X is 1 km northeast of Y. Y is 1 km southeast of Z. W is 1 km west of Z. P is 1 km south of W. Q is 1 km east of P. What is the distance between X and Q in km? A. 1 B. sqrt(2) C. sqrt(3) D. 2

GATE 2014 · General Aptitude · Direction Sense · medium

Answer: The distance between X and Q is sqrt(3) km. Answer: C.

1. Place all points on coordinate grid: Z=(0,0). Y = Z + SE = (1/sqrt(2), -1/sqrt(2)). X = Y + NE = (1/sqrt(2)+1/sqrt(2), -1/sqrt(2)+1/sqrt(2)) = (2/sqrt(2), 0) = (sqrt(2), 0). W = Z + (-1,0) = (-1,0). P = W + (0,-1) = (-1,-1). Q = P + (1,0) = (0,-1).
2. Apply distance formula between X and Q: X = (sqrt(2), 0), Q = (0, -1). d = sqrt((0 - sqrt(2))^2 + (-1 - 0)^2) = sqrt(2 + 1) = sqrt(3).