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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
Posts: 7471
GMAT 1: 760 Q51 V42
GPA: 3.82
4 points a, b, c and d are placed on the number line in that order.  [#permalink]

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25 Dec 2017, 18:08
00:00

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

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Math Expert Joined: 02 Aug 2009 Posts: 7755 4 points a, b, c and d are placed on the number line in that order. [#permalink] ### Show Tags 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 _________________ Math Revolution GMAT Instructor 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] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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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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