On a certain number line, conditions are a<b<c<d<

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Wed Sep 14, 2016 1:00 am

On a certain number line, conditions are a<b<c<d<e and abcde>0. Which of the following must be true?
I ab>0 II cd>0 III de>0

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

*An answer will be posted in 2 days

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regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Wed Sep 14, 2016 9:16 am

The following number lines are possible that satisfy the conditions:

----------------------0 ----abcde....

------------------ab--0------cde.....

-----------------abcd-0---e----------

The only answers that work with all of the possible number lines are I and II, therefore D

fiza gupta: Master | Next Rank: 500 Posts; Posts: 216; Joined: Sun Jul 31, 2016 9:55 pmFollowed by: 7 members; Location: Punjab; Thanked: 31 times

by fiza gupta » Fri Oct 14, 2016 6:58 am

a<b<c<d<e and abcde>0
so out of five numbers 2 or 4 out of 5 can be negative or all can be positive
to make the product positive:
if 2 negative (a,b) can be negative
if 4 negative (c,d,a,b) can be negative
c,d,a,b all positive

I ab>0 - true
II cd>0 - true
III de>0 - cannot be true

SO D

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