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a day of bad luck

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by sanju09 » Sat Apr 03, 2010 1:35 am
All Sundays and the prime-numbered dates in the month September the last year amounted total holidays in the Factory X. How many nonprime-numbered dates in the month September the last year were holidays in the Factory X?

(1) There were exactly 14 holidays in the month September the last year in the Factory X.

(2) Friday the 13th occurred in the month September the last year, which superstition holds to be a day of bad luck.
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Source: — Data Sufficiency |
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by neoreaves » Sat Apr 03, 2010 3:38 am
IMO D

The number of days in september = 30
Number of holidays = number of primes + sundays - (days which are prime and sundays)
Number or primes -> Number of primes from 2 to 29 = 2,3,5,7,11,13,17,19,23,29 = 10
Number of Sundays = 4 or 5

Number of non prime holidays = Number of sundays that dont fall on prime dates

Max number of Sundays = 5 (Sunday on 1st or 2nd of Sept)

1) 14 holidays ...
this means
p + s - d = 14
10 + s - d = 14
s - d = 4

Thus we know that these 4 will be the non prime holidays so Sufficient

2) From this we can calculate the number of sundays and the number of sundays that fell on prime dates ..which will help us in finding the non prime sundays .....Sufficient
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