Quantitative Aptitude - Arithmetic Ability Questions

In this type of problems the formulae is 5x-30×1211
x is replaced by the first interval of given time Here i.e 8
5*8-30*1211
= 12011min

Therefore the hands will be in the same straight line but not
together at 12011 min.past 8.

Let the total number of children be x. 

Then, x * (20% of x) = 405  

=> x * 20x/100 = 405 

15x2 = 405 

=> x=45 

Number of sweets received by each child = 20% of 45 = 9.

Let the number be x, Then 

75% of x + 75 = x 

=> x - 75x/100 =75 

=> x =  300 .

Angle traced by the hour hand in 6 hours=(360/12)*6

Here the series follows,

194

194 - (1x1 - 1) = 194

194 - (2x2 - 1) = 191

191 - (3x3 - 1) = 183

183 - (4x4 - 1) = 168

168 - (5x5 - 1) = 144

log 27 = 1.431
log33 = 1.431
3 log 3 = 1.431
log 3 = 0.477
log 9 = log(32)= 2 log 3 = (2 x 0.477) = 0.954

17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)
Odd days in 1600 years = 0
Odd days in 300 years = 1
97 years has 24 leap years + 73 ordinary years.
Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.
Jan. Feb. March. April. May. June.
(31 + 28 + 31 + 30 + 31 + 17) = 168 days
168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday.