Statistics and averages: GRE Math Practice Question#64

Try this GRE question that tests your ability to manipulate the equation of average (arithmetic mean) of a large set of numbers.

After finding the average of \(35\) scores, a student carelessly included the average with the \(35\) scores and found the average of these \(36\) numbers. The ratio of the second average to the true average was

  1. \(\quad 1:1 \)

  2. \(\quad 35:36 \)

  3. \(\quad 36:35 \)

  4. \(\quad 2:1 \)

  5. \(\quad \textrm{None of the above} \)


GRE Math Practice#63: Intersection of Rectangle and a Circle

Try this geometry question that tests your understanding of rectangles, circles, arcs, and standard right triangles.

An \(8\) by \(2\sqrt{2}\) rectangle has the same center as a circle of radius \(2\). The area of the region common to both the rectangle and the circle is

  1. \(\quad 2\pi \)

  2. \(\quad 2\pi + 2 \)

  3. \(\quad 4\pi - 4 \)

  4. \(\quad 2\pi + 4\)

  5. \(\quad 4\pi - 2 \)


Exponents and manipulations: GRE Math Practice Question#62

Try this GRE question that tests your ability to rewrite exponents terms in commonly used bases and simplify them by factoring terms.


  1. \(\quad \sqrt{2} \)

  2. \(\quad 16 \)

  3. \(\quad 32 \)

  4. \(\quad 12^{2/3} \)

  5. \(\quad 512.5 \)


Word problems and algebraic formulation: GRE Math Practice Question#61

Try this GRE question that tests your ability to formulate algebraic equations in the context of a word problem.

Some marbles in a bag are red and the rest are blue. If one red marble is removed, then one-seventh of the remaining marbles are red. If two blue marbles are removed instead of one red, then one-fifth of the remaining marbles are red. How many marbles were in the bag originally?

  1. \(\quad 8 \)

  2. \(\quad 22 \)

  3. \(\quad 36 \)

  4. \(\quad 57 \)

  5. \(\quad 71 \)

Video Explanation


My review of GRE PowerPrep Plus Online Practice Tests

ETS the organization behind the GRE tests released a new set of two online practice tests called PowerPrep Plus in the summer of 2017. The tests can be purchased directly from ETS by logging on to their online store. You will need to use your gre account with ETS to access the store and to purchase the two online tests.

The two official practice tests are exactly identical to the actual computer-delivered GRE general test that you will be taking at a test center. The two official tests contain a completely new set of never-before-published real GRE test questions. The tests are section adaptive, meaning the dificulty of the second quantitative reasoning or verbal section will depend on how well you did in the first section. You will also receive a score and how you did relative to other students.

The tests are priced at $39.95 each, which is a bit steep for a GRE product. And although I don't like the price tag, I do recommend students to stick to the official GRE practice tests. I know a lot of the test prep outfits offer similar tests for free or at significantly lower cost, however the quality of those tests is inferior and I would instead urge students to spend the money and practice with the official PowerPrep Plus online tests. The structure and style of the quantitative reasoning questions is very close to what I see on the real GRE test, and the score you will receive on these practice tests is very close to what you will obtain on a real test. If you cannot afford these tests, then my recommendation is to at least practice with the two free online tests that are called GRE PowerPrep online tests.

I have also published video explanations to all of the math sections of the PowerPrep Plus online tests. You will find that the Section 3 Quantitative Reasoning in both Test 1 and Test 2 is identical for all students. So far I have only published the hard version of Section 5 Quantitative Reasoning, and I plan to publish the other two versions in the next couple of months.

And finally, I have summarized all the important links for you to get your online GRE practice started: