The idea of this topic started during these holidays. My immoderate passion for visual art and the stunning, dazzling pictures that GreenlightTestPrep (aka Brent Hanneson) creates for his top-notch replies induced me to gather the hardest quant questions from 2021 that include informative graphics as part of their solution.

The result is:

1) The toughest quant questions (with graphics) on the board are mainly geometry questions, but there are also questions that test the concepts of mixtures, overlapping set, word problems, and some others;
2) The questions are all GRE-like, and it's likely that you will encounter similar questions on test day;
3) Brent's replies are among the best explanations you can have in the entire GMAT/GRE galaxy. He is not only one of the most skilled tutors for this test but also his explanations are amazing and ultra-detailed. I have a hard time thinking of someone who is able to add a different perspective;
4) He is one of the most if not the most active quant experts in this community and for a very good reason: he has already addressed over 5,000 (five thousand) math questions. Even though, I dare someone to find a verbal question explained by him

I hope you enjoy this post both for your test and for practicing.


1) What is the radius of the largest sphere that can fit into a box of di





2) The figure represents the design




3) A rectangle is inscribed in a hexagon that has all sides of equal leng




4) If a circle of radius length 4 and an equilateral triangle of side 4




5) In the figure above, which of the following are true?




6) If y = |x + 5| - |x - 5|, then y can take how many integer values?



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7) The figure above shows two lines intersecting at the point O




8) In the circle above, PQ is parallel to diameter OR, and OR has length




9) A normal distribution has a mean of 25 and standard deviation




10) Let S be a point on a circle whose center is R




11) In the x-y coordinate plane, line k passes through



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12) In rectangle ABCD below, and Find the following. AB=5,AF=7




13) If O is the center of the circle with diameter



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14) In the figure AB and CD are two diameters




15) A cube has a volume of 72. If it is divided into 8 equal cubes,




16) The random variable X has a normal distribution with a mean




17) In the figure above, ABCD




18) Four semicircular arcs of length




19) PQRS is a parallelogram and ST




20) What is the perimeter of an equilateral triangle inscribed in a circle



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21) Triangle BDC is an equilateral triangle





22) Triangle XYZ is an isosceles right triangle. If side XY is longer than




23) In the given isosceles triangle, if AB = BC = 2 and x = 30°





24) Given the three points below, what is the area of the triangle formed





25) What is a + b + c + d?





26) O is the center of both circles





27) R, S, T, and U are points on a line, and U is the midpoint of line





28) In the figure above, side AB is parallel to side DE





29) If there are 10 liters of a 20%-solution of alcohol, how much water





30) Solution Y is 40 percent sugar by volume, and solution X is 20 percent



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31) 48% of respondents to a survey consisted of those who used both M



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32) In the figure above, ABCD is a square, and the two diagonal lines



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33) The diameter of the circle is 10



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34) Trapezoid OPQR has one vertex at the origin





35) In the figure shown, two rectangular regions overlap to form