$$\frac{{126}}{7}$$ = 0 Each day of the week is repeated after 7 days. So, after 126 days, it will be Friday. After 126 days, it will be Friday
52.
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.
Odd days ⇒ The number of days more than complete number of weeks in the given period are odd days. 123 = 7 × 17 + 4 ⇒ 4 odd days.
55.
If today is Monday, what will be the day 350 days from now?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday
Solution:
350 days, $$\frac{{350}}{7}$$ = 50, no odd days, so it will be a Monday.
56.
What was the day of the week on 16th August, 1947?
(A) Sunday
(B) Monday
(C) Saturday
(D) Thursday
Solution:
15th August, 1947 = (1946 years + Period from 1st Jan., 1947 to 15th ) Counting of odd days: 1600 years have 0 odd day. 300 years have 1 odd day. 47 years = (11 leap years + 36 ordinary years) = [(11 x 2) + (36 x 1) ] odd days = 58 odd days = 2 odd days Jan Feb Mar Apr May Jun Jul Aug = 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15 = 227 days = (32 weeks + 3 days) = 3, Total number of odd days = (0 + 1 + 2 + 3) odd days = 6 odd days. Hence, the required day was 'Saturday'.
57.
If 25th of August in a year is Thursday, the number of Mondays in that month is
(A) 5
(B) 7
(C) 9
(D) 11
Solution:
Given that 25th August = Thursday Hence 29th August = Monday So 22nd,15th and 8th and 1st of August also will be Mondays Number of Mondays in August = 5
58.
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.
59.
Today is Thursday. What day of the week it was 30 days?
(A) Sunday
(B) Monday
(C) Tuesday
(D) Wednesday
Solution:
30 days = 4 x 7 + 2 = 2 odd days The day is 2 days before Thursday i.e Tuesday
60.
If today is Saturday, what will be the day 350 days from now ?
(A) Saturday
(B) Friday
(C) Sunday
(D) Monday
Solution:
350 days = $$\frac{{350}}{7}$$ = 50 weeks, i.e No odd days, So it will be a Saturday.