TS Police SI Mains 2018 Arithmetic and Reasoning

Given, the number 19585*2 is divisible by 3

The sum of all the digits apart from * is 30

So * can be 0 and the number would still be divisible by 3

hence, 0 is the answer.

The number formed by last 3 digits of any number should be divisible by 8 for the original entire number to be divisible by 8. 
The number formed would be 5*2
502 is not divisible by 8. 
512 is divisible by 8
Hence, smallest whole number in place of * is 1.

Different methods are possible to solve this question. 
One can work backwards and determine the day of 28 May in 2008

Number of days from 28 May to 4 October = 129 
129 divided by 7 gives remainder 3. 
So, if 4 October was a Saturday, then 28 May in same year has to be 3 days prior to Saturday i.e. Wednesday
Now, 28 May from 2008 to 2014 respectively would be on:
Wednesday, thursday, Friday, Saturday, Monday, Tuesday, Wednesday. 

Angular distance between hour hand and minute hand at sharp 2 PM would be 60 degrees.
Relative velocity of minute hand with respect to hour hand = 5.5 degrees per minute

Hence, the 2 hands coincide at = 60/5.5 = 120/11 minutes after 2 PM
Hence, option A

The actual time taken by minute hand to overtake the hour hand every hour must be = 360/5.5 = 720/11 minutes.
However, the time getting taken in the incorrect clock = 63 minutes.

Thus the time gained every hour = (720/11) - 63 = 27/11 minutes 
Hence, the time gained during the entire day = Just slightly over 56 minutes i.e. option A

Total relative distance = 160 meters
Let the speed of each train be s m/s 

Hence, $$\frac{160}{2s}=3$$ 
Hence, s = (80/3) m/s 
s converted into kmph = $$\frac{80}{3}\cdot\frac{18}{5}=96\ kmph$$

Let the speed of A be a kmph and speed of B be b kmph

Hence, in first case: a + b = (45/3) = 15 kmph
In second case, a - b = 45/5 = 9 kmph 

Addding the 2 equations, we get a = 12 kmph 

Let the distance travelled at 60 kmph be d km 
Hence, distance travelled at 90 kmph be (340-d) km. 

Hence, $$\frac{d}{60}+\frac{340-d}{90}=4$$
Solving this, we get d = 40 km 

Total number of students from P = 360*5 = 1800
Total number of students from Q = 520*(5/4) = 650
Total number of students from R = 540*(10/9) = 600
Total number of students from S = 420*(10/7) = 600

Hence, total number of students = 3650 

Number of students of Q failing the exam = 520/4 = 130
Number of students of R failing the exam = 540/9 = 60
Number of students of S failing the exam = (3/7)*420 = 180 

Hence, total number = 370