Ques: Suppose you have three identical prisms with congruent equilateral triangles as the end-polygons. Suppose you attach them by the rectangular faces so they are perfectly aligned. There will be some large faces created by two or more co-planar faces of the individual prisms: count each such large face as one. Given that, how many faces does the resultant solid have
Options:
(A) 4
(B) 9
(C) 6
(D) 10
(E) 12
Ans: (C)
CoT: To arrange them as described I did as follows on my scratch paper (see the file attached), where I counted 4 sides and added top and bottom, hence 4+2 = 6.

Ques: 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
Ans: (E)
CoT: (555 + 445) * 2 * 110 + 25 = 220000 + 25 = 220025

Ques: Find the smallest number which should be multiplied with 560 to make it a perfect square.
Options:
(A) 60
(B) 55
(C) 45
(D) 25
(E) 35
Ans: (E)
CoT: 560 = 2*2*2*2*7*5
Required smallest number = 7 * 5 = 35
35 is the smallest number which should be multiplied with 560 to make it a perfect squar

Ques: In wardrobe Karan has 3 trousers. One of them is grey the 2nd blue and the 3rd brown. In his wardrobe he also has 4 shirts. One of them is grey and the other 3are white. He opens his wardrobein the dark and pick out one shirttrouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey?
Options:
(A) 1/2
(B) 2/3
(C) 4/5
(D) 6/11
(E) 4/5
Ans: (A)
CoT: Probability that trouser is not grey = 2/3
Probability that shirt is not grey = 3/4
Required probability = 2/3 x 3/4 = 1/2