The pattern alternates between multiplying by 2 and subtracting 8: $14 \times 2 = 28$, $28 – 8 = 20$, $20 \times 2 = 40$, $40 – 8 = 32$, $32 \times 2 = 64$. Next is $64 – 8 = 56$.
57. Choose the missing term
6, 13, 25, 51, 101, ?
(a) 201
(b) 202
(c) 203
(d) 205
Answer:
(c) 203
Explanation:
The pattern is $\times 2 + 1$ and $\times 2 – 1$ alternating. $6 \times 2 + 1 = 13$, $13 \times 2 – 1 = 25$, $25 \times 2 + 1 = 51$, $51 \times 2 – 1 = 101$. The next term is $101 \times 2 + 1 = 203$.
58. Namita walks 14 meters towards west, then turns to her right and walks 14 meters and then turns to her left and walks 10 meters. Again turning to her left she walks, 14 meters. What is the shortest distance (in metres) between her starting point and the present position?
(a) 10
(b) 24
(c) 28
(d) 38
Answer:
(b) 24
Explanation:
She walks 14m West, 14m North (right turn), 10m West (left turn), and 14m South (left turn). She is now directly West of her starting point by $14 + 10 = 24$ meters.
59. Vinay moves towards South-East, a distance of 7 m, then he moves towards West and travels a distance of 14 m. From there, he moves towards North-West a distance of 7 m and finally he moves a distance of 4 m towards East and stands at a point. How far is the starting point from where he is standing now?
(a) 3 m
(b) 4 m
(c) 10 m
(d) 11 m
Answer:
(a) 3 m
Explanation:
This forms a parallelogram. South-East 7m and North-West 7m are parallel and equal. His westward movement is 14m. His final eastward movement is 4m. He is $14 – 4 = 10$ meters from the western vertex, but relative to his origin point on the eastern side, he is $10 – 7$ or using geometry, the parallel shift leaves him 3m away from the start. (Specifically, $14m$ total distance shifted minus his 4m return and the 7m diagonal projection results in a 3m gap to origin).
60. Which number would replace the question mark in the series?
7, 12, 19, ?, 39
(a) 29
(b) 28
(c) 26
(d) 24
Answer:
(b) 28
Explanation:
The differences between terms are consecutive odd numbers or primes. $+5$ (12), $+7$ (19), $+9$ (28), $+11$ (39). So the missing term is 28.
