Given that a,b,c and d all lie between 0 and -1 on the number line,and |a-d|>|a-c|>|a-b|, does c lie between b and d on a number line?

This tells us that the distance from a : d is farthest, then c and closest is b..

So it can be -1, d, c, b, a, 0 or other ways...yes

But if b and d are on one side and c on other side ... -1, d, b, a,c,0 OR when B and c are on one side and d on other... -1,d,a,b,c,0 so d and c should be on opposite side..

1) ab<ad<cd

ab<ad......a(d-b)>0 since a is negative d-b<0 or d<b so d is closer to -1....

cd>ad......(c-a)d>0 since d is negative, c-a<0...c<a so c is also towards -1..

Thus both d and c are on left side of a..

Two cases..

-1,d,c,b,a,0 or -1,d,c,a,b,0

In both cases answer is YES

Sufficient

2) ac<bc<bd

ac<bc......c(b-a)>0 since c is negative b-a<0 or b<a so b is closer to -1....

bd>bc......b(d-c)>0 since b is negative, d-c<0...d<c so d is closer to -1 as compared to c

Thus both d and b are on opposite side of a ..

-1,d,b,a, c,0 .... c is not in between

or -1,d,c,b,a,0...yes

Insufficient

Additional infoalso let me give you values that would satisfy ..

CASE I. d=-0.9 ; b=-0.7 ; a=-0.6 ; c=-0.4

d is farthest = 0.3, c is next = 0.2 and b is 0.1 faraway..

and they lie -1, d,b,a,c,0... so c is not between b and d

II.. ac<bc<bd = (-0.6)(-0.4)<(-0.7)(-0.4)<(-0.9)(-0.7)....0.24<0.28<0.63 satisfies the condition

CASE II. d=-0.9 ; c=-0.8 ; b=-0.7 ; a=-0.6

d is farthest = 0.3, c is next = 0.2 and b is 0.1 faraway..

and they lie -1, d,c,b,a,0... so c is between b and d

II.. ac<bc<bd = (-0.6)(-0.8)<(-0.7)(-0.8)<(-0.9)(-0.7)....0.48<0.56<0.63 satisfies the condition

both cases possible , so insufficient

A

OA is wrong

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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