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Updated on: 23 Oct 2018, 22:21
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.
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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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
26% (02:46) correct
74%
(02:35)
wrong
based on 92
sessions
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Not Attempted Yet
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?
1) ab<ad<cd
2) ac<bc<bd
Posted from my mobile device
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
1) ab<ad<cd
2) ac<bc<bd
Posted from my mobile device
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
23 Oct 2018, 18:52
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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?
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 info
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
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 info
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
23 Oct 2018, 21:49
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The screenshot of the answers are as follows:
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Posted from my mobile device
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23 Oct 2018, 21:50
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Posted from my mobile device
Part2 (continued)
Part2 (continued)
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IMG_20181024_101726.jpg [ 157.64 KiB | Viewed 2938 times ]
