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 large juice container measures 15 feet x 18 feet x 24 inches. A juice scoop measures 5"x3"x9". children are to be served one scoop juice during lunch. How may children can be fully served with one completely filled container?
#TJprep #HSPTprep #SSAT
The inner surface area of a cubic container without lid is 12500 square inches.
I. What is its volume in cubic yard?
II. If 1 inch = 2.5 cm, what is the volume of the container in cubic meters?
#TJprep #SHSAT
The figure below shows three equilateral triangles ABC, APQ and QCR and a parallelogram such that the ratio of AQ to QC is 2:3. What are
1. The ratio of the area of AQP to the area of QCR?
2. What is the ratio of the area of QCR to the area of ABC?
3. What is the ratio of the area of PQBR to the area of ABC?
#TJTEST #SHSAT
The figure below shows a triangular prism.
1. What is the volume of the prism?
2. What is the total surface area of the prism? #TJTESTprep #SHSAT
The Figures shows a number line (not drawn to scale) which shows four points P,U,T and K with ratios PU:PT and UT:UK as specified. What is TK:PK ?
#TJTEST #SHSAT
If 6 students eat 30 apples in 6 Hrs,. then at the same rate 15 students will take how many Hrs. to eat 300 apples? #TJtestprep #SHSAT
Box I has 6 cards with one letter each from the set {A , C, O, E, U, T} and Box II has 6 cards with one number each from set {1, 2, 3, 7, 8, 11}.
If you first pick a card from box I then pick a card from Box II, what is
1. the probability of picking a vowel followed by a prime number?
2.the probability of getting a consonant followed by an even number?
#TJHSST #SHSAT
A goat is tied to a 6 meter long rope. The other end of the rope is tied to a pole at the vertex of a small fenced garden in the shape of an equilateral triangle with sides of 6 mete; the goat must remain outside the triangular region. What is the area of the land the goat can graze on?
#TJprep #SSAT.
1/3rd of a number is how many times the difference between 1/4th and 1/6th of the number?
#TJprep #SSAT #HSPT #SHSAT
The figure below a right triangle with sides 6, 8 and 10 and two isosceles right triangles. What is the ratio of the area of the triangle BCD to that of Triangle ABE?
#TJHSST #TJprep #SHSAT
Tommy's collection of nickels and dimes has 75 coins. If the total value of these coins is $4.00, how many nickels are there? Write an expression describing this situation in terms of X where X is the number of nickels.
#TJHSST #SHSAT #SSAT #NEWSAT
A furniture store offered a 45% discount and then an additional 20% discount. What was the net (final total) percent discount was offered by the store?
#TJTESTprep #SHSAAT #HSPT
Two mathematically inclined ants are racing to a piece of candy. Ant 1 starts at point M and reaches for a candy at point Q. Ant 2 starts at point A and reaches for a candy at point M. The diagram is not drawn to scale. Ant 1 follows a semicircular path with diameter MN = NO = OP = PQ. Ant 2 follows a square path where AB = BC = CD = AD. MN = AD = X.
1. Express the distance traveled by ant 1 as f(X)
2. Express the distance traveled by ant 2 as g(X)
3. Express the difference between f(X) - g(X) as a function of X
4. Which ant chose the more efficient scenic route?
5. What would have been the most efficient path?
6. A science question- Why do you think ants often don't travel on a straight path?
#NewSAT #NewPSAT
The ratio of girls to boys in a class is 3:4. If 1/3 of girls and 2/3 of boys wear eyeglasses, what is the ratio of the number of boys without eyeglasses to the number of girls without eyeglasses?
#TJprep #Blairprep #HPT #SSAT #SATprep
How many pounds of peanuts ($2/lb) must be mixed with 40 pounds of cashews ($8/lb) to make a nut mixture with average price of $2,.50/lb?
#TJprep #AOS #SAT
What are the LCM and GCF of 16a^3 b^2 c, 36 a^2 b c^3 and 40 a b^3 c^2 ?
TJtestprep #HSPT
Abdul, Bob and Cathy are three friends who love to solve math problems. If the ratio of problem solving rate of Abdul to that of Bob is 3:5 and the ratio of Bob's rate to that of Cathy is 2:3, what is the ratio of the Abdul's rate to Cathy's rate?
#TJprep #HSPTprep #Poolesvileprep
Eighteen kids decided to get a birthday cake for their friend. The price of the cake, $D, was to be shared equally among the 18 kids. On the part day, the price of the cake went up by $m and n kids did not show up. What was the cost share of each kid who attended the party?
#TJprep #HSPT #SSAT
The figure below shows two quantitative comparison problems.
#MontgomeryBlairprep #Poolesvilleprep
If 6 athletes consume 60 bagel pizzas in 15 minutes, eating at the same rate, 15 athletes will take how many hours to eat 300 bagel pizzas?
#TJprep #HSPT #SSAT #Blairprep #SATprep
