>0\), denominator must be negative: \(x-y<0\) or \(x<y\). Hence, we need to find: is \(x\) less than \(y\)?

(1) Don't know anything about \(y\). Insufficient
(2) Don't know anything about \(x\). Insufficient

(1)+(2) Since \(x>0\) and \(y<0\), we have \(x>y\). Sufficient

The correct answer is C.


I tried this way.

we have 1/(x-y) < y-x

1) says x is positive, we have no value of Y, not sufficient

2) says y is negative, no value of x defined, not sufficient.

1+2 , x is +ve and y is -ve => 1/+ve < -ve => +ve < -ve, not possible.

Answer is C
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Re: Is 1/(x-y) < (y - x) ? [#permalink] New post 12 Aug 2014, 06:17
Expert's post
alphonsa wrote:
Is 1/(x-y) < (y-x) ?


1) x is +ve
2) y is -ve




I took a very long time to solve this :(

Does anyone know a shortcut? or a simpler method?
:|

Source: 4gmat


Merging topics. Please refer to the discussion above.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1, and 5. Thank you.


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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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.


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Re: Is 1/(x-y) < (y - x) ?   [#permalink] 12 Aug 2014, 06:17
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