Cities – answers for the synonyms exercise

1c 2r 3l 4d 5h 6t 7a 8q 9k 10f 11j 12s 13i 14n 15p 16b 17e 18o 19g 20m
a7 b16 c1 d4 e17 f10 g19 h5 i13 j11 k9 l3 m20 n14 o18 p15 q8 r2 s12 t6

7a a rise in the number of
16b starting
1c synonymous with, closely associated with
4d series
17e yield good or profitable results
10f increasing
19g at any rate
5h short-lived, lasting for a short time
13i statistics
11j ensuring
9k more stringent, stricter
3l particularly, in a way which can or should be noticed
20m praiseworthy, commendable
14n more polluted
18o calculates
15p is logical, adds up
8q achieved this
2r very unpleasant (usually used of an atmosphere because of anger, or tension)
12s markedly
6t lowered

to be able to cut the air with a knife is usually used of an atmosphere because of anger, or tension
You could have cut the atmosphere with a knife would suggest there had been some serious disagrement or unpleasantness which you could still sense, even if no-one was actually saying anything about it. Here, more unusually, the author is using this idiom more literally.
to pay off – phrasal verb – to be worth doing, to yield good or profitable results
to add up = to make sense – it all adds up = it all seems logical