q: How many positive four-digit integers do not contain any digits other than 1 or 0 and are such that the sum of the first two digits equals the sum of the last two digits?
Options:
(A) 3
(B) 4
(C) 8
(D) 10
(E) 12
a: Stream of consciousness: The sum of the first two (last two) digits cannot be 0 because 0000 is not a four-digit integer. If the sum of the first two digits is 1, two variants are possible: 1001 and 1010 (we have to remember that 0 cannot be the first digit). If the sum of the first two digits is 2, one variant is possible: 1111. In all, there are three numbers that satisfy the given conditions: 1001, 1010, and 1111. The answer is (A).

question: BCB, DED, FGF, HIH, ___
Options:
(A) KOP
(B) QLM
(C) JKJ
(D) PSQ
(E) IOP
answer: Stream of consciousness: This series consists of a simple alphabetical order with the first two letters of all segments: B, C, D, E, F, G, H, I, J, K. The third letter of each segment is a repetition of the first letter. The answer is (C).

q: Find a a prime number from below options?
Options:
(A) 84
(B) 97
(C) 98
(D) 100
(E) 102
a: Stream of consciousness: Clearly, 97 is a prime number. The answer is (B).

question: If X is the sum of first 40 positive even integers and Y is the sum of first 40 positive odd integers, what is the value of x-y?
Please try to explain your answers
Options:
(A) 0
(B) 25
(C) 40
(D) 75
(E) 100
answer: Stream of consciousness: First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
We can see the patterns here, so the sum of first 40 positive even integers minus the sum of first 40 positive odd integers will be 40. The answer is (C).

q: The no. of girls in a class are seven times the no. of boys, which value cannever be the of total students?
Options:
(A) 23
(B) 25
(C) 30
(D) 36
(E) 39
a: Stream of consciousness: Let the boys are X, then girls are 7X, total = X+7X = 8X
So it should be multiple of 8, 30 is not a multiple of 8. The answer is (C).

q: The average length of the sides of triangle ABC is 12. What is the perimeter of triangle ABC?
Options:
(A) 4
(B) 6
(C) 12
(D) 24
(E) 36
a:
Stream of consciousness: (average) = (perimeter)/3;
12 = (perimeter)/3;
(perimeter) = 36. The answer is (E).