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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: 53066
If xy > 0 and x + y < 0, then which of the following must be true?  [#permalink]

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23 Jan 2019, 01:39
00:00

Difficulty:

55% (hard)

Question Stats:

63% (02:07) correct 38% (02:01) wrong based on 35 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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Joined: 09 Mar 2018
Posts: 1002
Location: India
Re: If xy > 0 and x + y < 0, then which of the following must be true?  [#permalink]

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23 Jan 2019, 02:45
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, 06:02
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

_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

Re: If xy > 0 and x + y < 0, then which of the following must be true?   [#permalink] 23 Jan 2019, 06:02
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