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Math Expert V
Joined: 02 Sep 2009
Posts: 57193
If x and y cannot be equal to zero, is x/y > y/x ?  [#permalink]

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1
1 00:00

Difficulty:   65% (hard)

Question Stats: 58% (01:51) correct 42% (01:50) wrong based on 145 sessions

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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

Kudos for a correct solution.

Source: Chili Hot GMAT

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Manager  Joined: 21 Sep 2012
Posts: 211
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE: General Management (Consumer Products)
Re: If x and y cannot be equal to zero, is x/y > y/x ?  [#permalink]

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2
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
Manager  Joined: 21 Jul 2014
Posts: 121
Re: If x and y cannot be equal to zero, is x/y > y/x ?  [#permalink]

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2
Bunuel wrote:

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

Kudos for a correct solution.

Source: Chili Hot GMAT

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.
Manager  Joined: 12 Sep 2014
Posts: 142
Concentration: Strategy, Leadership
GMAT 1: 740 Q49 V41 GPA: 3.94
Re: If x and y cannot be equal to zero, is x/y > y/x ?  [#permalink]

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1
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
Math Expert V
Joined: 02 Sep 2009
Posts: 57193
Re: If x and y cannot be equal to zero, is x/y > y/x ?  [#permalink]

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Bunuel wrote:

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

Kudos for a correct solution.

Source: Chili Hot GMAT

Yes, the correct answer is E.
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Intern  Joined: 08 Jan 2015
Posts: 25
If xy ≠ 0, is x/y > y/x ?  [#permalink]

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If xy ≠ 0, is x/y > y/x ?

1. x > y

2. xy > 0
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14824
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If xy ≠ 0, is x/y > y/x ?  [#permalink]

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1
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:

GMAT assassins aren't born, they're made,
Rich
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Manager  Joined: 15 May 2014
Posts: 62
Re: If x and y cannot be equal to zero, is x/y > y/x ?  [#permalink]

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Given $$x\neq{0}$$ and $$y\neq{0}$$

$$is \frac{x}{y} > \frac {y}{x} ?$$
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
Manager  B
Joined: 20 Apr 2014
Posts: 86
Re: If x and y cannot be equal to zero, is x/y > y/x ?  [#permalink]

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Hi Bunuel
please add your ideal written approach to solve such questions.
Actually, I solved it correctly but in my mind not with written way which is more recommended from most of GMAT prep books for Data Suf. questions.
thanks in advance.
Retired Moderator B
Joined: 05 Jul 2006
Posts: 1629
Re: If x and y cannot be equal to zero, is x/y > y/x ?  [#permalink]

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Bunuel wrote:

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

Kudos for a correct solution.

Source: Chili Hot GMAT

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/</x/)

from 1

x-y>0 .... insuff

from 2

yx has same sign but we dont know whether or not /y/</x/....... insuff

both

usingy: y(x-y) /yx = (unknown sign*+Ve ) / +ve.... still insuff

E
Non-Human User Joined: 09 Sep 2013
Posts: 12052
Re: If x and y cannot be equal to zero, is x/y > y/x ?  [#permalink]

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_________________ Re: If x and y cannot be equal to zero, is x/y > y/x ?   [#permalink] 05 Aug 2019, 12:00
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