A store held a special sale during which it offered each customer two coupons, one with 10% off and the other with 15% off, to be used one after the other. 1) Which coupon should be used first to achieve maximum advantage. 2). Together, both coupons will equal a single coupon of what %?
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 Problem for TJ/AOS/ SHSAT/Blair Prep (Medium). Target Time. 25-40 seconds.
A, B and C are positive integers. If ST = 6, TU = 4 and US = 6, then what is the value of STU?
A Geometry Problem for TJ/AOS/SHSAT/Blair Prep (Medium). Target Time. 35-45 seconds.
A bakery makes bagel pizzas or pan pizza from dough. The diameter of the bagel pizza is 1/6th the diameter of the pan pizza whereas the thickness of the bagel pizza is 1/4th the thickness of the pan pizza. The bakery has sufficient dough to make 144 pan pizzas. How many bagel pizzas can be prepared from the same amount of dough?
Blair Prep. Target Time. 20-25 seconds.
What is the value of X if 3 [ 2 - 3 (3 - 2X)] = 15 ?
A Mixture Problem for TJ/AOS/SHSAT/SAT Prep (Medium). Target Time. 30-55 seconds.
Salad dressing A contains 2 part blue cheese and 5 parts olive oil; salad dressing B contains 7 parts blue cheese and 2 parts olive oil. How many cups of A and B must be mixed to make a mixture with equal amounts of blue cheese and olive oil?
A Probability Problem for TJ/AOS/Blair/SHSAT Prep (Medium). Target Time. 20-35 seconds.
Mr. Potatoehead has the following clothes: 5 pants, 4 shirts, 2 hats and 1 cap. If, at one time, he can wear a pant, a shirt and a hat or a cap, how many different way can Mr. Potatoehead can dress?
A Geometry Problem for TJ/AOS/Blair/SHSAT Prep (Difficult). Target Time. 25-40 seconds.
The figure below shows a square and a circle with radius 1 and center O. An equilateral is inscribed in the circle. What is the area of region shaded green?
A Geometry Problem for TJ/AOS/Blair Test Prep (Easy). Target Time. 20-30 seconds.
The figure below shows a path comprising a straight line segment PQ with two semicircles (with radius 3/Pi) at each end. If the length of the entire path from A to B is 20, what is the length of the straight path from P to Q?
An Algebra Problem for TJ/AOS/Blair/SHSAT Test Prep (Medium). Target Time 20-45 seconds
If the product of A and B is 6 times the sum of A and B, what is the value of 1/A + 1/B. Assume A and B are non zero.
A Geometry Problem for TJ/SHSAT/Blair Test Prep (Medium). Target Time. 15-40 seconds.
The figure below shows multiple triangles. What is the measure of angle C?
A Geometry Problem for TJ/AOS/Blair/SHSAT Test Prep (Medium). Target Time. 20-35 seconds.
On a map 1 cm equals 40 km. What is the area of of a region represented by a rectangle 3 cm x 8 cm?
A Geometry Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 20-30 seconds.
Three squares are drawn as shown in the figure below. The second square is created by connecting the midpoints of the sides of the largest squares. The smallest square is created by connecting the midpoints of the sides of the middle square. What is the ratio of the area of the yellow region to the white region?
A Ratio Problem for TJ/AOS/Blair/SHSAT Test Problem (Easy). Target Time. 35-40 seconds.
Points P, Q and T are on a straight line in that order with PQ = 5 QT. U is the mid point of PQ and V is the mid point of QT. What is the ratio of UV:PT?
A Geometry Problem for TJ/SAT/AOS/Blair Test Prep (Medium). Targhet Time. 20-40 seconds.
What is the radius of a circle whose area and perimeter are equal in volume (disregarding units).
An Algebra Problem Test Prep (hard). Target Time. 20-30 seconds.
A Synthetic crystal with a mass of c grams is growing a rate of m milligrams/day. After 10 days, how much will the crystal weigh after n days?
An Arithmetic Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 30-40 seconds.
How many complete circular loops of radius 1 inch can be cut from a wire 65 inches long?
An Algebra Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 25-40 seconds.
Point A (-2,6) and B (8, 10) are on line l. Point C is 1/4 way from A towards B. What are the coordinates of point C?
An Arithmetic Problem for TJ/AOS/Blair Test Prep (Easy). Target Time. 25-35 seconds.
Find a number which will give a remainder of 2 when divided by 3, 5, 7 and 11.
A Word Problem for TJ/AOS/SHSAT Prep (Medium). Target Time. 25-40 seconds.
Michael has a cat and a dog. His cat runs at 40 ft/minute and his dog runs at 20 ft/minute. There is a tree house exactly 100 ft from Michael's house. If the cat and dog start at the same time to go to the tree house and immediately head back to Michael's house. At what time after they start and how far from the house will the dog ad cat meet?
An Arithmetic-Logic Problem for TJ/AOS/Blair Test Prep (Easy). Target Time. 20-30 seconds.
If today is a Tuesday, 1000 days after today will be what day?