DXC Quants Clocks and Calender Quiz 1

Solution: In 60 minutes the minute hand covers 360°. Therefore, angles of the minute hand can be denoted as 6n, where n depicts the number of minutes past midnight.

Similarly, in 60 minutes the hour hand moves 30 degrees, that is, the angle of the hour hand can be given by 0.5n.

The hands starts to move at midnight and the first time they subtend a right angle can be given by:

6n = 0.5n + 90

5.5n = 90

n = 16 4/11

The next time the right angle is formed when the minutes hand has gained 180 degrees on the hour hand, 

6n = 0.5n +270

5.5n = 270

n = 49 1/11

For every 180 degree the minute hands gain on hour hand will be one right angle:

• 49 1/11 – 16 4/11


• 32 8/11

• 1440 / (32 8/11) = 44


• Every 24 hours the minute hand and hour hand form right angles 44 times.

Solution: The hands of the clock coincide 11 times in 12 hours. So in a day it coincides 22 times.

Solution: On 31st December, 2005 it was Monday.

Number of odd days from the year 2005 to the year 2009 = (1 + 1 + 1 + 2+1) = 6 days.

 Thus, on 1st Jan, 2010 it is Saturday.

Explanation:
If a month has 31 days, and it starts with sunday, Then Sundays, Mondays, tuesdays are 5 for that month. If this month starts with monday, then mondays, tuesdays, and wednesdays are 5 and remaining days are 4 each. so this month starts with Monday.

Explanation: Reference day : May 25th Monday

Days from May 23th to July 15 = 8 + 30 +15 = 53

No of odd days : 53/7 = 4

so the day will be  Friday.

Solution:

In an ordinary year, there are 365 days which means 52 weeks and 1 odd day but in a leap year there are 366 days which means 52 weeks and 2 odd days

So between 2005 and 2009 only 2008 is a leap year so total odd days between 2005 and 2009 are 5 days.

As given the Mother’s Day in 2005 falls on Monday

So Monday + 5 odd days = Saturday

So Mother’s Day will fall on Saturday in 2009.

Explanation:
Rahul speak lies on Monday,Tuesday,Wednesday;
Rahul speak truth on Sunday,Thursday,Friday,Saturday;
Rohit speak truth on Sunday,Monday,Tuesday,Wednesday;
Rohit speak lie on Thursday,Friday,Saturday;
Suppose,Rahul tells truth on thursday that Yesterday(Wednesday)
was one of the day which
he/she tells lies.
Then Rohit tells lie on thursday that Yesterday(Wednesday) was one of the
day which he/she tell lying.
So Yesterday is Wednesday.

Explanation:
7 days from thursday will be thursday
Then 8th day will be Friday

Explanation:
During the interval we have two leap years as 1992 and 1996 and it contains February of both these years.
∴ The interval has ( 6 + 2 ) = 8 days = 1 odd day.
Hence, January 7, 1998 was Wednesday.

Explanation
On 31st December, 2021 it was Friday
Number of odd days from the year 2022 to the year 2026 = (1 + 1 + 2 + 1) = 5 days.
On 31st December 2025, it was Wednesday.
Thus, on 1st Jan, 2026 it is Thursday