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If x < y < 0, which of the following must be true?

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If x < y < 0, which of the following must be true?  [#permalink]

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New post 21 Jan 2019, 01:31
1
2
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

69% (01:20) correct 31% (01:33) wrong based on 105 sessions

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Re: If x < y < 0, which of the following must be true?  [#permalink]

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New post 21 Jan 2019, 02:08
Answer is A only

As x and y are negative with Mode of X always greater than Mode of Y

Second and third condition are may be true or may not bw

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If x < y < 0, which of the following must be true?  [#permalink]

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New post 21 Jan 2019, 03:37
Bunuel wrote:
If x < y < 0, which of the following must be true?

I. |x| > |y|
II. x/y > 1
III. x^y < 0

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


x and y are both negative numbers. Imagine the number line: y is to the left of 0 and x is to the left of y.
e.g. x = -2 and y = -1
or
x = -1/2 and y = -1/3
and so on.
The absolute value of x will be greater than absolute value of y to make x "more negative".

Since x and y are both negative, x/y is positive. Since absolute value of x is greater than absolute value of y, x/y > 1

So both I and II will hold.

III may not hold if y is even. e.g. x = -3, y = -2 so x^y = (-3)^(-2) = 1/9 (not negative)

Answer (D)


You can prove I and II algebraically too.

x and y are negative.

x < y
Multiply both sides by -1 to get -x > -y
Since x and y are negative, |x| = -x and |y| = -y
So |x| > |y|

x < y
Divide both sides by y (which is negative) to get
x/y > 1 (the inequality sign flips)
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If x < y < 0, which of the following must be true?  [#permalink]

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New post 21 Jan 2019, 04:22
Bunuel wrote:
If x < y < 0, which of the following must be true?

I. |x| > |y|
II. x/y > 1
III. x^y < 0

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


Given x<y< 0

x and y are -ive.

I. |x| > |y|, will always be true, just plug in these values -2 < -1 < 0 or - 0.50 < - 0.25 < 0

II. x/y > 1, in this case, y will always be less than x, -4/-2 > 1, -0.1/ - 0.05 > 1, -6/-5 > 1

At this stage, we can just mark D and go ahead.

Still, III. x^y < 0,
if y is an even power, the relationship will become +ive which wont be < 0
if y is an odd power, the relationship will become -ive which is < 0

Answer D
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Re: If x < y < 0, which of the following must be true?  [#permalink]

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New post 21 Jan 2019, 08:44
Bunuel wrote:
If x < y < 0, which of the following must be true?

I. |x| > |y|
II. x/y > 1
III. x^y < 0

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


from given relation we can say that whether x & y are fractions or integers they would both be -ve values since <0 is mentioned

test the relations with x = -2 and y = -3 and fractions y= -1/3 and x = -1/2

upon reviewing the options we can conclude that options 1 & 2 would stand correct
IMO D
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Re: If x < y < 0, which of the following must be true?   [#permalink] 21 Jan 2019, 08:44
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If x < y < 0, which of the following must be true?

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