K, L, M, N, O, P, A, and B are sitting in a row but not necessarily in the same order. Only three persons face south direction. All of them got different ranks in an examination i.e. 371, 153, 785, 1256, 474, 865, 784, 302 but not necessarily in the same order. N sits 3rd right of M and O faces south. M sits immediate left of O, and his rank is 3 digits Armstrong number which is divisible by 7. M and Pare immediate neighbors of A. K sits 4th left of M. N rank is 5 times of 157. P faces south direction. K's rank is average of L and A's rank. B's rank is an Armstrong number. L sits right of M. O sits 3rd from the extreme end of the row and his rank is a perfect square. A's rank is 1.6 times of N's rank. Psits fifth to the right of N.
Who sit extreme ends of the row?

Options

A. K,P
B. N,O
C. N,K
D. O,M

Answer

C

Explanation

From the condition, O sits 3rd from the extreme end of the row whose rank is a perfect square, hence O can sit either 3rd from left or 3rd from right end of the row and his rank is 784, because this is the only number which is perfect square, O faces south. M sits immediate left of O and M.s rank is 3 digit Armstrong number which is divisible by 7, there is 2 Armstrong number 371 and 153, only 371 is divisible by 7 it means M.s rank is 371. (An Armstrong number of three digits is an integer such that the sum of the cubes of its digits is equal to the number itself.) B.s rank is an Armstrong number, only 1 Armstrong number (153) is remaining, means B.s rank is 153. K sits 4 left of M. N rank is 5 times of 157, hence N rank is 785. From above conditions we will get 2 possible conditions

N sits 3rd right of M. P and M are the immediate neighbours of A, from this condition case 2 will be eliminated. Only case -1 will be continued. . From the rest conditions, L sits right of M. A.s rank is 1.6 times of N.s rank, it means A.s rank is 1256). K.s rank is average of L and A.s rank, there is only one possibility that L.s rank is 474 and K.s rank is 865. P sits 5th place away from the N, so N faces north direction and P.s rank will be fixed that is 302. M and P are immediate neighbors of A. B position will be fixed. P faces south direction. We will get final answer.