olimpiade Matematika

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Time    : 60 minutes

MATH OLYMPIC GLORYPOWEROCK

1. What day of the week does May 28 2006 fall on

2. What will be the day of the week 15th August, 2010?

3. Today is Monday. After 61 days, it will be

4. On what dates of April, 2001 did Wednesday fall?

5. How many days are there in x weeks x days

1. What day of the week does May 28 2006 fall on
A. Saturday	B. Monday
C. Sunday	D. Thursday

Answer: Option C

Explanation:

28th May 2006 = (2005 years + period from 1-Jan-2006 to 28-May-2006)

We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)

Number of odd days in the period 2001-2005
= 4 normal years + 1 leap year
= 4 x 1 + 1 x 2 = 6

Days from 1-Jan-2006 to 28-May-2006 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 28(may)
= 148

148 days = 21 weeks + 1 day = 1 odd day

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

Hence May 28 2006 is Sunday.

2. What will be the day of the week 15th August, 2010?
A. Saturday	B. Monday
C. Sunday	D. Thursday

Answer: Option C

Explanation:

15th Aug 2010 = (2009 years + period from 1-Jan-2010 to 15-Aug-2010)

We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)

Number of odd days in the period 2001-2009
= 7 normal years + 2 leap year
= 7 x 1 + 2 x 2 = 11 = (11 - 7x1) odd day = 4 odd day

Days from 1-Jan-2010 to 15-Aug-2010
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31(may) + 30(Jun) + 31(Jul) + 15(Aug)
= 227

227 days = 32 weeks + 3 day = 3 odd day

Total number of odd days = (0 + 4 + 3) = 7 odd days = 0 odd day
0 odd day = Sunday
Hence 15th August, 2010 is Sunday.

3. Today is Monday. After 61 days, it will be
A. Sunday	B. Saturday
C. Monday	D. Thursday

Answer: Option B

Explanation:

61 days = 8 weeks 5 days = 5 odd days

Hence if today is Monday, After 61 days, it will be = (Monday + 5 odd days)
= Saturday

4. On what dates of April, 2001 did Wednesday fall?
A. 2nd, 9th, 16th, 23rd	B. 1st, 8th, 15th, 22nd, 29th
C. 4th, 11th, 18th, 25th	D. 3rd, 10th, 17th, 24th

Answer: Option C

Explanation:

We need to find out the day of 01-Apr-2001

01-Apr-2001 = (2000 years + period from 1-Jan-2001 to 01-Apr-2001)

We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)

Days from 1-Jan-2001 to 01-Apr-2001 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 1(Apr) = 91
91 days = 13 weeks = 0 odd day

Total number of odd days = (0 + 0) = 0 odd days
0 odd day = Sunday. Hence 01-Apr-2001 is Sunday.

Hence first Wednesday of Apr 2011 comes in 04^th and successive Wednesdays come in 11^th, 18^th and 25^th

5. How many days are there in x weeks x days
A. 7	B. 14x
C. 7x2	D. 8x

Answer: Option D

Explanation:

xx weeks xx days =(7×x)+x=7x+x=8x=(7×x)+x=7x+x=8x days