A Large fruit basket contains grapefruits and kiwis in the ratio of 7:2. If the basket has 350 grapefruits, how many more kiwis must be added to make ratio of grapefruits: kiwis to equal 5:3?
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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.
A Geometry Problem for SAT/PSATACT Prep (Hard). Target Time. 25-45 seconds.
ABCD is a square of side 4. Four equilateral triangles are drawn, outside the square, with each side of the square as the base of one triangle. When the process is completed ABP, BCQ, CDR and DAS are four equilateral triangles. P, Q, R and S lie on a circle O. O is also the center of the square. What is the area of the region that lies inside the circle but outside the square and the triangles?
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An Algebra Problem for SAT/PSAT/ACT Prep. (Medium). Target Time. 20-25 seconds.
Line s has slope of -3 and goes through points (2, -4) and (-4, y). What is the value of y?
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A Word Problem for SAT/PSAT/ACT Prep (Medium). Target Time. 20-40 seconds.
A piggy bank contains $60 in nickels, dimes and quarters. If the ratio of dimes:quarters is 5 to 3 and the ratio of quarters:nickels is 2 to 5, how many quarters, dimes and nickels are there?
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A Probability Problem for SAT/ACT/PSAT Prep. (Medum). Target time 25-35 seconds.
Matthew, Vivek and Cal are three friends who live in the same school district. There are 2 ways to go directly from Matthew's home to Cal's and there are 4 ways to go from Matthew's home to Vivek's home. Vivek has 3 ways to go to Cal's home from his home. There are how many ways to go from Matthew's home to Cal's home?
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A Speed-Distance Problem for SAT/ACT/PSAT Prep (Hard). Target Time. 15-35 seconds.
Isabella drove for n Hrs at p mph and continued her journey far 300 additional mile. If the total trip took T Hrs, What was Isahella's average spreed for the entire trip?
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An Algebra Problem for SAT/ACT/PSAT Prep (Medium). Target Time 15-30 seconds.
Simplify and evaluate the expression in the image below:
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A Geometry Problem for SAT Subject Test Math II/ACT/SAT (Hard). 30-45 seconds.
Two balls (spheres) one with radius 16 and the other with radius 4, located on a horizontal flat surface, are touching each other at one point. What is the distance between the points of contact between each sphere and the flat surface?
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A Number Ptoblem for SAT/PSAT/ACT Prep (Hard). Target Time. 20-35 seconds.
S and t are integers. If S is even and t is odd and
V = S^2 + t^2,
W = S^2 + 6t and
U = 3S + 3t
Which of the following are true?
I. V is even
II. W is odd
III. U is even
An Algebra Problem for SAT/ACT/PSAT Prep. (Medium). Target Time. 15-25 seconds.
Ther figure below shows an equation in S and t. The number line shows two locations for t: A or B. Reason about the values of S and t and decide which is true, A or B?
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A Geometry Problem for ACT/SAT/PSAT Prep (Medium). Target Time. 15-30 seconds.
The figure below shows two triangle ABC and OPQ. If the area of triangles is equal, what is the value of b?
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A Geometry Problem for ACT/SAT/PSAT (Easy). Target Time. 15-25 seconds.
The figure below shows several polygons. What is the area of RPS:PTS?
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An Algebra-Geometry Problem for SAT/PSAT/ACT Prep. (Medium). Target Time. 25-35 seconds.
The figure below shows two rectangles ABCD and PQRS. If 3 AB = 5 PQ and h = 8 BC, what is the ratio of the area of ABCD to the area of PQRS?
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A Ratio Problem for SAT/PSAT/ACT Prep. (Medium). Target Time. 15-35 seconds.
A jar contains only yellow, green and purple marbles. If the ratio of green marbles to yellow marbles is 5:7 and the ratio of green marbles to purple marbles is 7:11. What is the smallest number of marbles that could be present in the jar?
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A Geometry Problem for SAT/PSAT Prep. (Hard). Target Time 20-45 seconds.
The figure below shows arc AOB = 60 deg of a circle with radius 4 and arc POQ = 20 deg of radius 8. What is the ratio of the yellow sector to green sector?
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A Geometry Problem for ACT/SAT Subject Test Prep (Medium). Target 20-40 seconds.
The figure below shows a circle with angle ACB = 15 deg, arc DE = 20 deg. What is the measure of angle APB?
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A Counting Problem for SAT/ACT/SAT Subject Test (Medium). Target Time. 20-35 seconds.
A small rural mobile teaching school has 5 teachers and 6 teaching assistants. If each team is to contain 1 teacher and 2 assistants, how many different teaching teams are possible?
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A Geometry Problem for ACT/SAT Subject Test Math I/II Problem (Medium). Target Time. 20-40 secionds.
The image below shows a quadrilateral ABCD with midpoints of four sides P, Q, R and S connected to create another quadrilateral, PQRS. If the angle PSR is 140 deg, what is the measure of angle PQR?
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An Algebra-Geometry Problem for SAT/PSAT/ACT Prep (Hard). Target Time 30-35 seconds.
The figure below shows a semicircle with equation Y^2 = 16 - X^2 and an inscribed rectangle ABCD as shown. The coordinates of C and D are as shown. What is the area of the rectangle ABCD?
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A Geometry Problem for SAT/PSAT/ACT Prep (Hard). Target Time. 25-40 seconds.
The figure below shows circle O and right triangles OCD and OAB. with OA = AB = OE = ED.
If the radius of the circle is 6, what is the area of the area shaded in green?
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