GMAT Question of the Day (Mar 1): Algebra and Critical Reasoning

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Math (PS)

Function F(x) is defined as follows:
if x is positive or 0 then F(x) = 1 - x;
if x is negative then F(x) = x - 1.

Which of the following is true about F(x)?

I. F(|x|) = |F(x)|

II. F(x) = F(-x)

III. |F(x + 1)| = |x|

(A) I only
(B) II only
(C) III only
(D) I and III only
(E) not I, II, or III

OA and Explanation

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Verbal (CR)

While Governor Verdant has been in office, the state’s budget has increased by an average of 6 percent each year. While the previous governor was in office, the state’s budget increased by an average of 11.5 percent each year. Obviously, the austere budgets during Governor Verdant’s term have caused the slowdown in the growth in state spending.

Which of the following, if true, would most seriously weaken the conclusion drawn above?

(A) The rate of inflation in the state averaged 10 percent each year during the previous governor’s term in office and 3 percent each year during Verdant’s term.
(B) Both federal and state income tax rates have been lowered considerably during Verdant’s term in office.
(C) In each year of Verdant’s term in office, the state’s budget has shown some increase in spending over the previous year.
(D) During Verdant’s term in office, the state has either discontinued or begun to charge private citizens for numerous services that the state offered free to citizens during the previous governor’s term.
(E) During the previous governor’s term in office, the state introduced several so-called “austerity” budgets intended to reduce the growth in state spending.

OA and Explanation

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