The figure below is created by combining multiple rectangular polygons. What is the area of the shape in terms of S, T, U, V, W, X, Y and Z?
TJ Prep Problems
TJ Prep practice problems for our students and readers. The problems provide a very small sampling of what Optimal TJ Prep students work with.
An Algebra-Geometry Problem for TJ/Blair/HSPT/SHSAT Problem (Medium). Target Time. 25-40 seconds.
The figure below shows two rectangles with dimensions as illustrated. What is the area of the yellow path?
A Geometry/Set Logic Problem for TJ/Blair/AOS Problem (Medium). Target Time 20-45 seconds.
The figure below shows the intersection of a pentagon and a circle. The circumference of the circle is 7 Pi and the area of the pentagon is 38.5. What is the ratio of the green area to the blue area in the figure. Pi = 3.14159.
A Number Line Math Question for TJ/AOS/HSPT/Blair Prep (Medium). Target Time. 20-45 seconds.
The number line in the figure below has equally spaced tick marks. Analyze the figure and determine the value(s) of m?
A Geometry Question for TJ/SSAT/Blair Prep (Easy). Target Time 15-35 seconds.
A square and an isosceles right triangle are shown in the figure below. What is the area of the right triangle?
An Algebra Question for TJ/AOS/HSPT/SHSAT Test Prep (Medium). Target Time. 20-50 seconds.
7 U = 11 ((T^3) A) / (B^2). If U is tripled, B is doubled and T is divided by 1/3, A must be multiplied by what number to keep the equation valid?
An Algebra Problem for TJ/SHSAT/AOS/HSPT Test Prep (Difficult). Target Time. 20-60 seconds.
A number line is described in the figure below. Find possible value(s) of p.
A Non-overlapping Sets Problem for TJ/HSPT/SHSAT Problem (Medium). Target Time 20-40 seconds.
A geometric shape is drawn in the figure below. The shape can be divided into how many non-overlapping regions by 2 straight line cuts and by 3 straight line cuts?
A Percent Question for Blair/HSPT/SSAT/TJ Prep (Medium). 20-30 seconds.
P & Q are positive integers. P increased by 20% = Q and Q decreased by 20% = T. Which is greater P or T?
A Quantitative Comparison Problem for Blair/HSPT/SSAT/TJ Prep (Medium). Target Time. 20-35 seconds.
S, T, U, and V are positive integers with S>T>U>V. Please read and answer the question described in the figure below.
A Word Problem for TJ/AOS/Blair/SSAT/HSPT Prep (Medium). Target Time. 25-40 seconds.
According to recent News Reports, India lost 20% of its languages over the last 50 years. If the number of languages lost was 220, how many languages are in use at present? How many languages were spoken 50 years ago?
A Word Problem for TJ/AOS/Blair Test Prep (Difficult). Target Time. 25-45 seconds.
Atul and five of his friends collect seashells. On a beach trip, together they collected 123 seashells. If there were no ties, what is the most possible shells could the fourth largest shell collector have collected?
A Math Problem for TJ/AOS/SHSAT/Blair/SSAT Prep (Medium). Target Time. 25-45 seconds.
In the junior class of 600 at a college, 2/5th are boys. 2/3 of the juniors study history and 1/3 study economics. If 3/5 of the boys study economics and the rest study history, what fraction of the girls study economics?
A Percent Word Problem for TJ/Blair/SSAT/HSPT/AOS Prep. Target Time. 30 20-35 seconds.
Mr. Mathwiz builds and sells high-performance computers. He wishes to make a 40% profit. He also wishes to offer his customer the good feeling of getting a 30% discount from the list (sticker price). If it costs Mathwiz $300 worth of parts to build the computer. What should be the list (sticker) price Mathwiz should choose so that the customer gets a 30% discount and Mathwiz gets a 40% profit (look at the beauty of math)?
A Percent Pproblem for TJ/AOS/SSAT Prep (Easy). Target Time 25-40 seconds.
A business makes a profit of 25% on the cost of a product. What is the store's percent profit on the selling price of the product?
A Triangle Area Question for TJ/Blair/AOS/HSPT Prep (Medium). Target Time. 15-50 seconds.
In the figure below the base of triangle ABD is 3 units and the base of triangle ABC is 5. If the area of triangle ABD is 60, what is the area of triangle ADC?
A Geometry Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 25-50 seconds.
An alien amoeba was created by removing or adding or removing 12 semicircles from a 6 unit square (see the figure below). What is the area of the amoeba. What is the perimeter of the amoeba? A nano virus created to invade and destroy the amoeba has a radius of 0.1 unit radius. How many nano viruses will be required to completely surround the planer amoeba?
A Venn Diagram Problem for TJ/AOS/Blair Prep (Medium). Target Time 25-40 seconds.
In a college dorm 80 students have skate boards,96 have bikes, 24 have both and 16 have neither. How many students live in the dorm?
A Quantitative Problem for Blair/SSAT/TJ Prep (Medium). Target Time. 30 seconds per question.
Three quantitative problem are described in the figure below. Please aim to solve each part in 30 seconds.
A Funny Function Question for Blair/TJ/SSAT/HSPT Prep (Medium). Target Time. 25-30 seconds.
A funny looking function is defined in the figure below? Answer the question defined in the figure.
