Question

Nia and Farah throw a surprise birthday party for Jenna in September. But this year, but they couldn't recall the exact date of her birthday.

Nia recalls that Jenna's birthday was before the ${19}^{th}$ but after the ${13}^{th}$, while Farah recalls that it was on a Sunday after the ${15}^{th}$ of September.

If $1^{st}$ September of the previous year was a Thursday, then find on which date Jenna's birthday falls this year.
Assumption: Both years are non-leap years.

• A. ${16}^{th}$ September
• B. ${17}^{th}$ September
• C. ${18}^{th}$ September
• D. ${19}^{th}$ September

Answer 1

The correct option is B ${17}^{th}$ September

The calendar advances 1 day in regular years.

Since $1^{st}$ September of the previous year was a Thursday, then this year, $1^{st}$ September will fall on Friday.

From this, we can say that Sunday will fall on $3^{rd}$ September.

Further, Sundays will fall on ${10}^{th}$, ${17}^{th}$, and ${24}^{th}$ September.

As per Nia, Jenna's birthday falls before ${19}^{th}$ but after ${13}^{th}$, and as per Farah, her birthday falls on the Sunday after ${15}^{th}$.

After ${15}^{th}$, Sunday falls on ${17}^{th}$ September.

Thus, Jenna's birthday falls on ${17}^{th}$ September.