If A = 96 and B = 95, what is the value of (A^2 - B^2) / (A + B) ?
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.
TJ Prep/Blair Prep Ratio Problem (Hard). Target Time. 20-60 seconds.
If 5 A = 7 B; 2 B = 3 C & 4 C = 5 D. What is D:A?
TJ Prep/Blair Prep Problem (Easy). Target Time. 20 seconds.
The difference between the squares of two consecutive integers is 191. Find the two integers.
A Word Problem (Medium). Target Time
The design for a novel flubber Robot (with human touch) calls for its composition to be 24% metal, 12% ceramic, 32% plastic and 32% a special alloy. If assembly of 1 such robot calls for 6 Kg of ceramic, 1) how many Kg of plastic will be required, and 2) what will be the weight of a fully assembled robot?
A Geometry Word Problem (Hard). Target Time. 30 seconds.
What is the area of an equilateral triangle whose perimeter is SQRT (12 X + 24)?
A % word problem (Easy). Target Time 15 seconds.
After a 40% discount a spectrophotometer cost $3600.00. What was its price before the discount?
A Fraction Word Problem (Medium). Target Time 30 seconds.
The seventh grade class has 25% more students than the eighth grade class.If 20% of the seventh grade students and 30% of the eighth grade students play soccer, what % of the two classes combined plays soccer?
A Blair Prep/TJ Test Prep Speed Distance Problem (medium). Target Time 30-45 seconds.
Lata averaged 30 MPH on her way to work due to traffic; she averaged 50 MPH on her way home. If her total commuting time was 2 Hrs, what is the distance between her home and office?
TJ Prep/ Blair Prep Problem (Medium). Target Time 30-45 seconds
A Gold cone with its height equal to radius is converted into a Gold cube by melting and solidifying. What is ratio of the side of the cube to the height of the cone?
TJ Test Prep CountingProblem (difficult). Target time. 20-45 seconds
Jack and Jill along with 5 other friends were hiking up a hill. Half way up
the hill they wanted to rest. They spotted a long bench. They wanted to sit only
if Jack and Jill could sit next to each other. How many different ways Jack, Jill and their friends could sit on the bench?
A Difficult TJ Prep/Blair Prep Problem. Target Time 40-60 seconds.
Jack and Jill have identical candles. Each candle burns completely in 6
Hrs at a uniform rate. Jack lit his candle at 6 PM while Jill lit her candle at 7 PM. At what time
Jill's candle will be exactly 50% taller than Jack's candle? You can solve it by making an equation or by making a table; try both ways!
A Probability Problem (Medium). Target Time 30-40 seconds.
At the TJHSST (TJ) graduation party, there are nearly 480 students. What is the probability that 1) at least five students have the same birth month and date?, 2) at least ten students have the same birth day (Mon-Sun)?, and 3) at least two students have the same birthday (matching birthday - date, month and year?
A TJ Test Prep Integer Logic Question (Medium). Target Time 15-20 seconds.
X and Y are non zero integers. If ( X^2)(Y) <0 and (X^3)(Y^2) >0, which of the following must be true?
A. X > 0
B. X < 0
C. Y > 0
D. Y < 0
Arithmetic Word Problem (Medium). Target Time 30 - 45 seconds.
Ed, Barbara and Bob ordered a pizza. If Ed ate 1/5th of the pizza,Barbara ate 1/3rd of the remainder and Bob ate the left over, what is the ratio of the pizza Ed ate to what Bob ate?
A % Word Problem (Easy) Target Time 30 seconds.
If A is 10% more than B and X is 10% less than Y, AX is what % more or less than BY?
A Counting Principle Question (Medium Difficulty). Target Time 60 seconds.
How many different four character (letters or numbers) passwords can be created if the first character is to be a non zero even number, the second character is to be a vowel and the remaining can be any letter or digit?
A Counting Principle Question (Medium Difficulty). Target Time 30-45 seconds.
How many different words can be created from letters in the word COLLEGE?
A Hard Algebra-Geometry Problem. Target Time 30-120 seconds.
If a large cube with a diagonal of 8 units is subdivided into 8 smaller congruent cubes, by dividing each of its edges into two equal segments, 1) what is the length of the diagonal of the smaller cube 2) what is the area of each face of the smaller cubes?
TJ Prep - A Medium Logic Problem. Target Time 50 seconds.
What is degree measure of the angle between the hour hand and the minute hand of an analog clock at 1140 PM?
TJ Prep - A Medium Algebra Problem. Target Time 30 seconds.
If the total price of 5 bean burritos and 8 tostadas is $31 and the total price of 6 bean burritos 3 tostadas is $24, how much will you pay for 60 bean burritos and 60 tostadas?