SAT Translating Word Problems

Correct Answer: D

Solution 1:

First we translate the words into math:

Which of the following is equal to $\underbrace{\text{half}}_{\frac{1}{2}} \quad \underbrace{\text{of}}_{\times} \quad \underbrace{37\ \text{percent}}_{\frac{37}{100}\ \text{or}\ 37\%} \quad \underbrace{\text{of}}_{\times}\quad 540$ ?

We notice from the answer choices that we need not actually compute the result. We find an expression which represents the given statement, simplify it, and then translate some of the math into words:

$\frac{1}{2}\cdot \frac{37}{100} \cdot 540=\frac{37}{100}\cdot270=37\%\ \text{of}\ 270$

We could have also done the following:

$\frac{1}{2}\cdot 37\%\ \cdot 540=37\%\ \text{of}\ 270$

Solution 2:

Tip: Use a calculator.
We use a calculator to compute the quantity in the problem.

$\frac{1}{2}\cdot \frac{37}{100} \cdot 540=99.9$

Again using a calculator, we compute the quantity in each of the answer choices, and we look for the choice that yields $99.9$ .

(A) $\frac{1}{2} \cdot 37 \cdot 540=9990 \neq 99.9$ . Eliminate (A).
(B) $37\%\ \text{of}\ 540=\frac{37}{100} \cdot 540=199.8 \neq 99.9$ . Eliminate (B).
(C) $37\frac{1}{2}\%\ \text{of}\ 540=\frac{75}{2} \cdot 540=20,250 \neq 99.9$ . Eliminate (C).
(D) $37\%\ \text{of}\ 270=\frac{37}{100} \cdot 270=99.9$ . This is the correct answer.
(E) $\frac{1}{2} \cdot 37\%\ \text{of}\ 270= \frac{1}{2} \cdot \frac{37}{100} \cdot 270=49.95\neq99.9$ . Eliminate (E).

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Incorrect Choices:

(A) , (B) , (C) , and (E)
See Solution 2 for why we can eliminate these choices.