HOT Competition: If x is not equal to y, is 1/(x - y) xy?

Question

If x is not equal to y, is  \frac{1}{x - y} > xy ?

(1)  \frac{x}{y }> 1

(2)  x > y

Archit3110 · Answer

Given X is not equal to y
Target is 1> XY(X-Y)
#1
X>y
Pair possible (2,1);(-1,-2);(3/2,1/2) We get yes and no to our target Insufficient
#2 X>y
Same as 1
Insufficient
From 1&2
We do not get any common value
Insufficient
IMO E

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p05eid0n · Answer

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AliciaSierra · Answer

X is not equal to Y.

\frac{1}{x-y} >xy

Option 1.

\frac{x}{y} >1  
 x>y

Let's take x=10, y =8 then Is  \frac{1}{10-8} > 10*8  Ans is No

Let's take x=.9 and y= .1 then Is  \frac{1}{.9-.1} > .09  Ans is Yes

We do not have certain answer. Eliminate option A, D

option 2.

x>y  is similar to option 1. Eliminate option B.

combining option 1 and 2 doesn't give additional information, so eliminate option C.

Remaining Answer is E   .

GMATinsight · Answer

Question: If x is not equal to y, is 1/x−y>xy?

STatement 1: x/y>1

i.e.x and y have same sign and lxl > lyl

CAse 1: x = 1.1 and y = 1, 1/x−y>xy
CAse 2: x = 3 and y = 2, 1/x−y<xy

NOT SUFFICIENT

STatement 2: x>y

CAse 1: x = 1.1 and y = 1, 1/x−y>xy
CAse 2: x = 3 and y = 2, 1/x−y<xy

NOT SUFFICIENT

COmbining the statements

CAse 1: x = 1.1 and y = 1, 1/x−y>xy
CAse 2: x = 3 and y = 2, 1/x−y<xy

NOT SUFFICIENT

Answer: Option E

amlanbanerjee · Answer

IMO Anser Choice E

Statement1  : 
Now when x>y two acses are possible 
Case 1a : both x and y >1. Note that x is also positive since it is greatre than y and y itself is positive
 Here the question stem will never hold true
Case 1 b: Both X and Y > 0 but less than 1 . In this case the question stem will hld true

Since We have already found Insufficiency with Statement 1 we are not dealing with Case 2 which itself has few subcases

Statement 2: 
 X>y . here Case 1a and case 1 b from statement 1 be referred(since the condition is same) to prove insufficiency of statememt 2

Combining 1 +2  
Case 1a and Case 1b both hold true . Thus  INSUFFICIENT

AlessandraReyes · Answer

Is a Yes or No question, plug numbers in different scenarios to find out

(1) Positives numbers higher than 1: If x=2 and y=1 then 1>2, so the answer is no.
Positives numbers higher between 0 and 1: If x=1/2 and y=1/4 then 4>1/8, so the answer is yes.
Two different answers so not sufficient.

(2) Here happens the same, if x=2 and y=1 then 1>2, so the answer is no and if x=1/2 and y=1/4 then 4>1/8, the answer is yes.
Two different answers so not sufficient.

(1) and (2) still not sufficient.

Crytiocanalyst · Answer

(1)  \frac{x}{y }> 1  
let x= 4 and y=2 then no

when x=1 , y=1/2 , yes

Clearly insufficient

(2)  x > y 
Similar line of reasoning as A

Even when 1 and 2 is combined we can use similar reasoning therefore IMO E

HOT Competition: If x is not equal to y, is 1/(x - y) > xy?

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