find a day without reference day Practice Questions Answers Test with Solutions & More Shortcuts

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: (b)

28^th August 2009 means,

2008 complete years + First 7 months of the year 2009 + 28 days of August

Number of odd days in 2000 yrs = 0

Number of odd days from 2001 yrs to 2008 yrs

2001 2002 2003 2004 2005 2006 2007 2008  1 1 1 2 1 1 1 2

=1+1+1+ 2+ 1+1+1+2 = 10

= 7 x1+ 3 = 3 odd days

Number of odd days in 2009,

January February March April May July  August 3 0 3 2 3 2 3 0

= 3 + 0 + 3 + 2 + 3 + 2 + 3 + 0

= 16 = 7 x 2 + 2 = 2 odd days

Total number of odd days till 28^th August 2009

= 0 + 3 + 2 = 5

So, the required day is Friday.

Answer: (d)

1^st January 1901 means

= (1900 yrs and 1 day)

Now, 1600 yrs have 0 odd days,

300 yrs have 1 odd day and 1 day has 1 odd day.

Total number of odd days = 0 + 1 + 1 = 2 days

∴ the day on 1st January, 1901 was Tuesday.