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# If xy > 0 and x + y < 0, then which of the following must be true?

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Joined: 02 Sep 2009
Posts: 58460
If xy > 0 and x + y < 0, then which of the following must be true?  [#permalink]

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23 Jan 2019, 02:39
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45% (medium)

Question Stats:

64% (02:04) correct 36% (01:54) wrong based on 74 sessions

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TRICKY

If $$xy < 0$$ and $$x + y < 0$$, then which of the following must be true?

I. $$x - y > 0$$

II. $$x > 0$$ or $$y > 0$$

III. $$\frac{x}{y} < 1$$ or $$\frac{y}{x} < 1$$

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

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Posts: 994
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Re: If xy > 0 and x + y < 0, then which of the following must be true?  [#permalink]

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23 Jan 2019, 03:45
Bunuel wrote:

TRICKY

If $$xy < 0$$ and $$x + y < 0$$, then which of the following must be true?
I. $$x - y > 0$$

II. $$x > 0$$ or $$y > 0$$

III. $$\frac{x}{y} < 1$$ or $$\frac{y}{x} < 1$$
A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

IMO D

If $$xy < 0$$ and $$x + y < 0$$, for these statements to be true together

x < 0 or y > 0, also magnitude of x has to be greater than y

x = -2 and y = 1, -2< 0 and -1<0 (a)

x > 0 or y < 0, also magnitude of y has to be greater than y

x = 1 and y = -2, -2<0 and -1<0 (b)

I. $$x - y > 0$$ => False when (a), True when (b)

We can eliminate A and E

II. $$x > 0$$ or $$y > 0$$
Now this is an "or" statement, if either one of the condition is met we are good. As per my cases in (a) and (b), this holds good.

Now IMO this the tricky option, but still i will go with this.

III. $$\frac{x}{y} < 1$$ or $$\frac{y}{x} < 1$$

This will always be true, because we will get a negative term.
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Re: If xy > 0 and x + y < 0, then which of the following must be true?  [#permalink]

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23 Jan 2019, 07:02
best way to solve these type of quesitons is to consider following range
(-2,-3/2,-1/2,-1,0,1,1/2,3/2,2)

so for the expression xy<0 and x+y<0
to be valid either of x or y has to be -ve and the -ve value has to be >+ve value

so we can take x=-2 and y = +1
we would then get the expression
expression 2 & 3 to be valid only
IMO D

Bunuel wrote:

TRICKY

If $$xy < 0$$ and $$x + y < 0$$, then which of the following must be true?

I. $$x - y > 0$$

II. $$x > 0$$ or $$y > 0$$

III. $$\frac{x}{y} < 1$$ or $$\frac{y}{x} < 1$$

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
Manager
Joined: 05 Oct 2017
Posts: 79
Re: If xy > 0 and x + y < 0, then which of the following must be true?  [#permalink]

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23 May 2019, 03:32
Archit3110 wrote:
best way to solve these type of quesitons is to consider following range
(-2,-3/2,-1/2,-1,0,1,1/2,3/2,2)

so for the expression xy<0 and x+y<0
to be valid either of x or y has to be -ve and the -ve value has to be >+ve value

so we can take x=-2 and y = +1
we would then get the expression
expression 2 & 3 to be valid only
IMO D

Bunuel wrote:

TRICKY

If $$xy < 0$$ and $$x + y < 0$$, then which of the following must be true?

I. $$x - y > 0$$

II. $$x > 0$$ or $$y > 0$$

III. $$\frac{x}{y} < 1$$ or $$\frac{y}{x} < 1$$

A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III

Hi,
Here statement 3 has or condition. Shouldn't we assume that the statements means either of these expressions would be correct.
x/y < 1 is correct and y/x < 1 is also correct. I ruled out statement 3 because of "or" condition.
TIA!

Bunuel Archit3110
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Re: If xy > 0 and x + y < 0, then which of the following must be true?   [#permalink] 23 May 2019, 03:32
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