GRE Practice Question 2 – Number Properties

Try this GRE quantitative question on Number properties [Difficulty Level – Hard] If (a – b)c < 0, which of the following cannot be true? a. a < b b. c < 0 c. |c| < 1 d. ac > bc e. (a + b)(a – b) > 0 Here is the solution: If (a – b)c < 0, the expression (a – b) and the variable c must have opposite signs. Let's check each answer choice: (A) UNCERTAIN: If a < b, a – b would be negative. It is possible for a – b to be negative according to the question. (B) UNCERTAIN: It is possible for c to be negative according to the question. (C) UNCERTAIN: This means that -1 < c < 1, which is possible according to the question. (D) FALSE: If we rewrite this expression, we get ac – bc > 0. Then, if we factor this, we get: (a – b)c > 0. This directly contradicts the information given in the question, which states that (a – b)c < 0. (E) UNCERTAIN: If we factor this expression, we get (a + b)(a – b) < 0. This tells us that the expressions a + b and a – b have opposite signs, which is possible according to the question. The correct answer is...

Read More

GRE Practice Question 1 – Percentages

Try this GRE quantitative question [Difficulty Level – Medium] The original price of an item was increased by 35 percent, resulting in a new price. The new price of the item was increased by 20 percent, resulting in a final price. What percent greater than the original price is the final price? A. 42% B. 49% C. 55% D. 62% E. 70% Here is the solution: This is a good question to solve by Picking Numbers. Let’s say that the original price is 100 dollars. The new price, in dollars, is 100 + 0.35(100)= 100 + 35 = 135. The final price, in dollars, is 135 + 0.2(135) = 135 + 27 = 162. Thus, the original price is 100 dollars, and the final price is 162 dollars. The final price of 162 dollars is 62 dollars greater than the original price of 100 dollars. The percent that the final price of 162 dollars is greater than the original price of 100 dollars is...

Read More