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If A<Y<Z<B, is |Y-A|< |Y-B|? [#permalink]
 18 Aug 2009, 18:47
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If A<Y<Z<B, is |Y-A|< |Y-B|? (1) |Z-A| < |Z-B| (2) |Y-A| < |Z-B|
Last edited by Bunuel on 09 Aug 2012, 01:11, edited 1 time in total.
Edited the question and added the OA.
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Re: If A<Y<Z<B, is /Y-A/< /Y-B/? [#permalink]
18 Aug 2009, 20:26
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yezz wrote: If A<Y<Z<B, is /Y-A/< /Y-B/?
1) /Z-A/ < /Z-B/
2) /Y-A/ < /Z-B/ Consider A,Y,Z,B lying on the straight line Given that A<Y<Z<B 1) statement 1 talks nothing about Y but however it clearly brings out the fact that the distance between B&Z is greater than the distance between A&Z. Now we know that since Y<Z, Y lies closer to A than Z and farther from B than Z. hence answers our question 2) Statement 2 : it says distance between Y&A is less than the distance between Z&B. As already stated Y lies closer to A than Z and farther to B than Z, hence this answers the question as well So choice is Either statement alone is sufficient
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Re: If A<Y<Z<B, is /Y-A/< /Y-B/? [#permalink]
28 Oct 2009, 17:44
I think both are insufficient Take an example A = -5 , Y= 1 , Z = 2 , B = 3 |Y- A| < | Y-B| |1+5| < |1-3| i.e. 6 < 2 ... no A = 1 , Y= 2 , Z = 3 , B = 4 |2-1| < |2-4| i.e. 1 < 2 ... yes So, A not suff similarly B - not suff I think i have mistaken somewhere , can some one correct me
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Re: If A<Y<Z<B, is /Y-A/< /Y-B/? [#permalink]
28 Oct 2009, 20:41
D
I drew a number line for this which helped me conceptualize the problem (4 points A, Y, Z and B).
(A) Given distance between Z and B is greater than Z and A is sufficient as Y lies between A and Z.
(B) Similar approach as A. Sufficient.
Please correct this if wrong.
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Re: If A<Y<Z<B, is /Y-A/< /Y-B/? 1) /Z-A/ < /Z-B/ [#permalink]
08 Aug 2012, 21:14
Bunuel
can you please clarify is this makes sense
If a < y < z < b, is |y – a| < |y – b|? (1) |z – a| < |z – b| (2) |y – a| < |z – b|
a < y < z < b
a< y implies
0< y-a or y-a >0
2) y < B (y-b ) < 0
Implies
y-b --------------- 0-------------y-b
Yes proved
2) If a < y < z < b
|y – a| < |z – b|
0 < y-a y-a >0
Z<b z-b< 0
Y< z-b implies
y-b < 0
(y-a) -------------0--------------y-b
D
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Re: If A<Y<Z<B, is |Y-A|< |Y-B|? [#permalink]
09 Aug 2012, 01:26
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If A<Y<Z<B, is |Y-A|< |Y-B|? Since given that A<Y ( Y-A>0), then |Y-A|=Y-A; Since given that Y<B ( Y-B<0), then |Y-B|=B-Y; So, the question becomes: is Y-A<B-Y? --> is 2Y<A+B? (1) |Z-A| < |Z-B|. The same way as above: Since given that A<Z ( Z-A>0), then |Z-A|=Z-A; Since given that Z<B ( Z-B<0), then |Z-B|=B-Z; So, we have that: Z-A<B-Z --> 2Z<A+B. Now, since Y<Z, then 2Y<2Z, so 2Y<2Z<A+B. Sufficient. (2) |Y-A| < |Z-B|. The same way as above: Since given that A<Y ( Y-A>0), then |Y-A|=Y-A; Since given that Z<B ( Z-B<0), then |Z-B|=B-Z; So, we have that: Y-A<B-Z --> Y+Z<A+B. Now, since Y<Z, then 2Y<Y+Z ( 2Y=Y+Y<Y+Z ), so 2Y<Y+Z<A+B. Sufficient. Answer: D. Hope it's clear.
