A year is a leap year if and only if the year number is divisible by 4

Question

A year is a leap year if and only if the year number is divisible by 400 (such as 2000) or is divisible by 4 but not 100 (such as 2012). The 200th anniversary of the birth of novelist Charles Dickens was celebrated on February 7, 2012, a Tuesday. On what day of the week was Dickens born?

(A) Friday
(B) Saturday
(C) Sunday
(D) Monday
(E) Tuesday

(A) Friday
(B) Saturday
(C) Sunday
(D) Monday
(E) Tuesday

chetan2u · Accepted Answer

1. A normal year has 365 days or 7*52+1, so a date falling on Sunday this year will be Saturday last year.
2. A leap year has 366 days or 7*52+2, so a date falling on Sunday this year will be friday last year.

Now let us check leap years in 1812 to 2012..
200 years means 200/4 or 50 leap years, but 1900 is not a leap year so 49 leap year and 151 normal years..
So we will go back by 2*49+151*1..
2*49 is a multiple of 7 and so will not make any difference.
151=7*21+4..
Thus we go back by four days..
Tuesday ->1->Monday ->2-> Sunday ->3-> Saturday ->4-> Friday

A

CrackverbalGMAT · Answer

Here, we need to move to the left as decreasing the year or date number and we have to move to right as increasing the year or date number.
Every non leap year we move to the left results in moving one day to the left.
[As 365 ≡ 1 mod 7=>A remainder of 1 when 365 is divided by 7]

Every leap year we move to the right results in moving two days to the right.
[As 366 ≡ 2 (mod 7)=> A remainder of 1 when 365 is divided by 7]

Now 200 years would have 200/4= 50 leap years as leap year occurs once in 4 years.
[b]1900 here doesn’t count as a leap year by the problem.[/b]

Thus there would be 151 regular years and 49 leap years and thus
1(151) + 2(49) =249 days back.

249 ≡ 4 mod 7=> A remainder of 4 when 249 is divided by 7
Hence 4 days back from Tuesday would be Friday. (A)

Hope this helps. Keep studying

nazii · Answer

HELLO
would you pls say how did you reach to this point? "1900 here doesn’t count as a leap year by the problem." I mean among all the years between, HOW our attention should go for 1900? why not others? how we can understand it in other questions
Best regards in advance for you help

GMATGuruNY · Answer

Every year that is a multiple of 4 is a leap year with one exception:
For a year that ends in 00 to be a leap year, it must be a multiple not just of 4 but of 400.
Thus:
1900 is NOT a leap year.
Implication:
Every 4-year increment starting on February 7, 1812 will include a leap year except for the increment from  January 1, 1900 to December 31, 1903 .

Since there are fifty 4-year increments during the 200-year span, but one of these increments -- the increment in red above -- does not include a leap year, there will be a total of 49 leap years (leaving 151 regular years).

Note:
364 = 52*7 = 52 complete weeks

Each regular year is composed of 365 days, while each leap year is composed of 366 days.
Calculating the number of days for 151 regular years + 49 leap years, we get
(151*365) + (49*366)
= 151(364+1) + 49(364+2)
= (151*364) + 151 + (49*364) + 98
= (200*364) + 249
= (200*364) + (35*7) + 4

The first two terms are multiples of 7 and thus represent complete weeks.
The last term -- 4 -- implies that the day of the week in 2012 will be 4 days beyond the day of the week in 1812.
Since Tuesday in 2012 must be four days beyond the day of the week in 1812, the day of the week in 1812 must be Friday.

A

AditiDeokar · Answer

Hi  chetan28 ,

I don't understand how do we draw our attention to 1900, also could you please explain  So we will go back by 2*49+151*1..
2*49 is a multiple of 7 and so will not make any difference.

A year is a leap year if and only if the year number is divisible by 4

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A year is a leap year if and only if the year number is divisible by 4

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