Six students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements are possible?
Options:
(A) 30
(B) 60
(C) 90
(D) 180
(E) 540

Ways of selecting group = 6C2 * 4C2 * 2C2 / 3! = 15
Three groups can select three subjects in 6 ways
Therefore total combinations = 15*6 = 90 So the answer is: (C).

A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 25 as remainder. Find the no. is?
Options:
(A) 145646
(B) 236578
(C) 645353
(D) 456546
(E) 220025

(555 + 445) * 2 * 110 + 25 = 220000 + 25 = 220025 So the answer is: (E).

In Sam's hanger there are 23 boxes, 19 out of the boxes are filled with toys and the rest are filled with electrical appliances. 8 boxes are for sale, 5 of them are filled with toys. How many boxes with electrical appliances are in Sam's hanger that is not for sale?
Options:
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(E) 5.

Total boxes = 23
Filled with toys = 19
Filled with appliance = 4
Total boxes for sale = 8
Toy boxes for sale = 5
Appliance boxes for sale = 3
Appliance boxes not for sale = 4 - 3 = 1 So the answer is: (A).

123 : 36 : : 221 : ?
Options:
(A) 52
(B) 69
(C) 72
(D) 25
(E) 32
(1+2+3)^2 = 36
(2+2+1)^2 = 25 So the answer is: (D).