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# Numbers And Operations - Basic

When 25 is added to one-half of a certain number, the total is 54. What is the original number?

A) 54
B) 55
C) 56
D) 57
E) 58

If $$a$$ and $$b$$ are positive integers, what are all the solutions $$(a,b)$$ of the equation

$3a + 4b = 19?$

A) $$(1, 4)$$ only
B) $$(3, 3)$$ only
C) $$(5, 1)$$ only
D) $$(1, 4)$$ and $$(5, 1)$$ only
E) $$(1,4)$$ and $$(3,3)$$ only

If $$a+b = 4$$ and $$(a+b) c = 20$$, what is the value of $$c$$?

A) 3
B) 4
C) 5
D) 6
E) 10

When 50,000 is written as $$5.0 \times 10^n$$, what is the value of $$n$$?

A) 3
B) 4
C) 5
D) 6
E) 7

The farmer Chuck planted soybeans on $$\frac{ 1}{3}$$ of his land. If he planted $$30$$ acres of soybeans, how many acres of land does he own?

A) 10
B) 30
C) 90
D) 150
E) 300

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