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Expert replies
by shashank.ism » Tue Feb 09, 2010 1:12 pm
How many years in the 18th century had no such day that satisfied yy = mm × dd?


20
23
18
21
19
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Source: — Problem Solving |

by komal » Wed Feb 17, 2010 4:40 am
shashank.ism wrote:How many years in the 18th century had no such day that satisfied yy = mm × dd?


20
23
18
21
19
We have to find two digit numbers 'yy' such that they are prime numbers greater than 31. There are 14 prime numbers
greater than 31 and less than 100. There are 6 more cases:
a. The second multiples of 37, 41, 43 and 49 will give us 4 cases.
b. The second multiple of 29 and 31 will give us two more
cases since if 'yy' = 58 or 62, in those year the month of
February will have only 28 days.
So, the total number of cases = 14 + 4 + 2 = 20.
Option (1) is the correct choice.
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