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# Suppose Sheetal’s birthday is on the Pth of October and Karthik’s birthday is on the Qth of November, where P and Q are perfect squares. If Sheetal was born 10 days before Karthik, then the value of P−2Q will be?

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Suppose Sheetal’s birthday is on the Pth of October and Karthik’s birthday is on the Qth of November, where P and Q are perfect squares. If Sheetal was born 10 days before Karthik, then the value of P−2Q will be __________

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1. The answer is 17 (Seventeen).

Explanation:
It’s given that –
P is a date in the month of October
Q is a date in the month of November.

P and Q both are perfect squares.

Perfect squares are numbers whose square root is a natural number, including 0.

The available dates in October that are perfect numbers are:

1*1 = 1st October
2*2 = 4th October
3*3 = 9th October
4*4 = 16th October, and
5*5 = 25th October

It’s mentioned that Pth October and Qth November are only 10 days apart.

As all the perfect square dates before 25th October do not occur 10 days before any date of November, the only choice we’re left with is 25th October.

10 days after 25th October comes 4th November.

here, both 25 and 4 are perfect squares.

thus, P = 25 and Q = 4.

Now, P – 2Q = 25 – 2(4) = 25 – 8 = 17 (Required Answer).

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