6Dec19 morning Q22
0. The smallest integer greater than 1 which is simultaneously a square and a cube of certain
- Option : D
- Explanation : Let the number 'k' is cube of number x and square of number (x + y). Then, k = x3 ... (i) k = (x + y)2 ... (ii) Here, 1 ≤ (x,y) < k/2 From (i) and (ii), x3 = (x + y)2 x3 = x2 + y2 + 2xy x3 - x2 = y2 + 2xy x2(x-1) = y(y + 2x) For x = 2, 22(2 - 1) = y(y + 4) This is not valid for any integer value of y. For x = 3, 32(3 - 1) = y(y+ 6) 18 = y(y+ 6) This is not valid for any integer value of y. For x = 4, 42(4 - 1) = y(y + 8) 48 = y(y + 8) 48 = 4(4 + 8) = 48 Thus x = 4,and y = 4 Hence, Number k = (x)3 = (4)3 = 64.
