A sales manager at an industrial company has an opportunity to switch

MANHATTAN GMAT OFFICIAL SOLUTION:

You may reason that in order to answer this question, we need to know how much his new salary will be, and how much his taxes will increase by. This reasoning will lead you to conclude that the answer is C. And you'll be right.

Of course, you need to be very careful about using this tactic. Many problems on the GMAT are designed to hoodwink your algebraic reasoning—usually to make you think that you need to know every value precisely to answer the question.

For example, suppose the question in the previous problem were changed to “Will the manager make more money at the new job, after state taxes?” The correct answer in this case would be B. The problem explicitly states that the new job is higher-paying, so we only need to check to see whether the change in state tax might lead to a lower after-tax compensation. Statement (2) tells us indirectly that his new state taxes ($2,200) will be lower than his current state taxes (5% of $50,000 = ($2,500), so his after-state-tax compensation will definitely be higher in the new job. We do not need to find out how much higher his pre-tax salary would be to answer this question.

Because the GMAT frequently uses traps involving basic algebraic reasoning, you should only resort to using it if you are truly stuck.

"If his current annual salary is $50,000 and his current state tax rate is 5%, how much income after state tax would he make at the new job"

--> In the question stem, how do we know that the annual salary of $50000 is after 5% tax or before 5% tax?