Mrs. Zechman is seven times as old as her grandson. Two years ago, Mrs. Zechman was eight times as old as her grandson was then. How old is Mrs. Zechman today, and in how many years from today she will be five times as old as her grandson will be then?
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.
A Geometry Problem for TJ/Blair/AOS/SHSAT/SAT Prep (Difficult). Target 35-50 seconds.
There are two polygons, the first with n sides and the other with n+1 sides. If the average measure of n angles in the first polygon is 12 degrees less the average measure of n+2 angles ion the second polygon, what is the value of n?
An Arithmetic Problem for TJ/AOS/Blair/SHSAT/SSAT Problem (Medium). Target Time. 25-40 seconds.
A increased by 40% equals B and A decreased by 40% equals C. C must be increased by what % to become equal to B?
A Geometry Problem forTJ/AOS/SAT/Blair/SHSAT Prep (Medium). Target Time. 20-45 seconds.
The figure below shows three circles A, B and C with radii of x, y and z respectively. What is the ratio of the perimeter of triangle ABC and the sum of perimeters of the three circles?
An Arithmetic Problem for TJ/Blar/AOS/SSAT/SHSAT Prep (Medium). Target Time. 40-35 seconds.
If the ratio of an apple's weight to a pear's weight is 4:3 and a pear's weight to a banana's weight is 5:6, what is the ratio of an apple's weight to a banana's weight?
An Arithmetic Problem for TJ/Blair/SHSAT/SSAT Prep (Easy). Target Tine. 25 - 30 seconds.
A parent bought 7 pumpkins with average weight of 8 lbs. If the heaviest and the lightest pumpkins are not included, the average weight of the other five pumpkins is 6 lbs. What is the average weight of the other two pumpkins?
A Geometry/proportion prolem for TJ/AOS/SHSAT/Blair Prep (Medium). Target Time. 25-35 seconds.
The figure below (not drawn to scale) shows four angles a, b, c,d (a:b:c:d = 2:3:7:3). What is the difference between the measure of the biggest angle and the smallest angle?
A Word Problem for TJ/AOS/Blair/SHSAT/SSAT Prep (Medium). Target Time. 25-35 seconds.
Two teachers and 12 students go on a boat field trip. The average weight of a student is 1/16 of the total weight of the two teachers and 12 students. What is the ratio of the average weight of a teacher to the average weight of a student?
A Geometry Problem for TJ/AOS/Blair Prep (Easy). Target time. 20-40 seconds.
The figure below shows a scalene triangle ABC. Triangle DEF is created by connecting midpoints of the sides of ABC, and triangle GHI is created by connecting the midpoints of sides of triangle DEF. What is the total area of the yellow region to the total area of the white region?
A Geometry Problem for TJ/Blair/SHSAT/AOS/SAT Prep (Medium). Target Time. 30-35 seconds.
The figure below shows a square with an inscribed circle (R=2). Four circles (R+1) are circumscribed at each corner of the square (only the portion outside the square is shown). What is the ratio of the shaded to unshaped area?
A Geometry Problem for TJ/AOS/SHSAT/Blair Prep (Medium). Target Time. 25-35 seconds.
The figure below shows a large rectangle with three smaller rectangles inside. What is the ratio of the yellow area to the green area?
An Work Problem for TJ/AOS/Blair/SAT Prep (Easy). Target Time. 30-35 seconds.
If 8 boys can eat 60 bagel pizzas in 20 minutes, at the same rate, 15 boys will take how many minutes to eat 1200 bagel pizzas?
A Math Problem for TJ/SSAT/AOS/Blair Test Prep (Easy). Target Time. 20-45 seconds.
After traveling 200 miles, Sean found that he had completed 4/9th of the journey. How many miles are left in trip?
An Arithmetic Problem for TJ/SHSAT/AOS/SAT Prep (Medium). Target Time. 25-40 seconds.
A, B and C are integers. A/B = 3/5, B/C = 5/7 and A + B + C = 675. What are the values of A, B and C?
A Geometry Problem for TJ/SSAT/AOS/SHSAT Prep (Easy). Target Time. 25-40 seconds.
A right triangle M has height s and base t. A rectangle N has length 8t and width 5s. What is the ratio of the area of the right triangle M to the area of the rectangle N?
An Algebra Problem for TJ/Blair/AOS/SHSAT Prep (Medium). Target Time. 25-45 seconds.
Four lb bags of chocolate chip cookies cost M cents. Two lb bags of cookies of the same kind costs P cents (M < 2 P). What is the % cost saving achieved by buying four 4 lb bags instead of buying 8 two lb bags?
A Quantitative Comparison Problem for Blair/ISEE/TJ/AOS Problem (Easy). Target Time. 25-35 seconds.
The figure below shows quantitative comparison problems. Please provide answer to all parts.
An Algebra Problem for TJ/Blair/AOS Prep (medium). Target Time. 15-40 seconds.
A = C^3P/U^2. If C is divided by 1/3, P is doubled and U is quadrupled, what will happen to A?
A Math-Logic Problem for TJ/AOS/Blair/SHSAT Prep (Easy). Target Time. 25-35.
Which of the following must be true?
1. X^2 = Y^2 then X = Y
2. X > Y then X^3 > Y^3
3. X > Y then CX > CY
A Geometry Problem for TJ/AOS/Blair/SHSAT Prep (Easy). Target Time. 25-35 seconds.
The figure below shows three concentric circles with radius 2, 4 and 6 respectively. What is the ratio of the shaded area to the unshaded area?
