GRE Hard Questions

This is Raj and I am preparing fro GRE examination as per me I have done ample practice but checking my level I want some hard Questions of Math’s and English so please help me

[Shaleen]

As you are asking about the GRE Hard Questions of Math’s and English here I would like to provide you the same please have a look on that

Which of the following must be greater than x, where -1<x<0? Choose ALL that apply.

x^3
root{3}{x}
x^2+x
x^2-x^3
1+2x
This is a very difficult, time-consuming problem. Unfortunately, there will be a few such problems on the new GRE math section. The good news is that the new GRE will not have too many problems that are multiple answer questions. Out of the 20 questions on the quant section, you will only have about one or two such questions.

Choose Numbers

When dealing with variables in the answer choices, you should always plug-in your own numbers. Starting with (A), we can see that we will have a negative fraction: multiplying a negative times itself three times will yield a negative: (-)(-)(-) = (-). The question is will this fraction be greater or smaller than x?
Let’s plug in x=-1/2
(-1/2)(-1/2)(-1/2)=-1/8

On a number line, -1/8 is closer to zero than -1/2. Therefore, x^3 will be greater than x. This will hold in each case, because as you take any fraction between -1 and 0 to an odd power, you will always make this number approach zero. ONE ANSWER.

For (B), the opposite is true. Taking a cube root of a fraction between -1 and 0 will make that number more negative. At first, you may be hard-pressed to find a fraction in which you can easily take the cube root. From above, we cubed -1/2 to get -1/8. Therefore, the cubed root of -1/8 is -1/2. We are reversing what we did with answer choice (A); therefore, (B) will always be higher, not lower, than x.

Test Both Ranges

With (C), we can plug in -1/2 for x, giving us (-1/2)^2+(-1/2)=-1/4. In this case, the answer choice is greater than x. You shouldn’t stop there, but test using different numbers. I would suggest numbers closer to the far end of the range, i.e. numbers close to -1 or 0. Once you’ve established that this relationship holds true at both ends of the range, in this case, -1 is the lowest and 0 the highest, then you’ve done enough plugging in and can include (C) as one of the answers. ANOTHER ANSWER.

A more logical (and optimal) approach is to note that x^2 will always be positive. Since you are adding a positive number to x, which is negative, x will become less negative. There x^2+x < x.

Think in terms of Positive or Negative

For answer choice (D), x^2 has to be positive. x^3 is negative, but since you are subtracting this negative fraction, it is the same as adding it. Therefore, a positive plus a positive must be positive. For instance, plugging in 1/2 for xx^2: 1/4-(-1/8)=1/4+1/8 is clearly positive.

YET ANOTHER ANSWER.

Finally, we have answer choice (E). Let’s start with -1/2.
1+2(-1/2)= 0
0<-1/2
Do we stop there? Well, remember, the question is asking us for answer choices which MUST always be bigger than x. Just because we found value where that is the case does not mean that it holds true for all values. Let’s plug in -1/4 for x. We get 1+2(-1/4)=1/2

What happens when we make x more negative? Well, let’s work from extremes: x must be less than -1. But let’s say x is equal to -1. Plugging in x, we get -1+-2=-1. On the other extreme, x could be zero. Here we would get 1+0=1. Therefore, the range of x when we plug in x into the equation must be [pmath]-1

Final Answers: A, C, D, and E

GRE English Questions

Sample questions 1 to 3 below are based on this passage:
Policymakers must confront the dilemma that fossil fuels continue to be an indispensable source of energy even though burning them produces atmospheric accumulations of carbon dioxide that increase the likelihood of potentially disastrous global climate change. Currently, technology that would capture carbon dioxide emitted by power plants and sequester it harmlessly underground or undersea instead of releasing it into the atmosphere might double the cost of generating electricity. But because sequestration does not affect the cost of electricity transmission and distribution, delivered prices will rise less, by no more than 50 percent. Research into better technologies for capturing carbon dioxide will undoubtedly lead to lowered costs.

Sample Multiple-choice Question — Select One Answer Choice
1.
The passage implies which of the following about the current cost of generating electricity?

It is higher than it would be if better technologies for capturing carbon dioxide were available.
It is somewhat less than the cost of electricity transmission and distribution.
It constitutes at most half of the delivered price of electricity.
It is dwelt on by policymakers to the exclusion of other costs associated with electricity delivery.
It is not fully recovered by the prices charged directly to electricity consumers.
Answer: C

Sample Multiple-choice Question — Select One or More Answer Choices
Consider each of the three choices separately and select all that apply.

2.
The passage suggests that extensive use of sequestration would, over time, have which of the following consequences?

The burning of fossil fuels would eventually cease to produce atmospheric accumulations of carbon dioxide.
The proportion of the delivered price of electricity due to generation would rise and then decline.
Power plants would consume progressively lower quantities of fossil fuels.

Answer: B

Sample Select-in-Passage Question
3.
Select the sentence that explains why an outcome of sequestration that might have been expected would not occur.

Answer:
"But because sequestration does not affect the cost of electricity transmission and distribution, delivered prices will rise less, by no more than 50 percent."

Sample questions 4 to 6 below are based on this passage:
Reviving the practice of using elements of popular music in classical composition, an approach that had been in hibernation in the United States during the 1960s, composer Philip Glass (born 1937) embraced the ethos of popular music in his compositions. Glass based two symphonies on music by rock musicians David Bowie and Brian Eno, but the symphonies' sound is distinctively his. Popular elements do not appear out of place in Glass's classical music, which from its early days has shared certain harmonies and rhythms with rock music. Yet this use of popular elements has not made Glass a composer of popular music. His music is not a version of popular music packaged to attract classical listeners; it is high art for listeners steeped in rock rather than the classics.

Sample Multiple-choice Question — Select One Answer Choice
4.
The passage addresses which of the following issues related to Glass's use of popular elements in his classical compositions?

How it is regarded by listeners who prefer rock to the classics
How it has affected the commercial success of Glass's music
Whether it has contributed to a revival of interest among other composers in using popular elements in their compositions
Whether it has had a detrimental effect on Glass's reputation as a composer of classical music
Whether it has caused certain of Glass's works to be derivative in quality

Answer: E