Yes, if we know the line does not go through the origin then it cannot be y = x. It could be y = x + 1 or y = x - 3, but the y-intercept of the line cannot be 0. I hope that helps!

It's not just that they're both negative. The point (c, d) is to the left of the line y = x and both coordinates are negative. If we picked a point on the line y = x that has the same y-coordinate as (c, d) then we know that this point is (d, d) because any point on the line y = x will have the same x and y-coordinates. We could then move left until we reach (c, d). By doing this, the y-coordinate of out point remains the same and the x-coordinate becomes more negative. This is how we know that c < d. I hope that helps!

There are two ways of thinking about this: If we have -b < 0, we could add b to both sides to get 0 < b. Alternatively, if we have -b < 0, we can multiply both sides by -1. If we do this, we have to remember to flip the inequality sign because we're multiplying both sides by a negative number. This means we'd go from -b < 0 to b > 0. I hope that helps!

Exactly, but remember that the probability needs to be GREATER than 8/15 according to the question. So a solution that gives exactly 8/15 would not be sufficient.

That's a viable method, thank you for sharing it. However, we need to be a little more strict with the range of values that x can take or we'd end up selecting (D), which is not one of the correct answers, as one of our answer choices. While x can be -2, -1, or 1, x cannot be 2 because then (x - 2)(x + 3) = (0)(5) = 0 and this is not less than zero. Similarly, x cannot be between 2 and 3 because then (x - 2)(x + 3) will be positive and we want (x - 2)(x + 3) to be less than zero. By using either your method or the one shown in the video, we can say that x is between -3 and 2. This is why (B) and (C) are the answers to this question. I hope that helps!

16 2/3% is equivalent to a fraction of 1/6. If we wanted to know what 16 2/3% of x was, we could do [(16 2/3)/100]*x or we could do (1/6)*x. Both would give us the same answer. I hope that helps!

If we consider -x(x^2 -2), this is the same as saying (-1)x(x^2 - 2). If we multiply the whole expression by (-1), we could write this as (-1)(-1)x(x^2 - 2). The two (-1)s would multiply to give (1), so we could write the new expression as (1)x(x^2 - 2) which would simplify to x(x^2 - 2). In order to get x(-x^2 + 2), we would need to multiply our expression by another -1 to change the sign of everything inside that set of parentheses. However, we're only multiplying f(-x) by one -1 to give us -f(-x) so we won't get to x(-x^2 + 2). I'd make the same argument for (E) as I have for (D). I hope that helps, but please let me know if you have any further questions!

Thank you for the clarification.@@GRENinjaTutoring

This was an aside joke. Dana said the Europeans are bigger than the Americans, then clarified this to mean that she meant there are a greater NUMBER of Europeans than Americans and not that Europeans are BIGGER in size terms than Americans. I hope that helps!

Hi @Abkuyper, I'm sorry, I don't really know what you mean. The normal distribution Harry drew for this question has 65kg written at the middle point, which the question tells us is at the 50th percentile. Could you please rephrase your question and I'll do what I can to help.

If we make the length of all of the pieces of rope except the longest one equal to x, we will change the answer and it will not give us the correct answer. To find the maximum possible length of the smallest piece of rope, we want to minimize the other pieces' lengths. We were told in the question that the median piece of rope had a length of 72cm, so the fourth rope must have that length. We don't know the length of the fifth and sixth length of rope, but we know we want to make them as small as possible. We can't make them any smaller than 72cm, otherwise the fourth length of rope would no longer be the median, but we can make them 72cm. This is how we know the fourth, fifth, and sixth lengths of rope should all have a length of 72cm. I hope that helps!

We could test this out by setting p = -2 as an example. If we do that, then x > -28 and y < -18. We could follow the same process Harry used with the blue text and set x = -28 and y = -18 to test the extreme value. If we do that, (x - y)/5 = (-28 - (-18))/5 = (-28 + 18)/5 = (-10)/5 = -2. However, we know x > -28 and y < -18, so we could have something like x = -27.9 and y = -18.1 and in this case, (x - y)/5 = -9.8/5 = -1.96 > -2 = p. We could test this out for any other negative value of p and get the same results, so we can say that Quantity A is greater than Quantity B even if we use negative values for p. I hope that helps!

