Logical Reasoning Test - 5

Leap century year is a leap year in the calendar which is divisible by 4 as well as 400 without a remainder. Like all leap years, it has an extra day in February.

Leap year is a calendar year which is divisible by 4. Leap year contains an additional day in February. Every leap year has 29 days in February while ordinary year has 28 days in February. 

The century year which is divisible by 400 without leaving remainder is known as leap century year.

Checking in options:

1. 2000 → 2000 is divisible by 400. Hence, it is leap century year.

2. 1800 → 1800 is not completely divisible by 400. Hence, it is not a leap century year.

3. 1200 → 1200 is divisible by 400. Hence, it is leap century year.

4. 1600 → 1600 is divisible by 400. Hence, it is leap century year.

Therefore, 1800 is not a leap century year.

Note: Multiple of 400 years i.e. 800, 1200, 1600, 2000 have 0 odd days.

Calculating leap year: For Finding the number of leap year (1 - 99) years, divide the number of years by 4 and the quotient will be the number of leap years.

Code for weekdays:

1950 = we find out the odd days (the nearest leap century year + the nearest century year + completing year) = 1600 + 300 + 49

• In 1600 year the odd days = 0
• In 300 year the odd days = 1
• In 49 years, odd days = 49/4 = 12 leap years and 37 ordinary years
  • In 12 leap years, no. of odd days = 24
  • In 37 ordinary years, no. of odd days = 37
• So total = 24 + 37 = 61 odd days i.e. 61/7 = 5 odd days (remainder)
• Odd days in January = 25 i.e. 4 odd days

Total = 0 + 1 + 5 + 4 = 10 days = 3 odd days i.e Wednesday.

As the code of Wednesday is 3.

Hence, Wednesday is the correct answer. 

The logic followed here is:

Given Time: 3:30

Angle formula is: 11M/2 - 30H

H(Hour) = 3, M(Minute) = 30

Now, 11 × 30/2 - 30 × 3

= 165 - 90

= 75∘

Hence, the correct answer is "75∘".

Alternate Method

Time = 3: 30

\(Angle\;\left( \theta \right) = \left| {\frac{{60\; \times \;hour - \;11\; \times \;minute}}{2}} \right|\)

And another angle = (360 - \(\theta )^∘ \)

\(\therefore \;\theta = \;\left| {\frac{{60\; \times \;3 - \;11\; \times \;30}}{2}} \right|^∘ \)

\( = \;\left| {\frac{{180 - 330}}{2}} \right|^∘ \)

\( = \;\left| {\frac{{150}}{2}} \right|^∘ \)

\( = \;75^∘ \)

And another angle = (360 - \(\theta )^∘ \) = (360 - \(75)^∘ \) = 285

In the option, 75 is given.

1) 2007 → Leap year before 2007 is 2004, so 2007 is the 3^rd year after a leap year.

Same calendar for the year 2007 will be (2007 + 11) = 2018.

2) 2006 → Leap year before 2006 is 2004, so 2006 is the 2^nd year after a leap year.

Same calendar for the year 2006 will be (2006 + 11) = 2017.

3) 2008 → It is a leap year.

Same calendar for the year 2008 will be (2008 + 28) = 2036

4) 2009 → Leap year before 2009 is 2008, so 2009 is a year after a leap year.

Same calendar for the year 2009 will be (2009 + 6) = 2015.

We know on 22 April = Monday

And the number of days from 22 April to 12 June = 8 + 31 + 12 = 51 days

When 51 is divided by 7, 2 is the remainder.

Monday + 2 days = Wednesday

Hence, Rajat’s birthday is on ‘Wednesday’.

Clock gains 6 minutes in 24 hrs. i.e. in 24 hrs. it gains 6 minutes.

Time difference = 16 hrs.

So, the time gains = \(16\times6\over24\) = 4 minutes.

The given time = 1 P.M. and after 16 hrs, it will be = 5 A.M.

Therefore, the time = Tuesday at 4:56 A.M.

Hence, the correct answer is Tuesday at 4:56 A.M.

For every mirror image based on a clock,

Given :

The clock shows the time = 1:40

To find :

Time is shown in the mirror image 

Concept used :

For mirror image

(11 - hours) : (60 - minutes)

Solution :

Hours = 1

Minutes = 40

Mirror image = (11 - 1) : (60 - 40)

⇒ Mirror image = 10:20

If it is 12 hrs clock, then subtract the given timing from 11:60 hrs.

If it is 24 hrs clock, then subtract the given timing from 23:60 hrs.

Hence, the real time will be 10:20.

The angle between the hour hand and minute hand = \(60H -11M\over2\)

Here, H = hour M = minutes.

Given H = 4 and minutes = M and angle = 180°

So, 180 = \((11\times M - 60\times4)\over2\)

180 = 11M/2 - 120 

300 = 11M/2

600 = 11M

M = 54(6/11)

Therefore, the time will be 54(6/11) minute past to 4

Hence, the correct answer is 54(6/11) minute past to 4

The logic followed is:

According to Nitin's memory, Nidhi's birthday is either on Wednesday or Thursday.

According to Deepak's memory, Nidhi's birthday is either on Thursday or Friday.

The only common day is Thursday.

Hence, the correct answer is "Thursday".

Today is Saturday.

Each day of the week is repeated after every 7 days.

Hence, after 42 days it will be Saturday.

So after 43 days, it will be Sunday.