Updated Version. If the average prices of eight biology books, four medical books and twelve math books are $80,$140 and $100 respectively, what is the average price of all twenty four books ? #SATprep, #ACTprep, #PSATprep. Note. There is at least one way to solve this problem in 10 seconds after you read the question. If you are able to solve this in 10 or 15 seconds after reading the questions, please your method, answer the time you took to get your answer.
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/PSAT/ACT Prep. (Hard). Target Time. 25-40 seconds.
The figure below shows three right triangles PQR, PTQ and PTU. What is the ratio of PU:PR ? #SATprep, #PSATprep, #ACTprep
A Geometry Problem for #SATprep, #PSATprep, $ACTprep
New version. An equilateral triangle PQR is inscribed in circle O. What is the ratio of the area of the shaded region in blue to area in white (the triangle) ?
A Ratio Problem for the SAT/ACT/PSAT Prep (Medium). Target Time. 20-50 seconds.
An agricultural scientist is adjusting the size of his agricultural plot of land to find the optimal size. Initially, he increased the area of his plot by 80%, then he again increased the area by 25%. What was the net % change in the area of his plot after the two changes ?
A Geometry Problem for SAT/SAT Subject Test/PSAT Prep (Difficult). Target Time. 20-50 seconds. #SATprep
The figure below shows a square ABCD, a circumscribed circle O and four quarter circles. What is the ratio of blue area to the yellow area ?
A Geometry Problem for SAT/ACT/SAT II Prep. (Difficult). Target Time. 15-40 seconds. #SATprep
The figure below shows three equilateral triangles. AF is an altitude to BC. What is AF:AE ?
A Ratio Question for #SATprep,#ACTprep,#PSATprep (Medium). Target Time. 20-35 seconds.
Poopa, Koopa and Loopa are three variables that represent weights of three friends with the same name. If 5 Poopa = 3 Loopa and 4 Loopa = 7 Koopa, what is the ratio of Koopa:Poopa
An Algebra Problem for SAT/SAT II/PSAT Prep. (Medium). Target Time. 20-35 seconds.
What is the area of the triangle bound by the equations 3X + 4Y= 12 and 2Y + 4 = X, and the Y axis? #SATprep.
A Geometry Problem for PSAT/PSAT/ACT/SAT Subject Test Prep. #SATprep.(Medium). Target Time. 25-45 seconds.
A sphere (ball) sits snugly inside a cube. What is the ratio of the volume of the sphere to the volume of the cube?
An Algebra Problem for SAT/PSAT/ACT Prep #SATprep. (Medium). Target Time. 20-30 seconds.
If (a^2)(b^5) = 800, what is the value of (a^3)(b^2) ?
A Challenge Percent Problem for SAT/PSAT/ACT Prep. (Hard). Target Time. 10120 seconds. #SATprep
If A is t% of B then tA is what% of B/k? The answer must not contain any numbers as coefficients.
A Literal Percent Problem for SAT/PSAT and ACT Prep. (Medium). Target Time. 30-50 seconds. #SATPrep
If A is B% of C then C is what % of A? Please express the answer so that numbers are present only in exponents and nowhere else.
A Percent Problem for SAT/PSAT and ACT Prep (Easy). Target Time. 15-30 seconds. #SATprep
In the equation P =U^2K^3, if U is multiplied by 4 and K is divided by 2/5, P will increase by what percent?
An Algebra Word Problem for SAT/PSAT/ACT Prep (Easy). Target Time. 20-45 seconds. #SATprep
A restaurant sells 7 Tostadas and 5 cold drinks for $15 the restaurant sells 11 Tostadas and 13 cold drinks for $21. Assuming, there is a linear relationship between the number of items purchased and the total rice, what will be the total cost of 35 tostadas and 35 cold drinks?
A Ratio & Mixture Problem for SAT/PSAT/ACT Prep. (Medium). Target Time. 25-50 seconds.#SATprep
Salsa I and II are made by mixing tomato and celantro. Salsa I contains 3 part tomato and 2 part celantro; salsa II contains 7 part tomato and 1 part celantro. Adam mixed 5 cups of salsa I with 2 cups of salsa II. What is the ratio of tomato:celantro in Adam's mixture.
A Geometry Problem for SAT and SAT II (level II) Prep (Hard). Target 25-50 seconds.
A rectangle ABCD is inscribed in a semicircle of radius 3 (see the figure). What is the area of the blue region (Inside the semicircle but outside the rectangle)?
An Arithmetic/Algebra Problem for SAT/PSAT/ACT Prep (Medium). Target Time. 20-45 seconds.
The average grade of J students in Ms. James' class is 84 while the average grade of H students in Ms. Haile's math class is 96. When the two classes are combined., the average grade of J+H students increases to 92. What is the ratio of H:J ?
An Algebra Problem for SAT/ACT Prep (Medium). Target Time. 25-40 seconds.
h(x) = 4 - x^2.A line l intersects h(x) at points x = -1 and x = 3. What is the slope of line l?
An Algebra Word Problem for SAT/ACT prep. (Medium). Target time 20-45 seconds.
If 6 frogs take 30 minutes to catch 96 insects then 20 frogs will take how many minutes to catch 800 insects?