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The dates 3rd April, 2005; 6th August, 2010 and 5th December, 2013 when written in Date-Month-Year Form have a unique mathematical property. The Indian Independence Day of which year among the following has the same property?
- a)2017
- b)2016
- c)2018
- d)2015
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The dates 3rd April, 2005; 6th August, 2010 and 5th December, 2013 whe...
If we see carefully we can find that these dates have property yy2 = dd2 + mm2
3rd April, 2005 - 03/04/05
(05)2 = (03)2 + (04)2
6th August, 2010 - 06/08/10
(10)2 = (06)2 + (08)2
5th December, 2013 - 05/12/13
(13)2 = (05)2 + (12)2
Similarly,
Independence day 2017 - 15 August 2017 - 15/08/17
By above logic: (17)2 = (15)2 + (08)2
No other option satisfy the above condition. So, Indian Independence Day of 2017 has the same property.
3rd April, 2005 - 03/04/05
(05)2 = (03)2 + (04)2
6th August, 2010 - 06/08/10
(10)2 = (06)2 + (08)2
5th December, 2013 - 05/12/13
(13)2 = (05)2 + (12)2
Similarly,
Independence day 2017 - 15 August 2017 - 15/08/17
By above logic: (17)2 = (15)2 + (08)2
No other option satisfy the above condition. So, Indian Independence Day of 2017 has the same property.
Most Upvoted Answer
The dates 3rd April, 2005; 6th August, 2010 and 5th December, 2013 whe...
The given dates, 3rd April, 2005; 6th August, 2010; and 5th December, 2013, have a unique mathematical property when written in Date-Month-Year form. Let's analyze this property and find the Indian Independence Day with the same property among the given options.
Analysis:
To understand the mathematical property, let's write down the dates in the format of DD-MM-YYYY:
- 3rd April, 2005: 03-04-2005
- 6th August, 2010: 06-08-2010
- 5th December, 2013: 05-12-2013
Now, let's break down the dates into their components:
- 03-04-2005: Day = 3, Month = 4, Year = 2005
- 06-08-2010: Day = 6, Month = 8, Year = 2010
- 05-12-2013: Day = 5, Month = 12, Year = 2013
Pattern:
Upon observing the dates, we can notice that the product of the day and month is equal to the last two digits of the year.
- For 03-04-2005: 3 * 4 = 12 (last two digits of 2005)
- For 06-08-2010: 6 * 8 = 48 (last two digits of 2010)
- For 05-12-2013: 5 * 12 = 60 (last two digits of 2013)
Indian Independence Day:
Now, let's find the Indian Independence Day with the same property among the given options: 2017, 2016, 2018, and 2015.
For 2017:
- Day = 15
- Month = 8
- Year = 2017
The product of the day and month is 15 * 8 = 120. However, the last two digits of the year, 17, do not match this value. Therefore, 2017 is not the answer.
For 2016:
- Day = 15
- Month = 8
- Year = 2016
The product of the day and month is 15 * 8 = 120. The last two digits of the year, 16, match this value. Therefore, 2016 could be the answer.
For 2018:
- Day = 15
- Month = 8
- Year = 2018
The product of the day and month is 15 * 8 = 120. However, the last two digits of the year, 18, do not match this value. Therefore, 2018 is not the answer.
For 2015:
- Day = 15
- Month = 8
- Year = 2015
The product of the day and month is 15 * 8 = 120. However, the last two digits of the year, 15, do not match this value. Therefore, 2015 is not the answer.
Therefore, among the given options, the Indian Independence Day with the same mathematical property is
Analysis:
To understand the mathematical property, let's write down the dates in the format of DD-MM-YYYY:
- 3rd April, 2005: 03-04-2005
- 6th August, 2010: 06-08-2010
- 5th December, 2013: 05-12-2013
Now, let's break down the dates into their components:
- 03-04-2005: Day = 3, Month = 4, Year = 2005
- 06-08-2010: Day = 6, Month = 8, Year = 2010
- 05-12-2013: Day = 5, Month = 12, Year = 2013
Pattern:
Upon observing the dates, we can notice that the product of the day and month is equal to the last two digits of the year.
- For 03-04-2005: 3 * 4 = 12 (last two digits of 2005)
- For 06-08-2010: 6 * 8 = 48 (last two digits of 2010)
- For 05-12-2013: 5 * 12 = 60 (last two digits of 2013)
Indian Independence Day:
Now, let's find the Indian Independence Day with the same property among the given options: 2017, 2016, 2018, and 2015.
For 2017:
- Day = 15
- Month = 8
- Year = 2017
The product of the day and month is 15 * 8 = 120. However, the last two digits of the year, 17, do not match this value. Therefore, 2017 is not the answer.
For 2016:
- Day = 15
- Month = 8
- Year = 2016
The product of the day and month is 15 * 8 = 120. The last two digits of the year, 16, match this value. Therefore, 2016 could be the answer.
For 2018:
- Day = 15
- Month = 8
- Year = 2018
The product of the day and month is 15 * 8 = 120. However, the last two digits of the year, 18, do not match this value. Therefore, 2018 is not the answer.
For 2015:
- Day = 15
- Month = 8
- Year = 2015
The product of the day and month is 15 * 8 = 120. However, the last two digits of the year, 15, do not match this value. Therefore, 2015 is not the answer.
Therefore, among the given options, the Indian Independence Day with the same mathematical property is
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The dates 3rd April, 2005; 6th August, 2010 and 5th December, 2013 when written in Date-Month-Year Form have a unique mathematical property. The Indian Independence Day of which year among the following has the same property?a)2017b)2016c)2018d)2015Correct answer is option 'A'. Can you explain this answer?
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