hi ov25, for me it is also time-killer problem, and i am not sure that i solved it right, need your verification and expert`s replies. my way
|m-n|=15.
|n-p|=5
|m-q|=12. and we need to find |p-q|-?
1)m>n, and m>q.
m-n=15.
m-q=12. substract and left with m-n-m+q=3.

q-n=3
n-p=5 , if n>p now add q-n+n-p=8, q-p=8 looks like 2 answer is valid

2) n-m=15, if m<n, n-p=5 if n>p again substract both
n-m-n+p=10, p-m=10, and m-q=12 if m>q, now i want to add, p-m+m-q=22, p-q=22 third answer also looks valid

3)p-n=5 if n<p and m-q=12 if m>q, add both p-n+m-q=17, and m-n=15. if m>n here i substract
p-n+m-q-m+n=2, p-q=2
my answer is E

ov25 wrote:In a number line, there are points M, N, P and Q not necessarily in that order. If MN=15, NP=5, MQ=12, which of the following could be the distance between P and Q?
I) 2
II) 8
III) 22

A) I only
B) II only
C) III only
D) II and III
E) I, II and III

I tend to waste a lot of time to solve these questions. Is there a quick combination type method to encompass all the possibilities for solving such questions quickly? Appreciate your time

I dont think there is a shortcut to it except to think logically quick by drawing the picture.
its given the that the points are on number line.

Q......12......M.........15........N.....5....P
Dist between P and Q is 32

Q......12......M.....10.......P.....5...N
Dist between P and Q is 22

M.........12..Q....3..N.....5....P
Dist between P and Q is 8

M.....10....P..2..Q....3..N
Dist between P and Q is 2

Hence I, II and III are possible

pick E.

ov25 wrote:In a number line, there are points M, N, P and Q not necessarily in that order. If MN=15, NP=5, MQ=12, which of the following could be the distance between P and Q?
I) 2
II) 8
III) 22

A) I only
B) II only
C) III only
D) II and III
E) I, II and III

I tend to waste a lot of time to solve these questions. Is there a quick combination type method to encompass all the possibilities for solving such questions quickly? Appreciate your time

a potential speed-up is process of Elimination = eliminate answer choices as you come up with possible results.

Begin with the most banal, linear setting: Start with M, move 15 to the right to find N, add another 5 to get P. P is now 20 from M. With the last bit of MQ=12, we get that PQ=8, So II is a possible.
Before you move on, ask: Which answer choices can we eliminate? any answer choice that does not include II is gone, so we eliminate A and C, and are down to B, D and E.

Now shift one element of your chosen configuration: Start with M, move 15 to the right to find N, but now move 5 to the left to find P. P is now 15-5=10 away from M. With the last bit of MQ=12, we get that PQ=2, So I is a possible.

Again, now ask: Between B, D, E, what can we eliminate now? Everything that doesn't contain I is gone, so B and D are out, and we can choose E and move on - no need to search for a distance of 22.

In "statements" questions, it is better to eliminate answer choices as you go - you just might find that one (or more) of the statements does not need to be addressed because of POE.

M---12----Q
|
15
|
N--5---P

Just imagine the MQ and NP arms swinging in both directions, and then do quick mental math. It took me less than a minute to go through all three options.

This is good Woozler. Thanks you, experts and all others!