Select the most appropriate preposition from the given alternatives to fill in the blanks and make the sentence meaningfully complete.

Simulations of the $20\mathrm{th}$ century by climate models that exclude the observed increase _____ greenhouse gases fail to simulate the increase in temperature over the second half of the $20\mathrm{th}$ century.

Select the most appropriate preposition from the given alternatives to fill in the blanks and make the sentence meaningfully complete.

In extremely poor societies, children can be put to work _____ a young age and are therefore a source of income.

Select the most appropriate preposition from the given alternatives to fill in the blanks and make the sentence meaningfully complete.

People who are averse _____ hard work, generally do not succeed in life.

Select the most appropriate preposition from the given alternatives to fill in the blanks and make the sentence meaningfully complete.

I have known her _____ a long time.

Select the most appropriate preposition from the given alternatives to fill in the blanks and make the sentence meaningfully complete.

I accepted the offer ____ certain conditions.

Select the most appropriate preposition from the given alternatives to fill in the blanks and make the sentence meaningfully complete.

She is a woman _____ humble origin.

Select the most appropriate preposition from the given alternatives to fill in the blanks and make the sentence meaningfully complete.

There is no cure _____ the common cold.

Select the most appropriate preposition from the given alternatives to fill in the blanks and make the sentence meaningfully complete.

 I ran _____ John yesterday, and it was a pleasant surprise.

Select the most appropriate preposition from the given alternatives to fill in the blanks and make the sentence meaningfully complete.

My grandmother enjoyed boating _____ the lovely lake.