find a day without reference day Detailed Explanation And More Example

Answer: (a)

1^st January 2001 means 2000 complete years + 1 day of January 2001

Number of odd days in 2000 yrs = 0

Number of odd days in January 2001 = 1

Total number of odd days = 0+1 = 1

So, the required day was Monday

Answer: (b)

Odd days in 1600 yrs = 0

Odd days in 300 yrs = 1

46 yrs = (11 leap year + 35 ordinary year)

= (11x2 + 35 x 1) = 1 odd day

∴ Odd days in 1946 yrs = (0+ 1+ 1) = 2

Total  17  17 ÷ 7= remainder 3 odd days

Total odd days =2 + 3 = 5

∴ Required day = Friday

Answer: (c)

Odd days in 1600 yrs = 0

Odd days in 400 yrs = 0 5 yrs = (4 ordinary year + 1 leap year)

= (4 x 1+ 1 x 2) = 6 odd days

Total odd days = 8 + 6 = 14 = 0 odd day

∴ Required day Sunday

Answer: (c)

Answer: (d)

Answer: (b)

First of all, we have to find the day on 1^st April, 2012 1^st April 2012 means

(2011 years 3 months and 1 day)

Now, 2000 years have 0 odd days 11 years have

(2 leap years and 9 ordinary years)

= ( 2 × 2 + 9 × 1 ) odd days

= (4 + 9) odd days = 13

= 6 odd days

3 months and 1 day

= 92 days = 1 odd day

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

⇒ 0 odd day

Hence, it was Sunday on 1^st April 2012. (1^st Sunday).

Subsequently, Sundays of the month were on 1^st, 8^th, 15^nd, 22^nd, and 29^th.