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# Given that a,b,c and d all lie between 0 and -1

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Given that a,b,c and d all lie between 0 and -1  [#permalink]

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Updated on: 23 Oct 2018, 22:21
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95% (hard)

Question Stats:

23% (02:51) correct 77% (02:32) wrong based on 47 sessions

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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?

2) ac<bc<bd

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Originally posted by EncounterGMAT on 23 Oct 2018, 10:51.
Last edited by chetan2u on 23 Oct 2018, 22:21, edited 2 times in total.
Updated topic name and corrected the OA
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Re: Given that a,b,c and d all lie between 0 and -1  [#permalink]

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23 Oct 2018, 18:52
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..

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
also 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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Re: Given that a,b,c and d all lie between 0 and -1  [#permalink]

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23 Oct 2018, 21:49
The screenshot of the answers are as follows:

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Re: Given that a,b,c and d all lie between 0 and -1  [#permalink]

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23 Oct 2018, 21:50
Posted from my mobile device

Part2 (continued)
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IMG_20181024_101726.jpg [ 157.64 KiB | Viewed 568 times ]

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Re: Given that a,b,c and d all lie between 0 and -1  [#permalink]

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23 Oct 2018, 21:50
Posted from my mobile device

Part 3(continued)
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Re: Given that a,b,c and d all lie between 0 and -1  [#permalink]

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23 Oct 2018, 21:53
Pls suggest an easier approach for such questions. Thanks in advance.

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Re: Given that a,b,c and d all lie between 0 and -1  [#permalink]

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23 Oct 2018, 22:18
1
topper97 wrote:
Posted from my mobile device

Part 3(continued)

this is wrong..

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

Also the wordings in BOLD is even more confusing... on one hand it writes both are sufficient and then writes something else..

Although a good question but wrong OA and poor explanation
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Re: Given that a,b,c and d all lie between 0 and -1  [#permalink]

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23 Oct 2018, 22:29
chetan2u wrote:
topper97 wrote:
Posted from my mobile device

Part 3(continued)

this is wrong..

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

Also the wordings in BOLD is even more confusing... on one hand it writes both are sufficient and then writes something else..

Although a good question but wrong OA and poor explanation

Thanks a lot. This is easier now.
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Re: Given that a,b,c and d all lie between 0 and -1   [#permalink] 23 Oct 2018, 22:29
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