The GRE Quantitative Multiple-Choice Question Explanations below will not make much sense to you if you've happened upon this page randomly. Before reading below, I recommend reading the following two articles first, so you understand the questions I'm explaining!
GRE Quantitative Multiple-Choice Questions with One Answer
Revised GRE Quantitative Section
Question 1 Explanation
This cube will be cut into three parts per side. So there will be three sorts of smaller painted cubes. The corners will have paint on 3 sides. The inner pieces will have pain on one side. The cubes on an edge, but not on a corner will be painted on two sides. Since there are 12 edges and only one of these cubes will emerge painted on two sides per edge (since we cut it into 3’s) our answer is 12.
General Tip: Draw a picture when the question is asking a geometric problem. It can greatly help, even if you are sure of the math.
Question 2 Explanation
Since 6 is even, and since the product of an even number with any other number must be even, then any number times six plus three must be odd. In symbols, 6n + 3 will be odd for any integer n. Since our remainder is 3, that interprets that the number is three greater than a multiple of six. So I is true. II cannot be true, because 15 + 2 = 17 and 17 is prime. III cannot be true because 16 divided by 7 has a remainder of 2, not 3.
General Tip: Go over your rules for odd/even with addition and multiplication. (Odd + even = odd, but odd * even = even, etc.)
Question 3 Explanation
The slope of line l is found using the equation m = (y2 – y1)/(x2 – x1) where m is the slope. So we have m = (5-2)/(5-4) = 3/1 = 3. A parallel line will have the same slope. Here, the question is looking for a different line than l itself. There are only 2 answers with slope 3, so it looks like there might be two correct answers. But y = 3x – 10 is line l. You can check by plugging in a point ( y = 3*4 – 10 = 2 and we get the point (4,2)). So p must be y = 3x + 2.
General Tip: Remember that a parallel line will have the same slope. A perpendicular line will have a slop that is the negative inverse (so if the slope of an original line is 2/3, the perpendicular line will have slope -3/2).
