The figure below shows a parallelogram ABCD. PQ is parallel to DC which is 12 units long. If BQ and QC are are 6 and 2 units long respectively, what is the ratio of the area of the blue triangle to the area of the red triangle? Note. The diagram is not drawn to scale.
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 Percent Problem for TJ/AOS/Blair/HSPT Prep (Medium). Target Time. 25-45 seconds.
A, B, C and D are integers and A + B + C = D. A is 20% of D and C is 40% of D. If A is increased by 50% and C is decreased by 50%, B's percentage of D changes by what %? Assume that D does not change, and that B changes to accommodate the changes in A and C.
An Arithmetic Problem for TJ/AOS/HSPT/Blair Test Prep (Medium). Target Time. 25-40 seconds.
A school has sufficient funds to purchase 400 tablet computers for classroom use. If school budget is increased by 20% and the computer manufacturer offers the school a 30% discount over the original price, the school will be able to by k% more tablet computers, What is the value of k?
A Geometry Prolem for TJ/AOS/Blair/HSPT Prep (Difficult). Target Time. 15-55 seconds.
All sides of a triangle are integers. If the two sides of the triangle are 4 cm and 16 cm, what is the difference between the greatest possible and the least possible perimeter of the triangle
A Mixture Problem for Blair/TJ/AOS Prep (Medium). Target Time. 20-45 seconds.
Peanuts cost $2/Kg and cashews cost $8/Kg. To prepare 600 Kg of cashew-peanut mixture winch will cost $3/Kg, how many Kg of peanuts and cashews must be mixed?
A Geometry Problem for TJ/Blair/HSPT/AOS Prep (Medium). Target Time 25-50 seconds.
The figure below shows square ABCD. A circle is circle is inscribed and another larger circle is circumscribed around the square. The region between the square and the inscribed circle is colored blue. What is the ratio of the blue area to the white area?
A Mathematics Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 25-45 seconds.
A school has sufficient funds to purchase 400 tablet computers for classroom use. If the additional funds equal to the 20% of the original amount becomes available and the school is offered a 30% discount on the price of each tablet computer, the school will be able to purchase k% more computers than originally planned. What is the value of k?
An Arithmetic Problem for TJ/AOS/Blair/HSPT Prep (Easy). /Target Time. 15-40 seconds.
X and Y are positive digits (integers from 1 to 9) such that that XY = Z and Z is also a digit. What is the product of numbers 0.000000X and 0.000Y ?
A Speed-Distance Problem for TJ/AOS/Blair Prep (Easy). Target Time. 30-455 seconds.
On a long trip Barbara drove the first 100 miles at 40 MPH, the next 200 miles at 50 MPH and the last 300 miles at 60 MPH. 1) What was Barbara's average speed for the entire trip, and 2) for what fraction of her driving time she drove at 50 MPH?
A Simple Algebra Question for SSAT/TJ/AOS/Blair Test Prep (Easy). Target Time. 15-30 seconds.
Z = 2 P^2. If 4 P + 9 = 13 what is Z? Hint. If you have to solve for P you are doing the "long" thing?
A Sequence Problem for TJ/AOS/Blair/HSPT Prep. (Medium). 20-55 seconds.
Updated. A paintball gun shoots balls of three colors, yellow, hot pink and green. It shoots 2 yellow balls, followed by 3 hot pink balls followed by 3 green balls. It had a supply of 1800 balls but it jammed after shooting 731st ball. What color was the 731st ball?
A Speed Distance Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 25-45 seconds.
Jill estimated that if she drives at 40 MPH she will be 1 Hr late and if she drives at 60 MPH she will be 2 Hrs early. How miles long is Jill's trip and what should be Jill's speed (MPH) so that she arrive on time?
Corrected. An Algebra Question for TJ/SSAT/HSPT/Blair Prep (Easy). Target Time. 20-40 seconds.
Bill and Hill have saved some money . They have equal number of quarters and dimes and the number of nickels is 3/10 of the number of quarters. If all their coins value a total of $91.25, how many nickels, dimes and quarters are there?
A Geometry Problem for TJ/AOS/Blair Prep (Medium). Target Time. 25-45 seconds.
Two adjacent triangles PQS and QRS are shown in the figure below. Using the information provided in the figure, determine which is the longest side in quadrilateral PQRS?
A Mathematics Problem for TJ/AOS/Blair Prep (Easy). Target Time. 15-35 seconds.
A rectangle of length 12 and width 6 is shown in the figure below. Five semicircles are drawn as shown in the figure below. What is the total area enclosed in the rectangle and the semicircles?
A Mathematics Problem for TJ/HSPT/SSAT/SHSAT/Blair Prep (Medium). Target 30-45 seconds.
In a jar here are 60 green balls and 45 blue balls. 1) How many green balls must be added to the jar so that the fraction of green balls in the jar becomes 2/3, and 2) how many blue balls must be dropped in the jar so that the fraction of blue balls in the jar becomes 3/4?
A Funny Function Problem for TJ/AOS/HSPT Prep (Medium). Target Time 35-405 seconds.
A function is defined in the figure below. Please answer the three questions asked in the figure.
A Geometry Problem for TJ/HSPT/AOS/Blair Prep (Medium). Target Time. 25-40 seconds.
A triangle has sides of length X, 2X + 2 and 10- X. How many different integer values of X are possible and what are they?
A Math Problem for TJ/Blair/HSPT/AOS Prep (Medium). Target Time. 30-40 seconds.
Wheel 1 (r = 18") and wheel 2 (r = 6" ) are on testing ground for robot wheels. Wheel 2 travels at 20 RPM (revolutions per minute) for 12 minutes. If wheel 1 travels the same distance in 4 minutes, how many revolutions did wheel 1 make and what was its speed in RPM?
An Arithmetic Problem for TJ/Blair/SOS/HSPT Prep (Easy). Target Time. 20-40 seconds.
An 8' x 15' bathroom floor is to be covered by small tiles of size 4" x 6". How many tiles will be required to cover the floor?