In a class of 100 students, 60 study math, 57 study music and 48 study history. If 27 study math and music, 34 study math and history, 24 study music and history and 12 study math,music and history, how many of the 100 students study none of the three subjects?
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/Algebra Problem for TJ/AOS/Blair/SSAT Prep Problem (Medium). Target Time. 20-35 seconds.
After two successive discounts (one after the other) of 20% each, a cellphone cost $48. What was the price of the phone before the two discounts?
An Arithmetic Problem for TJ/AOS/Blair/SSAT/SAT Prep (Medium). Target Time. 30-50 seconds.
Find the missing number in the following set of numbers:
11, 30, 67, 128, ___, , 346.
An Arithmetic/Algebra Problem for TJ/SHSAT/AOS/Blair Test Prep (medium). Target Time. 20-40 seconds.
Two self-adjusting 4th generation robots, Charlie and Delta, can adjust their heights so that Charlie's height is always 15 centimeters more than Delta's. What is the ratio of Charlie's height to Delta's height?
An Arithmetic Problem for TJ/Blair/AOS/SSAT/SAT Prep (Medium).. Target Time. 30-40 seconds.
You can buy P lbs of green peppers for m cents. During a sale, you can buy 40% more green peppers for 20% less money. What is the % reduction in the price of peppers (/lb)?
A Speed-Distance Problem for TJ/AOS/SSAT/Blair/SAT Prep (Medium). Target Time.30-45 seconds.
Ramesh is traveling D miles. If he drives at a speed which will make him half an hour early, the time taken at this speed will be 3/4 of the time taken at a speed,which will make him half an hour late. Ramesh takes how many hrs for his trip when he is neither early nor late?
A Thanksgiving Handshake Problem for TJ/Blair/SHSAT/AOS/SAT Prep (Easy).. Target Time. 15-25 seconds.
At a Thanksgiving dinner table. there are family and friends. All except one person can shake hands. If everyone shakes hands with everyone else exactly once, how many handshakes will occur at the table?,
A Geometry Problem for TJ/AOS/SHSAT/ISEE/Blair Prep (Hard). Target Time. 40-60 seconds.
The figure below shows two adjacent squares each with two overlapping inscribed circles. What is the ratio of the region shaded yellow to the rest of the area within the two squares?
A Quantitative Comparison Problem for Blair/ISEE/TJ/SHSAT Prep (Easy). Tsrget Time. 25-30 seconds.
The figure below (not drawn to scale), shows two triangles ABO and PQO. Which triangle has greater area?
A Geometry Problem for TJ/SHSAT/Blair/AOS Prep (Medium). Target Time. 20-35 seconds.
The figure below shows a semicircle with radius with r=4 and an isosceles triangle whose base is the diameter of the semicircle. What is the area of the entire figure (triangle + semicircle)?
An Algebra Problem for TJ/SHSAT/SSAT/Blair Prep (Easy). Target Time. 25-35 seconds.
James is playing a die game with Ram. James wins $6 when an even number shows up and he loses $4 when an odd number shows. If James played 15 games and won a total of $20, how many times even numbers showed up?
A Geometry Problem for TJ/AOS/Blair/SHSAT/SSAT Prep (Medium). Target Time. 25-35 seconds.
The ratio of the perimeter of an equilateral triangle and a square is 2:3. What is the ratio of the area of the triangle to the area of the square?
A Counting Problem for TJ/Blair/SHSAT/AOS Prep (Easy). Target Time. 25-35 seconds.
There are 18 students in a math class. If each student shakes hand with every other student in the class, how many handshakes will be registered?
An Arithmetic Problem for TJ/SHSAT/SSAT/Blair/AOS Prep (Medium). Target Time. 15-35 seconds.
While solving a math question, Jeffrey increased a number by 20% instead of decreasing it by 20%. The new number must be decreased by what % to achieve the desired result?
An Arithmetic Problem for TJ/SSAT/SHSAT/AOS Prep (Medium). Target Time. 20-35 seconds.
Silver foil is used on many sweets made in many parts of India. The cost of a very thin foil of silver is $30/square meter and a single piece of sweet (candy) has a surface area of 20 square cm. What will be the cost of silver foil for a single piece of candy?
An Arithmetic Problem for TJ/AOS/SSAT/SHSAT Prep (Easy). Target Time. 25-35 seconds.
A child's body has 70% water and 20% fat. If the fat alone weighs 18 lb, how much does the child weigh?
An Arithmetic Problem for TJ/SSAT/AOS/Blair/SHSAT Prep (Easy). Target Time, 15-25 seconds.
In his spare time, Father James McClure likes to solve Math problems for fun. 2013 is specially attractive to him. This year, Father's age is a special number such that when his age is divided by the three consecutive prime integers, a remainder of 1 is obtained each time. How old is Father McClure, if he is more than 50 years but less than 90 years old?
A Geometry Problem for TJ/AOS/Blair/SHSAT/SSAT Prep (Easy). Tareget Time. 30-35 seconds.
The figure below shows a triangle PQR with an inscribed rectangle as shown. What is the sum of degree measures of angles a, b and p?
An Arithmetic-Algebra Problem for TJ/AOS/Blair/SHSAT Prep (Easy). Target Time. 25-40 seconds.
Ramesh has some money in dimes, quarters and half dollars. The ratio of dimes to quarters is 2:3 and the ratio of quarters to half dollars is 2:5. If the total of these coins is $18.80, how many coins of each type does Ramesh have?
An Arithmetic Problem for TJ/Blair/AOS/SHSAT Prep (Easy). Target Time. 25-40 seconds.
If 24 frogs can catch 96 crickets in 20 minutes. At the same rate, 30 frogs will take how long to catch crickets?