Question

Guy's net income equals his gross income minus his deductions. By what percent did Guy's net income change on January 1,1989, when both his gross income and his deductions increased?
(1) Guy's gross income increased by 4 percent on January 1, 1989.
(2) Guy's deductions increased by 15 percent on January 1, 1989.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is E Statements (1) and (2) together are not sufficient.

• We have to determine by what percent Guy’s net income (gross income minus deductions) changed on January 1, 1989, when both his gross income and his deductions increased.

1. Considering statement 1, Guy’s gross income increased by 4 percent on January 1, 1989. However, no information is given about the values of Guy's gross income before Jan 1, his deductions after Jan 1, or his deductions before Jan 1, and so cannot be determined; NOT sufficient.
2. Considering statement 2, Guy’s deductions increased by 15 percent on January 1, 1989. However, no information is given about the values of Guy's gross income after Jan 1, gross income before Jan 1, or his deductions before Jan 1 and so cannot be determined; NOT sufficient.

• Taking (1) and (2) together is insufficient since the values of Guy's gross income before Jan 1 and his deductions before Jan 1 are unknown. The correct answer is E; both statements together are still not sufficient.