TJ Prep Problems

TJ test prep practice problems  for our students and readers. The problems provide a very small sampling of what Optimal TJ Prep students work with.

A Coin Problem for TJ, AOS, SHSAT and SSAT/HSPT Prep. (Easy). 25-40 seconds.

A collection of 43 coins (nickels, dimes and quarters) has a value of \$6.95. If the number of dimes is 4 less than the number of quarters, how many nickels, dimes and quarters are in the collection?

An Algebra Problem for TJ/AOS/Blair/ACT/SAT Prep (Easy). Target Time. 15-40 seconds.

Maya bikes for 24 minutes at 24 MPH. At what speed she must bike for the next 6 minutes so that her average speed for the entire trip will be 20 MPH?

Note. If you can't solve this problem within 40 seconds, you do not completely understand speed-distance problems. If you can solve it but take more than 20-30 seconds then there is room for significant improvement in your problem solving skills.

A Geometry Problem for TJ/AOS/SHSAT/NewSAT Prep. (Medium). Target Time. 20-35 seconds.

A Student built a tent shaped like a rectangular box for science experimentation, The tents is 3 yards wide, 5 yards long 2 yards high, what is the volume of the tent in cubic meters (m^3)?

An Arithmetic Problem for TJ/AOS/SSAT/SHSAT/ACT Prep. (Easy). Target Time. 15-25 seconds.

John wants to purchase a smartphone at 40% discount from the marked (bar code) price. He walks into a store with a 20% off coupon. By what additional percent additional discount the price of the phone must be reduced (through negotiation) so that John, a math wiz, obtains a net discount of 40% from the marked price?

#TJprep #SHSAT #AOS #ACT #SSAT

A Function Problem for TJ/SHSAT/AOS Prep. (Medium). Target Time. 15-20 seconds.

The figure below defines two "funny" functions as shown, followed by an expression. What is the value of the expression?

#TJprep #AOS #SHSAT

A Word Problem for TJ/AOS/SHSAT Prep. (Easy). Target Time. 10-20 seconds.

During a July 4th sale, a store clerk increased the price of an item by 20% instead of decreasing by 20%, By what %, the erroneous price must be decreased to achieve the desired result?

#TJprep #SHSAT #AOSprep

An Algebra Problem for TJHSST/SHSAT/ACT Test Prep. (Medium). Target Time. 20-30 seconds.

X^3 + X^2 - 6X = 0. What is a positive value of X for which the equation is true?

#TJprep #SHSAT #ACTprep

A Counting Problem for TJ/SHSAT/ACT/AOS Prep. (Easy). Target Time. 25-30 seconds.

Starting from the first of January, Austin plays tennis every third day and Arjun plays tennis every 5th day. During the year, how many times Austin and Arjun would play tennis on the same day?

#TJprep #AOS #SHSAT

An Algebra Problem for TJ/ACT/SHSAT Test Prep. (Medium). Target Time. 15-30 seconds.

L, Q, T and U are non zero integers. U = 3 Q T^2 / 7 U L. If U is multiplied by 4, T is divided by 1/2 and L is tripled, thenQ must be multiplied by what number to keep the equation valid?

#TJprep #ACT #SHSAT

A Geometry Problem for TJ/SHSAT/ACT/Montgomery Blair Test Prep. (Medium). Target Time. 20-25 seconds.

The figure below shows a quarter circle, a right triangle and two rectangles. What is

1. The area of the green region?

2. What is the perimeter of the green region?

#TJprep #SHSAT #ACT

A Simple Word Problem for TJ/AOS/SHSAT/Montgomery Blair Test Prep. (Medium). Target Time. 15-25 seconds.

Tom's weight is 60 percent more than Bill's weght. What is the total weight of Tom and bill in terms of Tom's weight?

#TJprep #SHSAT #AOSprep

An Algebra Problem for TJHST/SHSAT/Montogomery Blair Test Prep. (Medium). Target Time. 15-35 seconds.

T, U and V are integers, and

T + 2 U = 9

U + 2 V = 8 and

2T + V = 7. What is the average of T, U and V?

#TJprep #SHSAT

A Geometry Problem for TJHSST/SHSAT/Montgomery Blair Test Prep (Hard). Target Time. 35-60 seconds.

The figure below shows a trapezoid ABCD and an isosceles triangle BCE with altitudes m and n respectively such that m:n is 5: and AD:BC is 2:3. What is the ratio of the area of BCE to area of ABCD ?

#TJprep #SHSAT #ACT

A Geometry Problem for TJHSST/SHSAT/Montgomery Blair Test Prep (Medium). Target Time. 20-35 seconds.

The square ABCD contains an inscribed circle and four quarter circles. The intersection of the circle and the four quarter circles is shaded blue. What is the ratio of the blue area to the white area?

#TJprep #SHSAT

A Venn Diagram Problem for TJHSST/AOS/SHSAT Prep. (Easy). Target Time. 15-30 seconds.

In a certain year, 435 students were accepted to TJ, 279 students were accepted to AOS and 59 were accepted to both. How many students were accepted to TJ, AOS, or both?

#TJprep #AOS #SHSAT #Pollesville #Blairprep

A Word Problem for TJHSST/AOS/SHSAT/Blair/Poolesville Prep. (Easy). Target Time. 25-40 seconds.

A 100' long wood board is cut in to 4 smaller pieces such that the ratio of the lengths of the three smaller pieces is 1:2:3 and the ratio of the sum of the lengths of three smaller pieces to the length of the largest piece is 3:7. How long was the original piece of wood?

#TJprep #AOS #SHSAT #Blairprep #Poolesville

Algebra Problem for TJHSST/HSPT/AOS/BlairTest Prep. (Easy).Target Time. 10-25 seconds.

Simplify the fraction below:

#TJprep #AOS #AOS #Blairprep

A Geometry Problem for TJ/SHSAT/ACT Prep. (Medium). Target Time. 15-20 seconds for each part.

The figure below shows three triangles ABC, BPA and BPC with sides and angles as marked.

1. What is the ratio of BP:AC?

2. What is the ratio of the area of BPC to the area of BPA?

3. What is the perimeter of BPC?

#TJprep #SHSAT #ACT

A Number Poblem for TJHSST/SHSAT/AOS/ACT Prep. (Easy). Target Time. 15-35 seconds.

List one contains integers 1, 2, 3, 4 and 5 and list two contains integers 2, 3, 4, 5 and 6. If one integer each is selected from lists one and two and their sum is placed in list 3, what is the mode of the integers in list three?

TJprep #SHSAT #AOS #ACT

A number Problem for TJ/SHSAT/AOS prep. (Medium). Target Time. 25-40 seconds.

How many multiples of 3 are there between 1 and 500 which are not perfect squares or a perfect cubes?