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# 4 points a, b, c and d are placed on the number line in that order.

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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4 points a, b, c and d are placed on the number line in that order. [#permalink]

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25 Dec 2017, 17:08
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Difficulty:

25% (medium)

Question Stats:

71% (00:48) correct 29% (00:29) wrong based on 42 sessions

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[GMAT math practice question]

4 points a, b, c and d are placed on the number line in that order. If abcd>0, which of the following must be positive?

I. ab
II. bc
III cd

A. Ⅰonly
B. Ⅱonly
C. Ⅲ only
D.Ⅰ&Ⅲ only
E. Ⅱ&Ⅲ only
[Reveal] Spoiler: OA

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4 points a, b, c and d are placed on the number line in that order. [#permalink]

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25 Dec 2017, 19:28
MathRevolution wrote:
[GMAT math practice question]

4 points a, b, c and d are placed on the number line in that order. If abcd>0, which of the following must be positive?

I. ab
II. bc
III cd

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

Hi..
Number line.....a...b....c....d
Also abcd>0
THREE cases..
I. All four POSITIVE... So product of any two will be positive
II. All four NEGATIVE... So product of any two again will be positive
III. a and b NEGATIVE and c and d POSITIVE... So ab and cd will be positive.

Thus ab and cd are positive in all cases.
D
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Kudos [?]: 6417 [0], given: 122

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4676

Kudos [?]: 3309 [0], given: 0

GPA: 3.82
Re: 4 points a, b, c and d are placed on the number line in that order. [#permalink]

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27 Dec 2017, 00:03
=>

There are three cases we need to consider. Note that if $$a < 0 < b < c < d$$ or $$a < b < c < 0 < d$$, then $$abcd < 0$$.

Case 1) $$0 < a < b < c < d:$$
$$ab > 0, bc > 0$$ and $$cd > 0$$

Case 2) $$a < b < 0 < c < d:$$
$$ab > 0, bc < 0, cd > 0$$

Case 3) $$a < b < c < d < 0:$$
$$ab > 0, bc > 0, cd > 0$$

Only statements I and III are always true.

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Re: 4 points a, b, c and d are placed on the number line in that order.   [#permalink] 27 Dec 2017, 00:03
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