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What is the year next to 1990 which will have the same calendar as that of the year 1990?

A.

1992

B.

2001

C.

D.

1996

Answer with explanation

Answer: Option BExplanation

For a year to have the same calendar with 1990, total odd days from 1990 should be 0. Take the year 1992 from the given choices.

Total odd days in the period 1990-1991 = 2 normal years

⇒ 2 x 1 = 2 odd days Take the year 1995 from the given choices.

Number of odd days in the period 1990-1994 = 4 normal years + 1 leap year

⇒ 4 x 1 + 1 x 2 = 6 odd days Take the year 1996 from the given choices.

Number of odd days in the period 1990-1995 = 5 normal years + 1 leap year

⇒ 5 x 1 + 1 x 2 = 7 odd days = 0 odd days

(As we can reduce multiples of 7 from odd days which will not change anything) Though number of odd days in the period 1990-1995 is 0, there is a catch here.

1990 is not a leap year whereas 1996 is a leap year.

Hence calendar for 1990 and 1996 will never be the same.Take the year 2001 from the given choices. Number of odd days in the period 1990-2000 = 8 normal years + 3 leap years

⇒ 8 x 1 + 3 x 2 = 14 odd days = 0 odd days

Also, both 1990 and 2001 are normal years.

Hence 1990 will have the same calendar as that of 2001

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Ayesha says

i didn’t get this

Ayesha says

i am unable to understand this one.

Vamsi says

For a year to have the same calendar with 1990 ,total odd days from 1990 should be 0.

Take the year 1992 from the given choices.

Total odd days in the period 1990-1991= 2 normal years

≡ 2 x 1 = 2 odd days

Take the year 1995 from the given choices.

Number of odd days in the period 1990-1994 = 4 normal years + 1 leap year

≡ 4 x 1 + 1 x 2 = 6 odd days

Take the year 1996 from the given choices.

Number of odd days in the period 1990-1995= 5 normal years + 1 leap year

≡ 5 x 1 + 1 x 2 = 7 odd days ≡ 0 odd days

As we can reduce multiples of 7 from odd days which will not change anything

Though number of odd days in the period 1990-1995 is 0, there is a catch here.

1990 is not a leap year whereas 1996 is a leap year.

Hence calendar for 1990 and 1996 will never be the same.

Take the year 2001 from the given choices.

Number of odd days in the period 1990-2000= 8 normal years + 3 leap years

≡ 8 x 1 + 3 x 2 = 14 odd days ≡ 0 odd days

Also, both 1990 and 2001 are normal years.

Hence 1990 will have the same calendar as that of 2001