1. 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

Explanation: On 31

^{st}December, 2005 it was Saturday.

Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.

On 31

^{st}December 2009, it was Thursday.

On 1

^{st}Jan, 2010 it is Friday.

2. What was the day of the week on 28^{th} May, 2006?

a) Thursday

b) Friday

c) Saturday

d) Sunday

Explanation: 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

Jan. Feb. March April May

(31 + 28 + 31 + 30 + 28 ) = 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.

3. What was the day of the week on 17^{th} June, 1998?

a) Monday

b) Tuesday

c) Wednesday

d) Thursday

Explanation: 17

^{th}June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)

Odd days in 1600 years = 0

Odd days in 300 years = (5 x 3) ≡ 1

97 years has 24 leap years + 73 ordinary years.

Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.

Jan. Feb. March April May June

(31 + 28 + 31 + 30 + 31 + 17) = 168 days

168 days = 24 weeks = 0 odd day.

Total number of odd days = (0 + 1 + 2 + 0) = 3.

Given day is Wednesday.

4. What will be the day of the week 15^{th} August, 2010?

a) Sunday

b) Monday

c) Tuesday

d) Friday

Explanation: 15

^{th}August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)

Odd days in 1600 years = 0

Odd days in 400 years = 0

9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days ≡ 4 odd days.

Jan. Feb. March April Mayb June July Aug.

(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days

227 days = (32 weeks + 3 days) ≡ 3 odd days.

Total number of odd days = (0 + 0 + 4 + 3) = 7 ≡ 0 odd days.

Given day is Sunday.

5. Today is Monday. After 61 days, it will be:

a) Wednesday

b) Saturday

c) Tuesday

d) Thursday

Explanation: Each day of the week is repeated after 7 days.

After 63 days, it will be Monday.

After 61 days, it will be Saturday.

6. What was the day of the week on 26-January-1950?

a) Monday

b) Sunday

c) Thursday

d) Wednesday

Explanation: Formula : (Date + Month code + No.of years + No.of leap year + Century code)/7

$$\eqalign{ & = \frac{{26 + 1 + 50 + 12 + 0}}{7} = \frac{{89}}{7} \cr & = 5 \cr & = {\text{Thursday}} \cr} $$

7. Today is Thursday. What day of the week it was 30 days?.

a) Sunday

b) Monday

c) Tuesday

d) Wednesday

Explanation: 30 days = 4 x 7 + 2 = 2 odd days

The day is 2 days before Thursday i.e Tuesday

8. 01-Jan-2007 was Monday. What day of the week lies on 01-Jan-2008?

a) Monday

b) Tuesday

c) Wednesday

d) Thursday

Explanation: Given that January 1, 2007 was Monday.

Odd days in 2007 = 1 (we have taken the complete year 2007 because we need to find out the odd days from 01-Jan-2007 to 31-Dec-2007, that is the whole year 2007)

Hence January 1, 2008 = (Monday + 1 Odd day) = Tuesday

9. 1.12.91 is the first Sunday. Which is the fourth Tuesday of December 91?

a) 20.12.91

b) 22.12.91

c) 24.12.91

d) 25.12.91

Explanation: Given that 1.12.91 is the first Sunday

Hence we can assume that 3.12.91 is the first Tuesday

If we add 7 days to 3.12.91, we will get second Tuesday

If we add 14 days to 3.12.91, we will get third Tuesday

If we add 21 days to 3.12.91, we will get fourth Tuesday

⇒ Fourth Tuesday = (3.12.91 + 21 days) = 24.12.91

10. Today is Thursday. The day after 59 days will be?

a) Sunday

b) Monday

c) Tuesday

d) Wednesday

Explanation: 59 days = 8 weeks 3 days = 3 odd days

Hence if today is Thursday, After 59 days, it will be

= (Thursday + 3 odd days)

= Sunday