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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