ZS Associates AMCAT Clocks and Calendars Questions with Answers

The hands of a clock coincide 11 times in every 12 hours
(Since between 11 and 1, they coincide only once,
i.e. at 12 o'clock).
==> The hands coincide 22 times in a day.

55 min. spaces are covered in 60 min.
60 min spaces are covered in (60/55 × 60)min = 65 5/11 min
Loss in 64 min = ( 65 5/11- 64 ) = 16/11 min
Loss in 24 hrs = ( 16/11 × 1/64 × 24 × 60 ) min
= 32 8/11 min

Angle traced by the hour hand in 6 hours = ( 360/12 × 11/3 )degrees
=180º

Angle traced by hour hand in 21/4 hrs = ( 360/12 × 21/4)º = 157 1/2º
Angle traced by min. hand in 15min. = ( 360/12 × 15 )º = 90º.
Required angle = ( 157 1/2 )º - 90º = 67 1/2º

15 Aug, 1947 = (1946 years + Period from 1.1.1947 to 15.8.1947)







Odd days in 1600 years = 0







Odd days in 300 years = 1







46 years = (35 ordinary years + 11 leap years) = (35 x 1 + 11 x 2)= 57 (8 weeks + 1 day) = 1 odd day







Jan. Feb. Mar. Apr. May. Jun. Jul. Aug







( 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15 ) = 227 days = (32 weeks + 3 days) = 3 odd days.







Total number of odd days = (0 + 1 + 1 + 3) = 5 odd days.







Hence, as the number of odd days = 5 , given day is Friday.

Each day of the week is repeated after 7 days.

So, after 63 days, it will be Monday.

After 61 days, it will be Saturday.

Currently there is no PrepInsta Explanation. Did you know?

You can also submit your own version of explanations under user explanation section and also view other submitted explanations by other users.

16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)

Counting of odd days :

1600 years have 0 odd day.


100 years have 5 odd days.
75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2 days) = 2 odd days

1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.



Jan Feb Mar Apr May Jun Jul



31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 2 days)

Total number of odd days = (0 + 2) = 2.



Required day was 'Tuesday'.

28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0

Odd days in 400 years = 0

5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) 6 odd days

(31[jan] + 28 [Feb]+ 31[Mar] + 30[April] + 28[May] ) = 148 days

148 days = (21 weeks + 1 day) 1 odd day.

Total number of odd days = (0 + 0 + 6 + 1) = 7 0 odd day.

Given day is Sunday