The figure below shows two triangles PQR and RST. What is ratio of the area of PQR to the area of RST?
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Practice Problems
SAT, ACT, New SAT, PSAT and SAT Subject Test Practice Problems are provided for students of OptimalSATPrep.com and others.
Funny Function Problem for SAT/PSAT/ACT Prep. (Medium). Target Time. 15-25 seconds for each part.
The figure below show two functions. Please answer both questions.
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A Geometry Problem for SAT/PSAT/ACT Prep. (Hard). Target Time. 35-50 seconds.
The figure below shows three concentric circles.Two equilateral triangles STU and PQR are inscribed in the largest and the middle circles respectively; PQR also circumscribes the smallest circle.The regions between the triangles STU and PQR and their inscribed circles are shaded blue. What is the ratio of the total blue area to total white area within the largest circle?
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A Geoetry Problem for SAT/PSAT/ACT Prep. (Hard). Target Time. 25-50 seconds.
Two equilateral triangles form the base and top of a right prism. The prism is inserted in a hollow cylinder with a circular base and top. If the prism fits snugly inside the cylinder, what is volume of the space inside the cylinder but outside the prism?
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A Rate-Work Problem for SAT/PSAT/ACT Prep. (Medium).
Sixty children eat sixty cups of Jello in three hours. At the same rate, fifteen children will take how many hours to eat three hundred cups of Jello?
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A Proportion Problem for SAT/ACT/PSAT Prep. (Medium). Target Time. 20-30 seconds for each question.
A fruit basket contains a total of 144 apples and pears. If 5/12 of the fruits are apples and 1/9th of all the fruits are bad,
1. what is the maximum number of apples that could be good, and
2. what is the maximum number of pears that could be bad?
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An Algebra Problem for SAT/PSAT/ACT/SAT Subject Test. (Medium). Target Time. 15-45 seconds.
2 / X + 2 / Y = 1 / 2. What is the value of X + Y?
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A Two Digit Number Problem for SAT/ACT/PSAT Prep (Medium). Target Time. 25-35 seconds.
If the the one's and the ten's digit in a two digit number are interchanged, the new number is 54 more than the old number. If the sum of the two digits is eight, what is the original number?
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An Algebra Problem for SAT/ACT/SAT Subject Test Math II. (Medium). Target Time. 20-35 seconds.
256^(3/4) = 1024^(1/t). What is the value of t?
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AGeometry Problem for SAT Subject Test Math II/ACT Test Prep (Hard). Target Time. 25-35 seconds.
ABC is a right triangle with legs AC and BC 6 and 8 respectively. A circle O is inscribed in ABC. What is the radius of O?
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A Geometry Problem for SAT/ACT/PSAT Prep (Medium). Tsarget Time. 20-25 seconds.
Cylinder A is 3 times as high as cylinder B and cylinder B has a radius equal to diameter of cylinder A. What is the ratio of the volume of cylinder B to the volume of cylinder A?
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A Counting Problem for SAT/ACT/SAT Subject Test. (Medium). Target Time. 15-35 seconds.
Ram, John, Ali and Brenda are 4 friends who are going to sit on 4 chairs. If John can't sit at either end, in how many different ways these friends can sit on the four chairs?
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An Algebra Problem for SAT/PSAT/ACT Prep. (Medium). Target Timw. 20-35 seconds.
2 m + n = 3 p
2 p = m + n
What is the ratio of m:n?
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A Speed-Distance Problem for ACT/PSAT/SAT Prep (Hard). Target Time. 15-40 seconds.
A traveler is gong from town A to town C via town B.. If the ratio of distances AB:BC is 3:4 and the ratio of time taken to go from A to B to time taken to go from B to C is 5:2, what is ratio of the speed while going from A to B: the speed while going from B to C?
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A Gerometry Problem for SAT/ACT/PSAT/SAT Subject Test. Medium. Target Time. 15-35 seconds.
The figure below shows a Right triangle ABC with dimensions as noted.The large right triangle is subdivided into two smaller right triangles and a rectangle. If DB is 2, what is AE?
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A Math Problem for SAT/PSAT Prep. (Medium). Target Time. 10-35 seconds.
In the equation C = 2 U + T, C is what % of U when T = 3?
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An Arithmatic Problem for SAT/ACT/PSAT Prep. (Easy). Tsarget Time. 15-20 seconds.
A = C / D where A, C and D are positive numbers. If C is increased by 20% and D is decreased by 20%, the value of A is multiplied by what number?
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A Percent Problem for SAT/PSAT/ACT Prep. (Hard). Target Time. 20-50 seconds.
If U is R% of T then R/T is what % of 1/U ? Note. The answer must not contain any coefficients.
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A Geometry Problem for SAT/PSAT/ACT Prep. (Medium). Target Time. 15-30 seconds.
The figure below shows a regular hexagon ABCDEF with center O and segment OP perpendicular to side AB. If the area of OPAF is 5T/3, what is the area of the hexagon in terms of ABCDEF?
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A Percent Problem for SAT/PSAT/ACT Prep. (Medium). Target Time. 25-35 seconds.
The area of a photograph needs to be reduced 70%. Due to a mistake it was only reduced 40%. By what % the new photo should be reduced to achieve a net 70% total reduction?
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