If X, Y and Z are prime numbers, how many different factors are there for the product XYZ?
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 Arithmetic Problem for TJ/AOS/SHSAT/Blair Test Prep (Easy). Target Time. 20-35 seconds.
If A increased by 40% equals B decreased by 60%, what is the ratio of B:A?
A Percent Question for TJ?AOS/SHSAT/Blair Test Prep (Easy). Target Time 20-40 seconds.
A number A decreased by 60% yields B. B must be increased by what % to yield A?
An Algebra Problem for TJ/AOS/Blair/SHSAT Test Prep (Easy). Target Time 25-40 seconds.
If the square of the greatest of three consecutive integers equals the sum of squares of the two smaller consecutive integers, what are the integers? Which equation did you use to solve the question?
A Math-logic Problem for TJ/AOS/Blair Test Prep (Easy). Target Time. 15-30 seconds.
The sum of all positive odd integers less than 80 is how much greater than the sum of all positive even integers less than 80?
A Geometry Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 20-40 seconds.
Triangle A and rectangle B are such that the base of the triangle 40% greater than the base of the rectangle and height of the triangle is 20% smaller than the height of the rectangle. What is the ratio of the area of the triangle to the area of the rectangle?
A Percent Word Problem for TJ/AOS/AOS/Blair Test Prep (Medium). Target Time. 25-40 seconds.
After a 20% discount and 5% sales tax, an encyclopedia cost $252.00. What was the price before the discount.
A Geometry Problem for TJ/AOS/Blair/SHSAT Prep (Medium). Target Time. 20-45 seconds.
If the volume of a sphere is reduced by 87.5%, what must be the % reduction in the radius of the sphere? Hint. You should think about how to solve it without using the formula for the volume of the sphere. If you use the most efficient method, you can solve this question in 15-20 seconds.
A Geometry Problem for TJ/Blair/AOS Prep (Easy). Target Time. 20-30 seconds.
The figure below a circle with radius 6. If the central angle POQ is 100 degrees, what is the length of arc POQ and the arc is what fraction of the circumference of the circle?
An Algebra Problem for TJ/SSAT/Blair/AOS Prep (Easy). Target Time. 20-30 seconds.
The image below shows several equations or systems of equations. For each, find the value of X.
Literal Equation Problems for TJ/SHSAT/AOS/Blair Test Problems (Easy). Target Time. 20-35 seconds per question.
The figure below shows two literal equations followed by a question or two.
A Geometry Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 20-35 seconds.
The figure below shows a square with an inscribed circle and a circumscribed circle. What is the ratio of the green area to the white area?
A Rate Problem for TJ/AOS/Blair Test Prep Problem (Easy).
Two pumps are connected to fill a large tank. The smaller pump can fill the tank in 8 Hrs. Working together, the larger and the smaller pump take 3 Hrs. How many Hrs will the larger pump alone take to fill the tank?
A Geometry Problem for the TJ/AOS/Blair Test Prep (Medium). Target Time. 30-40 seconds.
An equilateral triangle with side 3 is inscribed in a circle. What is the area of the region inside the circle but outside the triangle?
A Quantitative Comparison Problem for Blair/ISEE/TJ Test Prep (Easy). Target Time. 16/25 seconds.
The figure below shows two quantitative comparison problems.
A Geometry Problem for TJ/AOS/SHSAT/SAT Test Prep (Medium). Target Time. 25-40 seconds.
An equilateral triangle ABC with side 5 and three circles with radius 1 are shown in the figure below. What is the ratio of the shaded area to the unshaped area?
A Word Problem for TJ/AOS/Blair/SHSAT Test Prep (Easy). Target Time. 25-40 seconds.
After completing 87.5% of his road trip, Jill had to go 14 miles to complete the trip. How long was the entire trip?
An Algebra Problem for Blair/TJ/AOS Test Prep (Difficult). Target Time. 40-90 seconds.
For X and Y not equal to 0, which is greater I. (1/Y - 1/X) or II. ((X^2 - Y^2) / (X^2 Y + X Y^2) ?
A Geometry Problem for TJ/AOS/Blair Test Prep (Easy). Target Time. 20-30 seconds.
The figure below shows squares ABCD and PQRS. AB is 6. AP = QB = RC = SD. What is the ratio of the area of the smaller square to the area of the larger square?
A proportion Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 30-45 seconds.
The figure below shows points on a number line with points P, T, U and R. PU: PR = 11:15 and PT:PU = 3:17. What is TU:PR? What is PT:UR?
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