Question

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.

Answer 1

Both statements provide relationships between variables, but without concrete numerical values, we cannot definitively answer whether the salesman's commission was larger than his base salary. Additional information or specific numerical values are needed to make a conclusive determination.

Statement 1: This tells us about the hypothetical scenario where the commission is 30 percent higher, resulting in a 10 percent increase in total income. However, it doesn't provide the actual values of the base salary or commission, making it insufficient to conclude whether the commission was larger.

Statement 2: This statement gives a relationship between the absolute difference of base salary and commission, but again, it lacks specific values. It states the difference is 50 percent of the base salary, but without knowing the base salary or commission, we cannot determine their relative sizes.

Combining the statements: Even when combined, the information is not enough to pinpoint the actual values of the base salary and commission. The 30 percent increase in commission and the 10 percent increase in total income do not provide a unique solution for the individual amounts.