Some people line up, the sum of people before ADAM and after

Some people line up, the sum of people before ADAM and after BETH is 18, how many people are lining up
1. Depending on whether 'Adam is before Beth' or 'Beth is before Adam' the number of people can vary. So, Insuff.
Why? because
We can have
B- - - - - - - -A => sum of people before Adam and after Beth is 18. In this case there actually only 10 people in total.

or - - - - - - - - - A - - - - - - - - B - - - - - - - -. Here we have 9+A+8+B+9 = 28 people in total. Still satisfying the criteria that sum of people before Adam and after Beth adds to 18.

2. Clearly Insuff. We dont know position of Beth and people before or after him, etc.

Combining both lets look at the possible scenarios..
a. we can say that Beth is before Adam and there 6 people after Adam. In essence we would have B - - - - - - - - A - - - - - -. This however does not meet the criteria in the question. So, not a possibility. Thanks for bringing this correction to me Saurya.
b. A - - - - - - -B - - - - - - - - - . A + 8 + B + 8 = 18. With this we have, No one before Adam, 8 after Beth, 8 between Adam and Beth, 6 after Adam included in the 8 and Sum is 18. All criteria met.

C still.

Two possibilities, A before B and B before A.
Items in bracket shows the number of ppl.

A before B:
(X) A (Y) B (Z)
Stem: X + Z = 18, X + Y + Z +2 = ?

B before A:
(X) B (Y) A (Z)
Stem: X + Y + Y + Z = 18, X + Y + Z +2 = ?

I: Y = 8. Gives different results case 1 (28) and in case 2 (12). Insufficient.
II: Y + Z = 6 for Case 1 and Z = 6 for Case 2. Insufficient.

Together: Case 1: Y + Z = 6 (Acceptable)
Case 2: Z = 6 (Not acceptable since after statement I substitution X+Z = 2)

C.

Venks, I am still not sure. With you arrangement does the criterion of 'the sum of people before ADAM and after BETH is 18' is satisfied?
S

Harworker, is B before A corect?
(X) B (Y) A (Z)
Stem: X + Y + Y + Z = 18, X + Y + Z +2 = ?
Should it be X + Y+1 + Y + Z +1 =18 ?
S

Yep , does this work?

Two possibilities, A before B and B before A.
Items in bracket shows the number of ppl.

Case1 - A before B:
(X) A (Y) B (Z)
Stem: X + Z = 18, X + Y + Z +2 = ?

Case2 - B before A:
(X) B (Y) A (Z)
Stem: X + Y + 1 + Y + Z +1 =18, X + Y + Z +2 = ?

I:
Case1: Y = 8. Result = 28
Case2: Y = 8 Result = 10.
Insufficient.

II:
Case1: Y + Z + 1 = 6
Case2: Z = 6.
Insufficient.

Together:
Case1: Y + Z + 1 = 6; Y = 8 (Not acceptable)
Case2: Z = 6; Y = 8; X+Y+Z+2 = 10 (Not acceptable)

E?

[img]Venks, I am still not sure. With you arrangement does the criterion of 'the sum of people before ADAM and after BETH is 18' is satisfied?
S[/img]

Yes 18 criteria is NOT satisfied. Not again. I took the total as 18 again. Oops sorry. E it is.