If a<y<z<b;

[Shobuj40]

If a<y<z<b; is ! y-a! < !y-b!
a. !z-a!<!z-b!
b. !y-a!<!z-b!
Ans : D

[RonPurewal]

the first thing you should do here is rephrase the question.
big takeaway:
if you see the ABSOLUTE VALUE OF A DIFFERENCE, you should recast it as the DISTANCE BETWEEN THE TWO THINGS on the number line.

therefore, |y - a| is the distance between y and a, and so on.

hence:

QUESTION: is y closer to a than to b ?
(1) z is closer to a than to b
(2) y is closer to a than z is to b

statement (1):
note that the distance y-a is less than the distance z-a, because y is placed between a and z.
also, note that the distance y-b is greater than the distance z-b, since z lies between y and b.
therefore:
distance y-a < distance z-a < distance z-b < distance y-b (note that these are color-coded to the statements above)
so, distance y-a < distance y-b
"yes"
SUFFICIENT

statement (2):
same thing as statement (1), except for the second term of the inequality above isn't there anymore.
i.e., distance y-a < distance z-b < distance y-b.
SUFFICIENT

ans = (d)

[supratim7]

the first thing you should do here is rephrase the question.
big takeaway:
if you see the ABSOLUTE VALUE OF A DIFFERENCE, you should recast it as the DISTANCE BETWEEN THE TWO THINGS on the number line.

therefore, |y - a| is the distance between y and a, and so on.

hence:

QUESTION: is y closer to a than to b ?
(1) z is closer to a than to b
(2) y is closer to a than z is to b

Fantastic concept/decoding. Thank you Ron

Going forward, If statement (2) were |y-a| = |z-b|, then also it would be sufficient. Am I right??

Regards | Supratim

[RonPurewal]

Going forward, If statement (2) were |y-a| = |z-b|, then also it would be sufficient. Am I right??

Regards | Supratim

yes.

[supratim7]

Thank you :)

[RonPurewal]

Thank you :)

sure thing.

[supratim7]

the first thing you should do here is rephrase the question.
big takeaway:
if you see the ABSOLUTE VALUE OF A DIFFERENCE, you should recast it as the DISTANCE BETWEEN THE TWO THINGS on the number line.

therefore, |y - a| is the distance between y and a, and so on.

hence:

QUESTION: is y closer to a than to b ?
(1) z is closer to a than to b
(2) y is closer to a than z is to b

Got another question Ron.

Is the reverse this takeaway valid?

e.g.
If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10 ?
(1) On the number line, z is closer to 10 than it is to x.
(2) z = 5x

Can we decode Stmt (1) as
|10 - z| < |x - z|?

I am aware that there are simpler ways to decode Stmt (1) e.g. number line visualization. Just want to know whether it is cool to recast DISTANCE BETWEEN THE TWO THINGS as ABSOLUTE VALUE OF A DIFFERENCE??

Many thanks | Supratim

[RonPurewal]

e.g.
If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10 ?
(1) On the number line, z is closer to 10 than it is to x.
(2) z = 5x

Can we decode Stmt (1) as
|10 - z| < |x - z|?

well... sure, you can do that, but i can't see how that could possibly help you. you've taken a relatively straightforward statement and turned it into something that's ... well, not straightforward at all.

i mean, it's sort of like taking
I turned 40 on January 15 of this year (a straightforward statement)
and turning it into
Exactly five years before Jan. 14 of this year was the last day when rounding my age to the nearest 10 years gave 30 (a statement that's much less straightforward).

so, you're extremely unlikely to ever transform anything in that direction... but, yes, that example works.
don't forget that the goal is to make things easier to understand!