## What amount did Jean earn…

## Solution:

We need to determine the amount that Jean earned from the commission on her sales in the first half of 1988.

**Statement One Alone: **

In 1988 Jean’s commission was 5 percent of the total amount of her sales.

Before analyzing statement one let’s define some variables:

a = Jean’s commission in the first half of 1988

b = Jean’s commission in the second half of 1988

A = Jean’s total sales in the first half of 1988

B = Jean’s total sales in the second half of 1988

We are trying to determine the value of a. In statement one we are given that in 1988 Jean’s commission was 5 percent of the total amount of her sales. Translating this into an equation gives us:

(a + b)/(A + B) = 0.05

Since we cannot determine a value for a, statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

**Statement Two Alone: **

The amount of Jean’s sales in the second half of 1988 averaged $10,000 more per month than in the first half.

Using the information in statement two we can create the following equation:

B/6 = (A/6) + 10,000

Multiplying the entire equation by 6 we obtain:

B = A + 60,000

Since we cannot determine a value for a, statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

**Statements One and Two Together: **

From statements one and two we have the following two equations:

1) (a + b)/(A + B) = 0.05

2) B = A + 60,000

We see that even if we substitute A + 60,000 for B in the equation (a + b)/(A + B) = 0.05, we still do not have enough information to determine the value of a.

**Answer: E**