We know that the day repeats every 7 days, 14 days, 21 days, ......... So if today is Monday, after 7 days it is again Monday, after 14 days again it is Monday. Hence, after 2 weeks i.e, 14 days the day repeats and is the same day.
42.
On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
(A) Tuesday
(B) Monday
(C) Sunday
(D) Wednesday
Solution:
The year 2004 is a leap year. It has 2 odd days. ∴ The day on 8th Feb, 2004 is 2 days before the day on 8th Feb, 2005. Hence, this day is Sunday.
43.
On what dates of July. 2004 did Monday fall?
(A) 6th, 10th, 21th, 30th
(B) 12th, 7th, 19th, 28th
(C) 5th, 10th, 24th, 17th
(D) 5th, 12th, 19th, 26th
Solution:
Let us find the day on 1st July, 2004. 2000 years have 0 odd day. 3 ordinary years have 3 odd days. Jan. Feb. March April May June July 31 + 29 + 31 + 30 + 31 + 30 + 1 = 183 days = (26 weeks + 1 day) Total number of odd days = (0 + 3 + 1) odd days = 4 odd days. ∴ 1st July 2004 was 'Thursday' Thus, 1st Monday in July 2004 as on 5th July. Hence, during July 2004, Monday fell on 5th, 12th, 19th and 26th.
44.
The calendar of year 1939 is same as which year?
(A) 1943
(B) 1964
(C) 1950
(D) 1956
Solution:
Given year 1939, when divided by 4 leaves a remainder of 3. NOTE: When remainder is 3, 11 is added to the given year to get the result. So, 1939 + 11 = 1950
45.
How many leap years does 100 years have?
(A) 25
(B) 24
(C) 4
(D) 26
Solution:
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.
46.
What was the day of the week on 24th July 2011?
(A) Sunday
(B) Monday
(C) Tuesday
(D) Wednesday
Solution:
Day Codes Saturday 0 Sunday 1 Monday 2 Tuesday 3 Wednesday 4 Thursday 5 Friday 6 Month Codes January 1 February 4 March 4 April 0 May 2 June 5 July 0 August 3 September 6 October 1 November 4 December 6 Century Codes 1500 - 1599 0 1600 - 1699 6 1700 - 1799 4 1800 - 1899 2 1900 - 1999 0 2000 - 2099 6 2100 - 2199 4 2200 - 2299 2 2300 - 2399 0 Formula : (Date + Month code + No.of years + No.of leap year + Century code)/7 $$\eqalign{ & = \frac{{24 + 0 + 11 + 2 + 6}}{7} \cr & = \frac{{43}}{7} \cr & = 1 \cr & = {\text{Sunday}} \cr} $$
47.
The last day of a century cannot be
(A) Monday
(B) Wednesday
(C) Tuesday
(D) Friday
Solution:
100 years contain 5 odd days. ∴ Last day of 1st century is Friday. 200 years contain (5 x 2) ≡ 3 odd days. ∴ Last day of 2nd century is Wednesday. 300 years contain (5 x 3) = 15 ≡ 1 odd day. ∴ Last day of 3rd century is Monday. 400 years contain 0 odd day. ∴ Last day of 4th century is Sunday. This cycle is repeated. ∴ Last day of a century cannot be Tuesday or Thursday or Saturday.
48.
Which two months in a year have the same calendar?
(A) October, December
(B) April, November
(C) June, October
(D) April, July
Solution:
If the period between the two months is divisible by 7, then that two months will have the same calendar. (a). Oct + Nov = 31 + 30 = 61 (not divisible by 7) (b). Apr + May + Jun + Jul + Aug + Sep + Oct = 30 + 31 + 30 + 31 + 31 + 30 + 31 = 214 (not divisible by 7) (c). Jun + July + Aug + Sep = 30 + 31 + 31 + 30 = 122 (not divisible by 7) (d). Apr + May + June = 30 + 31 + 30 = 91 (divisible by 7) Hence, April and July months will have the same calendar.
49.
It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
(A) Sunday
(B) Saturday
(C) Friday
(D) Wednesday
Solution:
On 31st December, 2005 it was Saturday. Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days. ∴ On 31st December 2009, it was Thursday. Thus, on 1st Jan, 2010 it is Friday.
50.
Prove that any date in March of a year is the same day of the week corresponding date in November that year.
(A) Same day
(B) Not same day
(C) Next day
(D) Previous day
Solution:
We will show that the number of odd days between last day of February and last day of October is zero. March April May June July Aug. Sept. Oct. 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 = 241 days = 35 weeks = 0 odd day Number of odd days during this period = 0. Thus, 1st March of an year will be the same day as 1st November of that year. Hence, the result follows