If x and y cannot be equal to zero, is x/y y/x ?

Question

Tough and Tricky questions: Inequalities.

If x and y cannot be equal to zero, is x/y > y/x ?

(1) x > y
(2) xy > 0

Source: Chili Hot GMAT

desaichinmay22 · Answer

statement 1 :- x > y

let x=3 and y=1
is x/y > y/x ? ..... True

let x=-1 and y=-3
is x/y > y/x ? ..... False

statement is insufficient.

statement 2 :- xy > 0

let x=3 and y=1
is x/y > y/x ? ..... True

let x=-1 and y=-3
is x/y > y/x ? ..... False

statement is insufficient.

1+2 combined,

let x=3 and y=1
is x/y > y/x ? ..... True

let x=-1 and y=-3
is x/y > y/x ? ..... False

statements are insufficient.

Ans - E

LighthousePrep · Answer

STATEMENT 1: I create two scenarios that match the condition of Statement 1 to see how they would answer the question in the premise. Scenario 1: If x = 1 and y = -2, then 1/(-2) > (-2)/1. Answer to question would be YES. Scenario 2: If x = -1 and y = -2, then (-1)/(-2) < (-2)/(-1). Answer to question would be NO. Since I get different answers, Statement 1 is insufficient. Eliminate A and D STATEMENT 2: Scenario 1: If x = 1 and y = 2, then 1/2 < 2/1. Answer to this question would be NO. Scenario 2: If x = 2 and y = 1, then 2/1 > 1/2. Answer to this question would be YES. Since I get different answers, Statement 2 is insufficient. Eliminate B. STATEMENT 1 and 2: In this, I have to meet both statements in my scenarios. (1) x > y (2) xy > 0 Scenario 1: If x = 2 and y = 1, then 2/1 > 1/2. The answer would be YES. Scenario 2: If x = -1 and y = -2, then -1/-2 < -2/-1. The answer would be NO. Eliminate C. Correct answer: E.

intheend14 · Answer

Statement 1 says that x>y. Let's try some values. If both are positive, then the answer is yes. 
x=3, y=1 says that 3/1>3/1
However, if both values are negative, the answer is no and the same conditions apply when one is positive and one is negative.
x=-1, y=-3 says that 1/3>3/1 or x=3, y=-2 says that 3/-2>-2/3 (both of these are not true)
Insufficient

Statement 2 says that xy>0, meaning that they both have the same sign. This doesn't help as we don't know their relative values. Insufficient

Combining also doesn't help as both having the same sign with x being greater than y is still insufficient to determine whether the inequality holds true.

Choose E

EMPOWERgmatRichC · Answer

Hi Awli,

This is another great opportunity to TEST VALUES.

We're told that neither X nor Y can equal 0. We're asked if X/Y > Y/X. This is a YES/NO question.

Fact 1: X > Y

IF....
X = 2
Y = 1
2/1 > 1/2 and the answer to the question is YES

IF...
X = 2
Y = -1
2/-1 is NOT > -1/2 and the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: XY > 0

This Fact tells us that X and Y have the SAME SIGN.

IF....
X = 2
Y = 1
2/1 > 1/2 and the answer to the question is YES

IF....
X = 1
Y = 2
1/2 is not > 2/1 and the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know...
X > Y
X and Y have the SAME sign

IF....
X = 2
Y = 1
2/1 > 1/2 and the answer to the question is YES

IF....
X = -1
Y = -2
(-1)/(-2) is NOT > (-2)/(-1) and the answer to the question is NO
Combined, INSUFFICIENT

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

sudh · Answer

Given  x
eq{0}  and  y
eq{0}

is \frac{x}{y} > \frac {y}{x} ? 
it will be  True  when

Case (i):   Both  x  and  y  positive 
 x > y

Case (ii):   Both  x  and  y  negative 
 |x| > |y|

Case (iii):    x  and  y  opposite signs 
 |x| < |y|

From Statement 1 and 2, there is no definitive information about signs of  x  or  y

Answer E

yezz · Answer

from stem x/y>y/x = x/y-y/x = y(x-y) / yx = 1-y/x , question asks is y/x<1 ( if yx has different signs or same sign and /y/0 .... insuff from 2 yx has same sign but we dont know whether or not /y/

Dhawal91 · Answer

Hi,

I am not sure how E is the answer

I solved it by below method

x/y>y/x

x/y-y/x>0

(x^2-y^2)/xy>0

1.x>y

This means x^2-y^2 is positive. But we don't know abt sign of xy. So Insufficient

2. xy>0

This tells us xy is positive. But we dont know abt sign of x^2-y^2.So insufficient

Taking 1 and 2 together

1.x^2-y^2 is positive
2.xy is positive

Therefore both together are sufficient

Can anyone help understand what am I missing here.

Thanks in Advance !!

GMATGuruNY · Answer

One approach:

\frac{x}{y} > \frac{y}{x}? 
 \frac{x}{y} - \frac{y}{x} > 0? 
 \frac{x^2 - y^2}{xy} > 0?

Statement 2: xy > 0 
Case 1: x=2 and y=1
In this case,  \frac{x^2 - y^2}{xy} = \frac{4-1}{2} = \frac{3}{2} , so the answer to the question stem is YES.

Case 2: x=-1 and y=-2
In this case,  \frac{x^2 - y^2}{xy} = \frac{1-4}{2} = -\frac{3}{2} , so the answer to the question stem is NO.

Cases 1 and 2 satisfy BOTH STATEMENTS.
Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.

E

hnhan · Answer

So, we have x≠0 and y≠0 for x/y and y/x to be possible divisions. The question is x/y > y/x
=> x/y - y/x > 0
=> (x^2-y^2)/xy > 0
=> ((x-y)(x+y))/xy > 0
To know the final sign of the equation, we need to know the signs of all individual factors, i.e. x+y, x-y, and x*y
(1) x > y => x – y > 0 => INSUFFICIENT
When x > y or x – y > 0, we cannot conclude anything about x + y or x*y.
Example:
x = 2, y = 1 => x + y = 3 > 0, x*y = 2 > 0
x = 2, y = -3 => x + y= -1 < 0, x*y = -6 < 0
(2) x*y > 0 => INSUFFICIENT
Similarly, when x*y>0, it only tells you that x and y either both negative or both positive (same sign). We cannot conclude anything about x - y and x + y.
Example:
x = 4, y = 5, x - y = -1 < 0, x + y = 9 > 0
x = -4, y = -5, x - y = 1 > 0, x + y = -9 < 0
Together (1) + (2) -> STILL INSUFFICIENT because we do not know anything about x + y.
So, E is the final answer.

If x and y cannot be equal to zero, is x/y > y/x ?

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