What is the difference between "blow up" and "blow off"?

[Horst]

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #98 "The Parliamentary Candidate (1)", question 8

That was the day he thought he was going to be blown ......... by a bomb.

(a) out
(b) over
(c) off
(d) up

English Language Proficiency Tests, Advanced Level

ESL/EFL Test #98 "The Parliamentary Candidate (1)", answer 8

That was the day he thought he was going to be blown up by a bomb.

Correct answer: (d) up

Your answer was: incorrect
That was the day he thought he was going to be blown off by a bomb.
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Idon´t understand the difference between up and off?

Horst

[Mister Micawber]

.
blow up,
a. to come into being: A storm suddenly blew up.
b. to explode: The ship blew up.
c. to cause to explode: to blow up a bridge.
d. to exaggerate; enlarge: He blew up his own role in his account of the project.
e. Informal. to lose one's temper: When he heard she had quit school, he blew up.
f. to fill with air; inflate: to blow up a tire.
g. Photography. to make an enlarged reproduction of.
h. Mathematics. (of a function) to become infinite.

blow off,
a. to allow steam to be released.
b. Informal. to reduce or release tension, as by loud talking.
.
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Native English teacher at Mister Micawber's