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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
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Joined: 16 Aug 2015
Posts: 7471
GMAT 1: 760 Q51 V42
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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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New post 25 Dec 2017, 18:08
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (01:14) correct 31% (01:26) wrong based on 86 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

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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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New post 25 Dec 2017, 20:28
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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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 7471
GMAT 1: 760 Q51 V42
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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New post 27 Dec 2017, 01:03
=>

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.

Therefore, the answer is D.

Answer : D
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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, 01:03
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