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A certain salesman's yearly income is determined by a base

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A certain salesman's yearly income is determined by a base

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A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Was the salesman's commission larger than his base salary last year?

1) If the amount of the commission had been 30 percent higher, the salesman's total income (salary plus commission) would have been 10 percent higher last year.

2) The absolute difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year.

The OA is A.

Source: Manhattan Prep

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swerve wrote:
A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Was the salesman's commission larger than his base salary last year?

1) If the amount of the commission had been 30 percent higher, the salesman's total income (salary plus commission) would have been 10 percent higher last year.

2) The absolute difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year.

The OA is A.

Source: Manhattan Prep
Given: Income = Base salary + Commision

Question: Was the salesman's commission larger than his base salary last year?

Let's take each statement one by one.

1) If the amount of the commission had been 30 percent higher, the salesman's total income (salary plus commission) would have been 10 percent higher last year.

Approach 1:

We see that despite the commission increasing by 30% (> 10%), the increase in income is proportionally lower, i.e., 10% (< 30%); it implies that base salary is larger than the commission. The answer is No. Sufficient.

Approach 2:

Say,

Income = I, Base salary = B, and Commission = C

Thus, I = B + C ---(1)

We have to determine whether C > B.

Given, "If the amount of the commission had been 30 percent higher, the salesman's total income (salary plus commission) would have been 10 percent higher last year," we have

1.1*I = B + 1.3*C ---(2)

Solving (1) and (2), we get B = 2C => B > C. The answer is No. Sufficient.

2) The absolute difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year.

|B - C| = B/2

Case 1: B - C = B/2 => B = 2C => B > C. The answer is No.
Case 2: -B + C = B/2 => B = 2C/3 => B < C. The answer is Yes.

No unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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