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Given the positions of numbers x and y on the number line BELOW, which

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Senior RC Moderator
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Given the positions of numbers x and y on the number line BELOW, which  [#permalink]

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New post 10 Jun 2017, 11:19
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A
B
C
D
E

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88% (00:46) correct 13% (00:00) wrong based on 33 sessions

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Given the positions of numbers x and y on the number line BELOW, which of the following must be true?
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I. xy > 0
II. x/y < 0
III. x – y > 0

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III

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Re: Given the positions of numbers x and y on the number line BELOW, which  [#permalink]

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New post 10 Jun 2017, 13:12
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SajjadAhmad wrote:
Given the positions of numbers x and y on the number line BELOW, which of the following must be true?

I. xy > 0
II. x/y < 0
III. x – y > 0

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II,

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SajjadAhmad, nice question -- and I think answer E is missing "and III."

Which of the options must be true?

From the number line, we know x is negative and y is positive. We know nothing about their absolute values. x could be -2,000 and y could be 1/2.

I. xy > 0.

Never true. Negative multiplied by a positive is always negative, i.e. less than zero.

If x is -4 and y is 2, xy = -8. REJECT. Answers A, D, and E are out.

II. x/y < 0

Always true. Negative divided by positive and vice-versa always equals negative. Conveniently, option I analysis just yielded that xy is negative, so x/y, inverse, must also be negative.

If x is -4 and y is 2, x/y = -2, less than 0.

KEEP. You could stop here because only B and C are left, and C doesn't include II.

III. x - y > 0
Never true. Negative minus positive is MORE negative. If x is -4 and y is 2, x - y = -6. REJECT.

ANSWER B
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Re: Given the positions of numbers x and y on the number line BELOW, which   [#permalink] 10 Jun 2017, 13:12
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Given the positions of numbers x and y on the number line BELOW, which

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