q: A, B, C, and D are four points, any three of which are non-collinear. Then, the number of ways to construct three lines each joining a pair of points so that the lines do not form a triangle is
Options:
(A) 7
(B) 8
(C) 9
(D) 24
(E) 23
a: OK... To construct 2 lines, three points can be selected out of 4 in 4 x 3 x 2 = 24 ways. Now, if third line goes from the third-point to the first point, a triangle is formed, and if it goes to the fourth point, a triangle is not formed. So, there are 24 ways to form a triangle and 24 ways of avoiding triangle.
The answer is (D).

q: The average of 11 results is 51, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?
Options:
(A) A) 46
(B) B) 45
(C) C) 66
(D) D) 76
(E) E) 74
a: OK... 1 to 11 = 11 * 51 = 561
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 561 = 45
The answer is (B).

q: Find the least number must be added to 433124 so that remaining no.is divisible by 17?
Options:
(A) 3
(B) 2
(C) 5
(D) 6
(E) 1
a:

Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
OK... On dividing 433124 by 17 we get the remainder 15, so 2 should be added
The answer is (B).