All fleeps are floops; no flips are floops. What can you conclude from the previous statement?
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/Blair/AOS Test Prep (Easy). Target Time. 20-45 seconds.
List A contains three number 2, 3, 4; list B contains 4,5, 6. If list C contains possible sums of one number in list A and one number in list B. What is the most likely value in C?
A Geometry Problem for TJ/AOS/Blair/SSAT Test Prep (Medium). Target Time. 25-40 seconds.
The figure below shows parallel lines l and m cut by line u and rays p and t. What is the degree measure of angles a and b?
A Percent Problem for TJ/SHSAT/Blair/SSAT Prep (Medium). 20-60 seconds.
If A = 2 B + 6, A is what % greater than B?
An Arithmetic Problem for TJ/SHSAT/Blair/AOS Test Prep (Medium). Target Time.35-55 seconds.
Equal volume of acetone is poured in to two containers of unequal volume so that the first container is filled 2/5 and the second container is empty 5/7th. If the liquid from the smaller container is transferred into the larger container, what fraction of the larger container is filled with liquid?
A Geometry Question for TJ/SHSAT/AOS/Blair Test Prep (Easy). Target Time. 15-45 seconds.
What is the ratio of the diagonal of a face of a cube to the diagonal of the cube?
An Easy Algebra Question for TJ/SHSAT/AOS/Blair Test Prep (Easy). Target Time. 25-5 seconds.
Evaluate the following:
- What is the value of XY -3X-XY^2 when X = -3, and Y = -4?
- What is the value of sqrt 2 (sqrt 12 + sqrt 18) - sqrt 3 (sqt 54 - sqrt 36) ?
An Algebra Question for TJ/Blair/AOS Test Prep (Easy). Target Time. 15-40 seconds.
If -5 U + 3 W = 8 and 3 W + 11 U = 10, what is the average of U and W?
A Geometry Problem for TJ/AOS/Blair Test Prep (Easy). Target Time. 25-45 seconds.
An equilateral triangle has the same Perimeter as a square. What is the ratio of the area of the equilateral triangle to the area of the square?
An Algebra Problem for TJ/AOS/Blair Test Prep (Medium. Target 30-50 seconds.
T and P are integers. If T:P = 2/3, which of the following three can be the values of T/P^2 ?
1. 2/3, 2. 1 and 3. 1/2.
A Math Problem for TJ/SHSAT/AOS/Blair Test Prep (Medium). Target Time. 25-45 seconds.
Two students, Mona and Sabrina, volunteered to paint their school classroom. The four walls add up to 77'. Mona's paint roller has diameter of 7" and Sabrina's paint roller has a diameter of 11" To make one one full round across the 77' feet of the wall, Sabrina's paint roller will make how many fewer revolutions than Mona's paint roller? Assume that the wheels do not slip or slide and assume Pi = 22/7.
A Logic Problem for TJ/Blair/HSPT Test Prep (Easy). Target Time. 20-40 seconds.
A bookshelf has space for five books: algebra, chemistry, physics, geology and calculus. If the algebra book is the left most book and if there are exactly two books between the algebra and calculus books and exactly one book between the physics and the chemistry books, what is one possible arrangement of books from left to right?
A Geometry Problem for TJ/SSAT/Blair Prep (Medium). Target Time. 25-40 seconds.
The figure shows a trapezoid ABCD with lengths (2a + 3) and (2a + 9) and height b. If a rectangle PQRS, with area equal to the area of ABCD has a width of 1/3 b, in terms of and b, what is the length of the rectangle PQRS?
A Percent Question for TJ/AOS/Blair/HSPT Test Prep (Easy). Target Time. 15-40 seconds.
If 5% of 20% of P is 4, what is P?
A Quantitative Comparison Problem for Blair/Poolesville Test Prep (Medium). Target Time 25-50 seconds.
The figure below presents three quantitative comparison questions.
A Geometry Question for TJ/AOS/Blair Test Prep (Medium). Target Time. 25-45 seconds.
An equilateral triangle has sides of length 2X+8, 3X-6 and 4X-20. What is the area of the triangle?
A Counting Problem for TJ/AOS/Blair/HSPT Test Prep (Medium-Hard). Target Time. 35-95 seconds.
The figure below shows points X, Y and Z on rectangular grid drawn in green. Starting on X, how may paths are to reach Y under the restriction that you can go right and/or up. How many ways are there to go from X to Z under the same restrictions. If the restriction is changed so that you can move up and/or to the left, how many ways or there to go from X to Y?
An Algebra Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 25-40 seconds.
The figure below shows a fraction where the numerator and the denominator is a polynomial.. Simplify the fraction to lowest terms.
An Algebra Problem for TJ/AOS/Blair/HSPT Prep (Difficult). Target Time. 25-60 seconds.
P10 and T43 are two different three digit integers.
If (P10)(T43) = 14400P + 420 + 10 what must be the value of T?
A Counting Problem for TJ/AOS/Blair Prep (Medium). Target Time. 15-45 seconds.
The figure below shows paths connecting points P, S, V and T. How many ways are there to travel from T to V? From S to T?
