If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be
Options:
(A) 2
(B) 5
(C) 6
(D) 7
(E) 14
Answer and stream of consciousness: (E)
Stream of consciousness: 3150*y = A^2
3 * 1050 * y = A^2
3*5*210*y = A^2
3*5*7*3*2*5*y = A^2
2*3^2*5^2*7*y = A^2
Concept: The factors of squared integer should occur in pair. So, the only numbers left are 2*7
Hence 14 ;

A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
Options:
(A) 5 mins
(B) 3 mins
(C) 7 mins
(D) 9 mins
(E) 2 mins
Answer and stream of consciousness: (B)
Stream of consciousness: D = 25 * 60 + 1500 = 3000 m
T = 3000/60 * 18/5 = 180 sec = 3 mins

In a school of 850 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
Options:
(A) 173
(B) 163
(C) 153
(D) 143
(E) 133
Answer and stream of consciousness: (C)
Stream of consciousness: 44 + 28 + 10 = 82%
100 82 = 18%
850 * 18/100 = 153

If X is the sum of first 100 positive even integers and Y is the sum of first 100 positive odd integers, what is the value of x-y?
Please try to explain your answers
Options:
(A) 0
(B) 25
(C) 50
(D) 75
(E) 100
Answer and stream of consciousness:
(E)
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 100 positive even integers minus the sum of first 100 positive odd integers will be 100.