Salad Dressing I has 5 parts blue cheese and 8 parts olive oil and salad dressing II has 9 parts blue cheese and 4 parts olive oil. Cal took X cups of I and Y cups of II to cread a new salad dressing. If Cal's dressing has 6 parts blue cheese and 5 parts olive oil, what is the ratio of X:Y ? #SAT #ACT #PSAT.
Practice Problems
SAT, ACT, New SAT, PSAT and SAT Subject Test Practice Problems are provided for students of OptimalSATPrep.com and others.
An Algebra Problem for SAT/PSAT/ACT Prep (Medium). Target Time, 20-40 seconds.
A and B are integers. If 18 A + 2 B = 912, what is one possible value of 2A + B?
A Speed-Distance Problem for SAT/ACT/PSAT Test Prep (Medium). Target Time. 25-35 seconds.
60 m long train A is traveling East at 60 km/Hr; on a parallel track 120 m long train B is traveling West at 120 km/Hr. From the moment, train B reaches next to the front most point of train A, how many seconds will elapse before train B will reach the rearrest point of train A? #SAT #ACT
A Word Problem for SAT/ACT/PSAT Prep (Medium). Target Time. 22-35 seconds.
An army courier on a critical mission ran 1/6 of the distance, traveled 1/3 of the distance on a river boat, drove 4/9th of the distance in a jeep and swam the remaining 6 miles of the trip. How many miles was the entire trip? #SAT #ACT #AOS
An Function Problem for SAT/ACT/SAT Subject Test (Hard). Target Time. 40-50 sdeconds/part.
A mobile phone manufacturer charges $200/phone and sells 20000 phones each month at this price. For every increase of $20 in price, the number of phones sold goes down by 1000. #SAT #ACT
1. How many phone will be sold/month if the price is set to $300?
2. What will be the monthly revenue from the sale of phones at $300/phone?
3. What will be the monthly revenue if each phone is sold at $X (200 =< X =< 600)?
A Ratio Problem for SAT/PSAT/ACT Prep (Medium). Target Time. 15-35 seconds.
X and Y are positive integers such that 4 <= X < Y <= 7 where "<=" means less than or equal to. What is the smallest possible possible value of (X+Y) / (XY) ? #SAT #ACT #PSAT
A Ratio Problem for SAT/PSAT/ACT/AOS/TJ Prep (Medium). Target Time 25-40 seconds.
In a collection of mangoes and apples, 4/5 of the fruits are good and 5/8 of all the fruits are mangoes. If 2/15 of all the apples are bad,
1. What fraction of all the fruits are bad mangoes? and
2. what fraction of mangoes are bad? #SAT #ACT
A Geometry Problem for SAT/ACT/PSAT Prep (Hard). Target Time. 30-50 seconds.
The figure below is not drawn to scale and shows a square ABPD and two triangles as marked. What is the length of CD? #SAT #ACT #PSAT (Updatedd, Sept 22, 2014).
A Geometry Problem for SAT/PSAT/ACT Prep. (Medium). Target Time. 20-30 seconds for each part.
The figures below show a quadrilateral and a triangle with angle measures as marked.
1. What is the value of 1/4 (t + u + r + s) - 1/3 (s + t + u)? #SATprep ACTprep
2. What is the value of 1/4 (a+b+c+d) - 1/3 (s + t + u) ?
A Geometry Problem for SAT/ACT/PSAT Prep. (Hard). Target Tme. 35-60 seconds.
The figure below shows a circle and concentric sectors and band (bound by concentric sectors. What is the ratio of the area of the yellow region to the area of the green region? #SATprep #ACTprep
A Geometry Problem for SAT/ACT/PSAT Prep (Medium). Target Time. 15-40 seconds.
The figure (not drawn to scale) shows triangle ABC and various smaller angles as marked. What is the ratio of X:Y?
A Variation Problem for SAT/PSAT/AOS/ACT Prep. (Medium). Target Time. 15-30 seconds.
The figure below describes the relationship between T, K, M and.D. If T is doubled, K is divided by 1/3 and D is divided by 4, M must be multiplied by what number to keep the equation valid? #SATprep #ACTPrep
A Geometry Problem for SAT/ACT/PSAT Problem. (Medium). Target Time. 15-35 seconds.
If the sides of the base of a triangular prism are tripled and its height is quadrupled, what will be the percent increase in its volume? #SATprep #ACTprep #PSATprep
A Ratio-Mixture Problem for SAT/ACT Prep. (Medium/Hard). TargetTime. 25-50 seconds.
Salsa I contains 3 parts celantro and 7 parts tomato whereas salsa II contains5 parts celantro and 1 part tomato. Mixing A cups of salsa I with B cups of salsa II produces salsa III in which the ratio of celantro:tomato is 3:2. What is A:B? #SATprep #ACTprep
A Geometry Problem for SAT/ACT/SAT Subject Test (Medium). Target Time. 20-45 seconds.
A (right circular) cone is cut by a plane parallel to the base of the cone at a distance k below the vertex of the cone and at a distance h above the base of the cone. If the area of the base of the cone is 16 and the area of the circular cross section where the plane intersects the cone (see the figure below), what is the ratio k:h? #SATprep #ACTprep
An Algebra Problem for SAT/ACT/PSAT Prep. (Medium). Target Time. 20-40 seconds.
Custom balloons are being ordered for Keyhan's birthday party. Keyhan's family wishes the balloons to be designed so their diameters are no smaller than 6 inches and no larger than 18 inches. The Balloon designer is not good in math and he needs to enter an absolute value equation into his 3-D printer to create the balloons. Write the absolute value equation to describe the diameter of acceptable balloons. #SATprep #ACTprep
A Function Problem for SAT Prep. (Medium). Target Time. 15-25 seconds/part.
The figure below shows graphs of f(x) and g(x).#SATprep
How many roots (zeros) of f(x) are there between x=2 and x= 6?
Which is greater f(6) or g(6)?
what is the approximate value of f(1) + g(1)?
Is g(7) - f(7) < 0?
A Speed-Distance Problem for SAT/ACT/PSAT Prep. (Hard). Target Time 30-35 seconds.
If a shark can travel 3 N km in 5 Hrs, how many minutes will the shark take to travel 600 K meters?
A Counting Problem for SAT/PSAT/ACT/SAT Subject Test Math Prep. (Medium).
A Mobile school has 4 teachers and 6 teaching assistants. How many different teams comprising 1 teacher and 2 teaching assistants can be created?
A Proportion Problem for SAT/ACT/PSAT Prep. (Medium). Target Time. 20-30 seconds.
Ms. Mills own flour mills. Instead of charging money, Ms. Mils keeps 1/7 of the amount of grain she mills as her fee. One day, Ms. Fuller brought a quantity of barley to Ms. Mills for milling. After milling was complete, Ms. Fuller took 600 Kg of flour. How many Kg of barley was milled by Ms. Mills?