Container A contains 20 L of 20% antifreeze and 80% water. Container B contains 400 L of 90% antifreeze solution. How many L of container A should be replaced with an equal volume from container B so that the final solution in container A will have 45% antifreeze and 55% water?
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 - A Medium Speed Distannce Problem. Target Time 45-50 seconds.
On a holiday weekend, if Mrs. Smith drives at an average speed of 20 miles per hour, she will arrive 10 hours late; if she can average a speed of 30 mph, she will arrive 4 hours late. How fast should Mrs. Smith drive so that she will arrive at the scheduled time?
TJ Prep - A Medium Airplane & jetstream problem. Target Time 40 seconds.
An airplane can fly 2000 miles in four hours against a jetstream as the headwind. The same plane can fly 1900 miles in 2 hours with the jetstream as the tailwind. What is the speed of the jetstream?
TJ Prep - A Difficult Speed-Distance Problem. Target Time 60 seconds.
Jim drives from Jamestown to Robertsville at 20 kilometers per hour. How fast should he drive from Robertsville to Jamestown during his return trip so that his average speed for the round-trip will be 30 kilometers per hour?
TJ Prep - A Medium Venn Diagram Problem. 35-40 seconds.
In a class, each student studies one or more of math, physics and chemistry. If 86 study physics, 72 study chemistry, 64 study math, 24 study math and physics, 25 study physics and chemistry, 26 study math and chemistry and 8 study all three, how many students are there altogether?
TJ Prep - An Easy Venn Diagram Question. Target Time 15 seconds.
Out of the 28 kids in a class, if 18 play basket ball and 14 play soccer, how many play both?
TJ Prep - A Difficult (for many) Problem. Target Time 20-30 seconds.
In a mystical land, there are three objects Loopa, Koopa and Poopa. If 3 Loopa = 5 Koopa and 2 Koopa = 7 Poopa, what is Poopa:Loopa?
TJ Prep - A Medium Algebra Problem. Target Time 50 sec.
The ratio of the ten's digit to the one's digit in a two digit number is 3:2. If the digits are reversed the new two digit number is 27 less than the original number. What was the original number. Solve by writing an equation.
TJ Prep - A Hard Three-Part Math Question. Target Time. 60 seconds.
Part 1. What is the % increase in the volume of a cube after each of its sides is tripled?
Part 2. What is the % increase in the volume of a tennis ball if its radius is doubled?
Part 3. What is the % increase in the volume of a cylinder if its radius is multiplied by K and its height is multiplied by H?
TJ Prep - A Medium Logic Problem. Target Time 25 seconds.
If three days before the day before yesterday was a Saturday, what day will it be 65 days after the day after tomorrow?
TJ Prep - A Medium Word Problem. Target time 40 seconds.
What is the total price in dollars of Y dozen mangoes and 300 Z apricots if mangoes sell for 8 dozen/ M cents and apricots sell for P cents for 200 apricots?
TJ Prep - An Easy Word Problem. Target Time 20 seconds.
In 15 years a boy will be N years old. What is the current age of his father, if the father is three times as old the boy.
TJ Prep - A Medium Counting Problem. Target Time 30-45 seconds.
A medical team must have two doctor and three nurses. How many different medical teams can be selected from a group of 4 doctors sand 6 nurses?
TJ Prep- A Medium Counting Problem. Target Time 30-45 seconds.
Four roads connect Motown to Centerton while five roads connect Centerton to Yotown. If you must travel from Motown to Yotown via Centerton and return to Yotown with the restriction that you cannot travel on the same road twice. How may different ways are there for your round trip road trip?
TJ Prep - A Medium Word Problem. Target Time 45 seconds.
Today Jill is 1/5 as old as her grandfather. Six years ago, her grandfather was 9 times as old as Jill was then. How many years from now will Jill be 1/3 as old as her grandfather will be then?
TJ Prep - A Difficult Word Problem. Target Time 90 -120 seconds.
From a square cardboard, four congruent smaller squares are cut out one from each corner; the side of the smaller square is 1/4 the side of the original cardboard square. After the cut squares are removed, the remaining intact piece is folded to make an open rectangular box. If the magnitude of the area of the original cardboard square is equal to the magnitude of the volume of the rectangular box, what is area of the original rectangular box?
TJ Prep- A Medium Word Problem. 45-60 secs.
H dozen widgets cost 500 P cents. 1) what is the cost of 1 widget in cents? 2) What is the cost of N dozen widgets in terms of $? 3) How many dpzen widgets can you buy for $3C?
TJ Prep - A Medium Problem. 30-40 seconds.
ABCD is a square. P, Q, R, S are mid points of AB, BC, CD and DA respectively. Connecting P, Q, R, S gives square PQRS. Connecting the mid points PQ, QR, RS and SP sequentially, creates the smallest square HIJK.
I. What is the ratio of the areas of squares HIJK and square ABCD?
II. What is the ratio of the perimeters of squares ABCD and HIJK?
TJ Prep - A Easy % Problem. Target Time 30 seconds.
A is 40% more than B. What is B when A= 100?
TJ Prep - A Difficult Geometry Problem. Target Time 30-60 seconds.
What is the ratio of the diagonal of a cube to the sum of the diagonals of the faces of the cube?