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Re: If A<Y<Z<B, is |Y-A|< |Y-B|? [#permalink]
09 Aug 2012, 10:54
yezz wrote: If A<Y<Z<B, is |Y-A|< |Y-B|?
(1) |Z-A| < |Z-B|
(2) |Y-A| < |Z-B| Use the meaning of the absolute value: distance between two points. Rephrasing the question: we are given 4 distinct points on the number line, A, Y, Z, B, from left to right (in increasing order). The question is: is the distance between A and Y smaller than the distance between Y and B? (1) A---Y--Z------B would visualize a typical situation, distance between A and Z less than the distance between Z and B. Since Y is between A and Z, the answer to the question "is the distance between A and Y smaller than the distance between Y and B" is definitely YES. Sufficient. (2) A---Y-Z----B this would be a typical situation, distance between A and Y, less than the distance between Z and B. Now Z is between Y and B, so again, the distance between A and Y is smaller than the distance between Y and B. Sufficient. Answer D
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Re: If A<Y<Z<B, is /Y-A/< /Y-B/? [#permalink]
09 Aug 2012, 11:31
gmattokyo wrote: D
I drew a number line for this which helped me conceptualize the problem (4 points A, Y, Z and B).
(A) Given distance between Z and B is greater than Z and A is sufficient as Y lies between A and Z.
(B) Similar approach as A. Sufficient.
Please correct this if wrong. You are absolutely right. Sorry, I missed your post and I have just presented a similar solution.
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Re: If A<Y<Z<B, is |Y-A|< |Y-B|? [#permalink]
18 Oct 2012, 05:21
Bunuel, For statement 1, everything works until z-a<b-z = 2z<a+b. y<z so 2y<2z ok but this does not mean 2z<a+b. we know that a<y<z<b. Now if we plug in values say 3<4<5<6 then 2(5) is not < 3+6 i.e 2z<a+b. What could I be doing wrong here Bunuel? Could you please help me with that. Thanks in advance!
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Re: If A<Y<Z<B, is |Y-A|< |Y-B|? [#permalink]
23 Oct 2012, 06:52
liarish wrote: Bunuel, For statement 1, everything works until z-a<b-z = 2z<a+b. y<z so 2y<2z ok but this does not mean 2z<a+b. we know that a<y<z<b. Now if we plug in values say 3<4<5<6 then 2(5) is not < 3+6 i.e 2z<a+b. What could I be doing wrong here Bunuel? Could you please help me with that. Thanks in advance! You derived yourself that 2Z<A+B and later you are negating that (blue parts). We know from (1) that 2Z<A+B (i) . We also know that Y<Z, so 2Y<2Z (ii). Now, combine (i) and (ii): 2Z is less than A+B and 2Y is less than 2Z, thus 2Y is less than A+B ( 2Y<2Z<A+B). Also, numbers you chose does not satisfy 2Z<A+B. Hope it's clear.
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Re: If A<Y<Z<B, is /Y-A/< /Y-B/? [#permalink]
06 Apr 2013, 10:56
alwynjoseph wrote: yezz wrote: If A<Y<Z<B, is /Y-A/< /Y-B/?
1) /Z-A/ < /Z-B/
2) /Y-A/ < /Z-B/ Consider A,Y,Z,B lying on the straight line Given that A<Y<Z<B 1) statement 1 talks nothing about Y but however it clearly brings out the fact that the distance between B&Z is greater than the distance between A&Z. Now we know that since Y<Z, Y lies closer to A than Z and farther from B than Z. hence answers our question 2) Statement 2 : it says distance between Y&A is less than the distance between Z&B. As already stated Y lies closer to A than Z and farther to B than Z, hence this answers the question as well So choice is Either statement alone is sufficient I've struggled with this question for 10 min., then I looked at first sentence and the light bulb turned on. It becomes quite, quite a simple task the minute you draw a straight line... thank you!
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Re: If A<Y<Z<B, is |Y-A|< |Y-B|? [#permalink]
06 Apr 2013, 20:30
By drawing a line with the given condition, it is easy to see |y-a| < |y-b|
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Re: If A<Y<Z<B, is |Y-A|< |Y-B|?
[#permalink]
06 Apr 2013, 20:30
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