If the x-intercept of the line was zero, then the product of the x-intercept and the slope would also be zero. We wouldn't then be able to say that the product of the slope of line m and its x-intercept is negative because this wouldn't be possible -- we've already said it is zero. The GRE will ask difficult questions, but it will never provide a scenario with contradictions or one that isn't possible. For this reason, if line m passed through the origin then option (C) would not be an answer choice. I hope that helps!

Exactly, so because the product is negative this means that answer C is clearly yes because if it had crossed over (0,0) then the product would have been zero. We didn’t have to do any algebra at all, all we had to do was recognize that the product is negative, meaning the slope is negative and the x-int is positive or vice versa.

I'm sorry to say it doesn't work like that. You say at the end of your post that "the product is negative", but the product cannot be negative if the x-intercept is zero. There is a contradiction in the question you're trying to construct that means this whole scenario would never occur. The GRE will not ask you a question with a contraction like this. If the question had stated that the line passed through the origin, then answer choice (C) would not be asked. I hope that helps!

I'm wondering this too. For example, if the numbers were prime then obviously they are not correct.

t = -1 does violate the original expression because then t / |t| = -1 and t = -1, so t/|t| = t instead of t/|t| < t. The reason Harry needed to follow two different solution paths is because the absolute value sign does different things depending on whether t < 0 or t >= 0. From those solutions paths, we find the initial inequality is satisfied if -1 < t < 0 or 1 < t. This means we cannot tell whether t is greater than, less than, or equal to 1, so the answer to this question is (D). I hope that helps!

The revenue a company makes is just the amount of money it brings in during a given period of time. A company's profit is its revenue minus its costs, so the formula you used in this question was the formula for the company's profit, not its revenue. I hope that helps!

In a situation like this, we need to know whether both sides of the equation have the same sign or different signs. If we're unsure whether the signs are the same or different on the two sides of the equation, we can express this by saying 3m = 5n or 3m =-5n. This can be expressed in a single equation as 3m = +/- 5n. This is why we only need to put the +/- on one side of the equation. I hope that helps!

Thinking about whether the numbers are positive or negative, as Alex did in his explanation, works whether the numbers are integers or decimals. If ef = -0.1 and de = -0.2, then either we know that d and f are positive and e is negative or we know that d and f are negative and e is positive. In either of those cases (d^5)(e^2)(f^3) will be positive, so the answer to this question is (A). I hope that helps!

It all depends on the phrasing of the question. In this case, we were told "the lawn is 8m long and 4m wide" and the longer side was the horizontal side in the diagram. This means that *in this question* the length is the horizontal side and the width is the vertical side. This could change in other questions, depending on how the question is written, how any potential diagram is displayed, and the context of the problem. I'm sorry I can't give you a more definite answer, but I hope that helps!

The information in the table tells us there are 26,159 students in tertiary education and 40,601 students in primary education in Europe. This means the ratio of students in tertiary education to students in primary education in Europe is 0.644. This is much greater than the ratio of 0.27 Harry found for Northern Africa. Since this question asks us to find the region for which the ratio is smallest, Europe is not the answer to this question. Instead, the answer is Northern Africa or (A). I hope that helps!

The probability that Bob will go bowling every weekend of the three is 0.3 * 0.3 * 0.3 = 0.027 and as Dana showed in the video, the probability Bob will go bowling on at least one weekend is 0.657. I hope that helps, but please let me know if you have any other questions!

Yes, you can. When multiplying numbers, the order you do the multiplication doesn't matter. In other words, if we do 2*3 and then multiply the result by 5, we'll get 30, and if we do 5*3 and then multiply the result by 2, we'll still get 30. In short, it doesn't matter whether you list the variables as ea or ae in this question. I hope that helps!