The ratio of two numbers is 5:7. When 12 is added to each number, the ratio of the new number is 4 :5. Find the original numbers.
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 Hard Algebra Problem. Target Time 45 seconds.
X^8 - 500 = 12 - X^8. How many negative values of X satisfy this equation? (Revised version)
TJ Prep - A Simple Algebra Problem. Target Time 30 seconds.
For which of the following one or more values of X: { -1.5, 0, 2, 4} , is (X-3)(X+2)(2X-2) > 0 ?
TJ Prep - A Medium Mixture Problem. Target Time 30-40 seconds.
How many Kg of sodium chloride should be added to a 60 Kg solution of 20% sodium chloride so that the resulting solution contains 25% sodium chloride?
TJ Prep- An Easy Mixture Problem. Target Time 15 seconds.
Container A has 6 Kg solution of 2% sodium bicarbonate (baking soda) and container B has 12 Kg solution of 6% sodium bicarbonate. If you pour the contents of both containers in to a sufficiently large container, the mixture will contain what % sodium bicarbonate?
TJ Prep - A Hard Work Problem. Target Time 30-40 seconds.
If 6 students can assemble N robots in 18 Hrs, then S students will take how many hours to assemble W robots?
TJ Prep - An Easy Work Problem. Target Time 20 seconds.
If 8 boys can bake 60 cookies in 42 minutes, then at the same rate 12 boys will take how many minutes to bake 300 cookies?
TJ Prep - A Medium Proportion Problem. Target Time 30-40 seconds.
If You can buy 8 pens for $P, then, at the same rate, how many dozen pens can you buy for 500 cents?
TJ Prep - An Easy Speed-Distance Problem Target Time 15 seconds
On a 40 km long journey, how many seconds do you save by driving at 80 km/Hr instead of 50 km/Hr?
TJ Prep - A Medium Percent word problem Target time 20-30 seconds
What is the percent increase in the volume of a cube when the area of each face of the cube is quadrupled?
TJ Prep - A Hard % problem. Target time 60 secs.
If A is B% of C then C/A is what % of B/C? (Note answer must not have any numbers except in the exponents, if applicable).
TJ Prep - A Medium % problem. Target time 30 seconds.
If A is 5% of B then A/7 is what % of 4B?
TJ Prep - An Easy % problem. Target time to solve: 20 secs.
0.05% of A is what % of 2 A?