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Adam packs either a ham sandwich or a peanut butter sandwich for his school lunch every day, except for days when the school is serving pizza during September.

During the month of September, he packed twice as many ham sandwiches as peanut butter sandwiches.

In the equation: $T = 3x + p$; $T$ represents the total number of days that Adam ate lunch at school during September, and $p$ represents the number of days that the school served pizza.

Which of the following must be a true statement?

(No Calculator)


The school served pizza less than half of the days in September.


Adam took his lunch $3$ times more often than the school served pizza.


$ x $ represents the number of days that Adam took a peanut butter sandwich.


Adam ate ham sandwiches for lunch more often than he ate pizza during September.

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