GATE Questions

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HIS RECENT SUCCESS HAS MADE HIM MORE ARROGANT THAN WHAT HE USED.

Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec.
[(25/2) x (18/5)] km/hr = 45 km/hr.
Let the speed of the train be 'S' km/hr.
Then, relative speed = (S - 5) km/hr.
S - 5 = 45 => S = 50 km/hr.

The letters move 2, 2, 3, 3, 4, 4, ... steps forward.

It is Charcoal which is black when we buy it or when not being used. It gets red in appearance when put in use means to say when burning. And eventually when it's been consumed by fire or after getting burned out or used up, changes into ashes which look grey in color.

Let distance = x km.
Time taken at 3 kmph : dist/speed = x/3 = 20 min late.
time taken at 4 kmph : x/4 = 30 min earlier
difference between time taken : 30-(-20) = 50 mins = 50/60 hours.
x/3- x/4 = 50/60
x/12 = 5/6
x = 10 km.

Ans. 
17 = 2 x 6 + 5
89 = 17 x 5 + 4
359 = 89 x 4 + 3
1079 = 359 x 3 + 2
? = 1079 x 2 + 1, i.e. ? = 2159

The given series follows a pattern that,

$$\begin{gathered} 4 + 32 = 4 + 9 = 13 \\ 13 + 52 = 13 + 25 = 38 \\ 38 + 72 = 38 + 49 = 87 \\ 87 + 92 = 87 + 81 = 198 \end{gathered}$$ 

Hence, the odd man in the given number series is 12.