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### Oliveboard Question of the day

**Uttam Singh, who claims to be a reincarnation of Nostradamus, has predicted that in the first year of the 22nd century, four disasters would strike earth, one in each quarter. They would be on the Pth, Qth, Rth and Sth Fridays of the year respectively such that P, Q, R and S are perfect squares. When will the third disaster strike?**

__Options:__

- Sep 2
- Sep 3
- Sep 4
- Sep 9
- None of these

### Answer and Explanation

Answer key: b
First of all, one must know that the first year of the 22nd century is 2100 and not 2101. Moreover, 2100 is a non-leap year as it is not a multiple of 400.
The year 2100 has 5 odd days, so the year starts with a Friday.
A year consists of 52 weeks hence a quarter has 13 weeks.
As given in the question, P, Q, R and S belong to the 1st, 2nd, 3rd and 4th quarters respectively and are perfect squares.
Thus,
P = 1 or 4 or 9
Q = 16 or 25
R = 36
S = 49
Since the disaster has to strike in the third quarter, it will be on the 36th Friday of 2016.
1st day of the year is Friday, so the 36th Friday will fall on 1 + 35 x 7 = 246th day of the year.
We know that 2100 is a non-leap year, so total days up to the end of August = 31+28+31+30+31+30+31+31 = 243
Hence the 246th day would be September 3.

sept 3(36th friday)

sept 9

SEP.9