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How many leap years does 100 years have?

A.

25

B.

24

C.

4

D.

26

Answer with explanation

Answer: Option BExplanation

Given year is divided by 4, and the quotient gives the number of leap years.

Here, 100%4 = 25.

But, as 100 is not a leap year => 25 – 1= 24 leap years.

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On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?

A.

Saturday

B.

Friday

C.

Monday

D.

Tuesday

Answer with explanation

Answer: Option BExplanation

The year 2006 is an ordinary year. So, it has 1 odd day.

So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.

But, 8th Dec, 2007 is Saturday

S0, 8th Dec, 2006 is Friday.

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What day of the week will be 8th June 2215?

A.

Tuesday

B.

Wednesday

C.

Monday

D.

Thursday

Answer with explanation

Answer: Option DExplanation

Calculate the number of odd days from starting till 8th June 2215

**Step 1:**

2000 = 0 odd days

200 = 3 odd days

14 years = 11 ordinary years + 3 leap years = 11 + 6 = 17 odd days = 3 odd days

Jan till June = 4 odd days

8 days = 8 odd days

**Step 2:**

Add all the odd days

3 + 3 + 4 + 8 = 18 odd days = 4 odd days

Hence, 4 odd days indicates a Thursday (According to reference chart)

Therefore, 8th June 2215 was a Thursday.

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What was the day of the week on 28th May, 2006?

A.

Thursday

B.

Friday

C.

Saturday

D.

Sunday

Answer with explanation

Answer: Option DExplanation

28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)

Odd days in 1600 years = 0

Odd days in 400 years = 0

5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) = 6 odd days

(31[jan] + 28 [Feb]+ 31[Mar] + 30[April] + 28[May] ) = 148 dayss = (21 weeks + 1 day) = 1 odd day.

Total number of odd days = (0 + 0 + 6 + 1) = 7 = 0 odd days.

Given day is Sunday

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How many times does the 29th day of the month occur in 400 consecutive years ?

A.

B.

C.

D.

Answer with explanation

Answer: Option AExplanation

Consider a set of every four years (So as to include the leap year with Feb 29). So in 3 years, 29 will occur 11 times, and once it would accur 12 times. So in 4 years, there will be 3*11 + 12 = 45 days in which you will have 29th. So in 400 years, it would be 4500 times.

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If 09/12/2001 happens to be Sunday, then 09/12/1971 would have been at

A.

Wednesday

B.

Tuesday

C.

Saturday

D.

Thursday

Answer with explanation

Answer: Option DExplanation

Every year day increase by 1 and if leap year come then by 2

=> leap year increase on day extra

2001 – 1971 = 30 years

so increase of 30 days

Leap years 1972 , 1976 , 1980 , 1984 , 1988 , 1992 , 1996 ( divisible by 4) , 2000 (divisible by 400)

8 Leap years

Total days increase = 30 + 8 = 38 days

38 = 5*7 + 3

3 days increased from 09/12/1971 to 09/12/1971

so it would be Thursday on 09/12/1971

Read more on Brainly.in – https://brainly.in/question/6133112#readmore

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How many times does the 29th day of the month occur in 400 consecutive years?

A.

5012

B.

4497

C.

4126

D.

1237

Answer with explanation

Answer: Option BExplanation

In 400 consecutive years there are 97 leap years. Hence, in 400 consecutive years February has the 29th day 97 times and the remaining eleven months have the 29th day 400 × 11 or 4400 times.

Therefore, the 29th day of the month occurs (4400 + 97) or 4497 times.

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On 2007, What was the date of last Saturday in May month?

A.

25

B.

21

C.

26

D.

22

Answer with explanation

Answer: Option CExplanation

1 – May – 2007

=(1 + 2 + 7 + 1 + 6)/7 = 17/7 = 3 = Tuesday

= May 1st –> Tuesday + 5 days = Saturday = 5th may

5th may + 7 days = Saturday = 12th may

12th may + 7 days = Saturday = 19th may

19th may + 7 days = Saturday = 26th may

= Answer = 26th may

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John was born on Feb 29^{th} of 2012 which happened to be a Wednesday. If he lives to be 101 years old, how many birthdays would he celebrate on a Wednesday?

A.

5

B.

3

C.

1

D.

4

Answer with explanation

Answer: Option DExplanation

Let us do this iteratively. Feb 29^{th} 2012 = Wednesday => Feb 28^{th} 2012 = Tuesday

Feb 28^{th} 2013 = Thursday (because 2012 is a leap year, there will be 2 odd days)

Feb 28^{th} 2014 = Friday, Feb 28^{th} 2015 = Saturday, Feb 28^{th} 2016 = Sunday, Feb 29^{th} 2016 = Monday

Or, Feb 29^{th} to Feb 29^{th} after 4 years, we have 5 odd days.

So, every subsequent birthday, would come after 5 odd days.

2016 birthday – 5 odd days

2020 birthday – 10 odd days = 3 odd days

2024 birthday – 8 odd days = 1 odd day

2028 birthday – 6 odd days

2032 birthday – 11 odd days = 4 odd days

2036 birthday – 9 odd days = 2 odd days

2040 birthday – 7 odd days = 0 odd days. So, after 28 years he would have a birthday on Wednesday

The next birthday on Wednesday would be on 2068 (further 28 years later), the one after that would be on 2096. His 84th birthday would again be a leap year.

Now, there is a twist again, as 2100 is not a leap year. So, he does not have a birthday in 2100. His next birthday in 2104 would be after 9 odd days since 2096, or 2 odd days since 2096, or on a Thursday.

From now on the same pattern continues. 2108 would be 2 + 5 odd days later = 7 odd days later. Or, 2108 Feb 29^{th} would be a Wednesday.

So, there are 4 occurrences of birthday falling on Wednesday – 2040, 2068 and 2096, 2108.

**Correct Answer:** 4.

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