q: A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Options:
(A) 20
(B) 99
(C) 88
(D) 77
(E) 66
a: Stream of consciousness: 1: 2/5 = 5: 2
2/7 * 70 = 20 The answer is (B).

question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
Options:
(A) 63
(B) 72
(C) 14
(D) 50
(E) 25
answer: Stream of consciousness: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = = 63. The answer is (A).

q: Given 3 lines in the plane such that the points of intersection form a triangle with sides of length 20, 20 and 30, the number of points equidistant from all the 3 lines is
Options:
(A) 1
(B) 3
(C) 4
(D) 0
(E) 2
a: Stream of consciousness: 4 points are possible in which 1 point is the incentre of the circle and other 3 are excentres The answer is (C).

question: What is the are of an equilateral triangle of side 12 cm?
Options:
(A) 363 cm2
(B) 743 cm2
(C) 643 cm2
(D) 645 cm2
(E) 143 cm2
answer: Stream of consciousness: Area of an equilateral triangle = 3/4 S2
If S = 12, Area of triangle = 3/4 * 12 * 12 = 363 cm2; The answer is (A).

q: Rs. 1300 is divided into three parts A, B and C. How much A is more than C if their ratio is 1/2:1/3:1/4?
Options:
(A) 222
(B) 300
(C) 99
(D) 88
(E) 67
a: Stream of consciousness: 1/2:1/3:1/4 = 6:4:3
3/13*1300 = 300 The answer is (C).

q: The average amount with a group of seven numbers is Rs. 30. If the newly joined member has Rs. 60 with him, what was the average amount with the group before his joining the group?
Options:
(A) s. 25.6
(B) s. 25
(C) s. 16.6
(D) s. 26
(E) s. 25.6
a:
Stream of consciousness: Total members in the group = 7
Average amount = Rs. 30
Total amount with them = 7 * 30 = Rs. 210
One number has Rs. 60. So, the amount with remaining 6 people = 210 - 60 = Rs. 150
The average amount with them = 150/6 = Rs. 25 The answer is (B).