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Which of the following year is not a leap year?

A.

1960

B.

2080

C.

2024

D.

2100

Answer with explanation

Answer: Option DExplanation

The two conditions that decide that a year is a leap year or not is:

• For a year to be a leap year, it should be divisible by 4.

• No century is a leap year unless it is divisible by 400.

Hence, the year 2100 is not a leap year as it is not divisible by 400.

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It was Sunday on Jan 1, 2006. Discover the week’s day on Jan 1, 2010.

Answer with explanation

Answer: Option CExplanation

On 31st December,2005 it was Saturday. Number of odd days frame the year 2006 to the year 2009=(1+1+2+1)=5 days. ∴ On 31st December 2009 , it was Thursday. In this way, on first jan, 2010 it is Friday

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Today is Thursday. The day after 59 days will be?

A.

Sunday

B.

Tuesday

C.

Wednesday

D.

Monday

Answer with explanation

Answer: Option AExplanation

59 days = 8 weeks 3 days = 3 odd days

Hence if today is Thursday, After 59 days, it will be = Thursday + 3 odd days = Sunday.

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If 5th March, 2005 is Monday, what was the day of the week on 5th March, 2004 ?

A.

Sunday

B.

Monday

C.

Tuesday

D.

Friday

Answer with explanation

Answer: Option AExplanation

The year 2004 is a leap year. So, it has 2 odd days.

But, Feb 2004 not included because we are calculating from March 2004 to March 2005. So it has 1 odd day only.

The day of 5th March 2005 will be 1 day beyond the day of 5th March 2004.

Given that, 5th March 2005 is Monday.

5th March 2004 is Sunday (1 day before to 5th March 2005).

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On 8th Feb 2005 it was Tuesday. What was the day of the week on 8th Feb 2004?

A.

Tuesday

B.

Sunday

C.

Monday

D.

Saturday

Answer with explanation

Answer: Option BExplanation

The year 2004 is a leap year. It has 2 odd days.

The day on 8^{th} Feb, 2004 is 2 days before the day on 8^{th} Feb, 2005.

Hence, this day is Sunday.

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On July 2, 1985, it was Wednesday. The day of the week on July 2, 1984 was

A.

Wednesday

B.

Tuesday

C.

Monday

D.

Thursday

Answer with explanation

Answer: Option BExplanation

Let us calculate the number of odd days between these two dates.

July month of 1984 has 29 days left. So odd days are 1.

Now August 1984 to June 1985 ===>> 3 + 2 + 3 + 2 + 3 + 2 + 0 + 3 + 2 + 3 + 2.

Now July 1985 till 2nd July contains 2 odd days.

Total 29 odd days. or 1 odd day.

So July 2, 1984, is 1 day before Wednesday. It is Tuesday.

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On 8th march,2005,wednesday falls what day of the week was it on 8th march,2004?

A.

Monday

B.

Tuesday

C.

Wednesday

D.

Friday

Answer with explanation

Answer: Option BExplanation

As a year contains 365 days with factors of 7(1week) gives 1(day) as a reminder which adjusts one day extra to the next year.

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How many leap years do 300 years have?

A.

74

B.

75

C.

76

D.

72

Answer with explanation

Answer: Option DExplanation

Given year is divided by 4, and the quotient gives the number of leap years. But, as 100,200 and 300 are not leap years => 75 – 3= 72 leap years.

OR

A 300-year period can have either 72 or 73 leap years. Each 400-year cycle of the Gregorian calendar has 97 leap years, so the average number of leap years for a 300-year period is 72.75.

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If Feb 12th,1986 falls on Wednesday then Jan 1st,1987 falls on which day?

A.

B.

Wednesday

C.

Thursday

D.

Saturday

Answer with explanation

Answer: Option CExplanation

The number of days more than the complete weeks are called odd days in a given period.

1 ordinary year ≡ 365 days ≡ (52 weeks + 1 day)

Hence the number of odd days in 1 ordinary year= 1.

1 leap year ≡ 366 days ≡ (52 weeks + 2 days)

Hence the number of odd days in 1 leap year= 2.

100 years ≡ (76 ordinary years + 24 leap years )

= (76 x 1 + 24 x 2) odd days = 124 odd days.

=> (17 weeks + 5 days)

≡ 5 odd days.

Hence the number of odd days in 100 years = 5.

Number of odd days—->Day of the week

==>0—->Sunday

==>1—->Monday

==>2—->Tuesday

==>3—->Wednesday

==>4—->Thursday

==>5—->Friday

==>6—->Saturday

last day of a century cannot be Tuesday or Thursday or Saturday.

because 100 century consists 5 odd days, means Friday is the last day.

