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• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### FREE Quant Workshop by e-GMAT! December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. # 4 points a, b, c and d are placed on the number line in that order.  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 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] ### Show Tags 25 Dec 2017, 17:08 00:00 Difficulty: 25% (medium) Question Stats: 70% (01:16) correct 30% (01:25) wrong based on 80 sessions ### HideShow timer Statistics [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$99 for 3 month Online Course"
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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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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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. &nbs [#permalink] 27 Dec 2017, 00:03
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