1985 AMC 12 Problem 7

Question

In some computer languages (such as APL), when there are no parentheses in an algebraic expression, the operations are grouped from right to left. Thus,

a\times b-c

in such languages means the same as

a(b-c)

in ordinary algebraic notation. If

a\div b-c+d

is evaluated in such a language, the result in ordinary algebraic notation would be

\frac ab-c+d

\frac ab-c-d

\frac{d+c-b}{a}

\frac{a}{b-c+d}

\frac{a}{b-c-d}

Answer: E

Concepts:algebraic manipulation order of operations

Difficulty rating: 1360

Small hint:

Begin with the rightmost operation,

c+d

Big hint:

Next subtract that result from

b,

and only then divide

a

Solution:

Grouping from the right first gives

c+d.

Subtracting this result from

b

gives

b-(c+d)=b-c-d.

Finally, dividing

a

by that quantity gives

\frac{a}{b-c-d}.

Thus the correct answer is E.