200 century consists 3 odd days, means Wednesday is the last day.

300 century consists 1 odd day, means Monday is the last day.

400 century doesn’t consist any odd day.

the cycle continues, hence proof.

Solution: First, we count the number of odd days for the leftover days in the given period.

Here,given period is 12.2.1986 to 1.1.1987

Feb Mar Apr May June July Aug Sept Oct Nov Dec Jan

16 31 30 31 30 31 31 30 31 30 31 1 (left days)

2 + 3 + 2 + 3 + 2 + 3 + 3 + 2 + 3 + 2 + 3 + 1(odd days) = 1 odd day

So,given day Wednesday + 1 = Thursday is the required result.

Workspace

The calendar of the year 2024 can be used again in the year?

A.

B.

C.

D.

Answer with explanation

Answer: Option BExplanation

**Repetition of leap year ===>** Add +28 to the Given Year.

**Repetition of non leap year**

Step 1 : Add +11 to the Given Year. If Result is a leap year, Go to step 2.

Step 2: Add +6 to the Given Year.

**Solution :**

Given Year is 2024, Which is a leap year.

So, Add +28 to the given year (i.e 2024 + 28) = 2052

Therfore, The calendar of the year 2024 can be used again in the year 2052.

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The calendar for the year 1993 will be same for the year

A.

B.

C.

D.

Answer with explanation

Answer: Option AExplanation

**Repetition of leap year ===>** Add +28 to the Given Year.

**Repetition of non leap year**

Step 1 : Add +11 to the Given Year. If Result is a leap year, Go to step 2.

Step 2: Add +6 to the Given Year.

**Solution :**

Given Year is 1993, Which is a non leap year.

Step 1 : Add +11 to the given year (i.e 1993 + 11) = 2004, Which is a leap year.

Step 2 : Add +6 to the given year (i.e 1993 + 6) = 1999

Therfore, The calendar for the year 1993 will be same for the year 1999

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If Mar 18th,1994 falls on Friday then Feb 25th,1995 falls on which day?

A.

B.

C.

D.

Saturday

Answer with explanation

Answer: Option DExplanation

The number of days more than the complete weeks are called odd days in a given period.

1 ordinary year ≡ 365 days ≡ (52 weeks + 1 day)

Hence the number of odd days in 1 ordinary year= 1.

1 leap year ≡ 366 days ≡ (52 weeks + 2 days)

Hence the number of odd days in 1 leap year= 2.

100 years ≡ (76 ordinary years + 24 leap years )

= (76 x 1 + 24 x 2) odd days = 124 odd days.

=> (17 weeks + 5 days)

≡ 5 odd days.

Hence the number of odd days in 100 years = 5.

Number of odd days—->Day of the week

==>0—->Sunday

==>1—->Monday

==>2—->Tuesday

==>3—->Wednesday

==>4—->Thursday

==>5—->Friday

==>6—->Saturday

last day of a century cannot be Tuesday or Thursday or Saturday.

because 100 century consists 5 odd days, means Friday is the last day.

200 century consists 3 odd days, means Wednesday is the last day.

300 century consists 1 odd day, means Monday is the last day.

400 century doesn’t consist any odd day.

the cycle continues, hence proof.

First,we count the number of odd days for the left over days in the given period.Here,given period is 18.3.1994 to 25.2.1995

Month | Mar | Apr | May | Jun | Jul | Aug | Sep | Oct | Nov | Dec | Jan | Feb |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Days | 13 | 30 | 31 | 30 | 31 | 31 | 30 | 31 | 30 | 31 | 31 | 25 |

Odd Days | 6 | 2 | 3 | 2 | 3 | 3 | 2 | 3 | 2 | 3 | 3 | 4 |

Therefore, No. of Odd Days = 6 + 2 + 3 + 2 + 3 + 3 + 2 + 3 + 2 + 3 + 3 + 4 = 36 = 1 odd day

So, given day Friday + 1 = Saturday is the required result.

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If the day after tomorrow is Monday, what day was tomorrow’s day before yesterday?

If the day, after tomorrow is Sunday, what day was tomorrow’s day before yesterday ?…

** **

A.

Saturday

B.

Friday

C.

Thursday

D.

Wednesday

Answer with explanation

Answer: Option BExplanation

As day after tomorrow is Monday, today will be Saturday and yesterday will be Friday…

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