U and T are positive numbers. U increased by 20% equals V and T increased by 10% equals W. VW is what % more than UT?
TJ Prep Problems
TJ Prep practice problems for our students and readers. The problems provide a very small sampling of what Optimal TJ Prep students work with.
A Percent Problem for TJ/Blair/AOS Prep (Difficult). Target Time. 40-60 seconds.
P is a positive integer. P increased by P% of P is what % greater than P decreased by P % of P? Express your answer in terms of P.
A Word Problem for TJ/AOS/SSAT Prep (Medium). Target Time. 25-40 seconds.
Two circus elephants are to climb ramps as shown in the figure below. Elephant A who can walk 3/4 m/sec starts climbing his 60 meter long ramp at 8 PM. 20 seconds later elephant B starts walking up his 80 meters long ramp. How fast must elephant B walk so he can reach the platform top where the ramps meet up for a cool trunk shake?
A Medium Math Logic Problem for TJ/AOS/Blair Test Prep. Target Time. 25-35 seconds.
A sequence is defined as follows. The first term is n.Thereafter, every even term is obtained by multiplying the preceding term by -1 and every odd term is obtained by adding 1 to the preceding term. What is the 12th term?
An arithmetic Problem for TJ/Blair/AOS Prep (Medium). Target Time 30-50 seconds.
A Hybrid car requires 12000 Kilo Joules of charge. There are 2 chargers available: A fast charger which can charge 400 Joules/second (and should be used after midnight) and a slow charger which can only charge 100 Joules/second. Robert starts charging his car at 8 PM. At midnight fast charger kicks in and both chargers continue charging until the car is totally charged. At what time, Robert's car will be fully charged?
A Medium Geometry Problem for TJ/AOS/Blair Test Prep. Target Time 20-40 seconds.
A semicircle with diameter CD and center P is drawn (see the figure below) with an inscribed circle with center at O. Another circle is inscribed with diameter OQ. What is the ratio of the shaded area to the unshaded area?
An Easy Geometry Problem for TJ/AOS/Blair Prep. Target Time. 32-40 seconds.
A sphere of radius 2 is inscribed in a cube. What is the volume of space outside the sphere but inside the cube?
An Arithmetic Problem for TJ/AOS/SSAT/Blair/HSPT Prep (Medium). Target Time. 20-40 seconds.
Bobby's average of three math tests is 85. What should be his grade on the next test to make his average on the 4 tests 90?
A Quatitative Comparison Geometry Problem for Blair/SSAT/TJ Prep (Medium). Target Time. 30-50 seconds.
A scalene triangle ABC is drawn as shown in the figure below. Line segments PQ and PT are drawn . Please answer the two part question in the figure. Column A always greater (A), column B always greater (B), the two columns always equal (C) or the answer can't be determined (D).
A Probability Question for TJ/AOS/Blair Prep (Easy). Target Time 25-50 seconds.
Two Magic spinners, one with letters and the other with numbers, are available as shown in the figure below. Once spun,, the pointer in each stops only at a letter or a number as appropriate. Nasim first spins I and then spins II. Please answer the following questions:
1. How many different outcomes are possible if both are spun?
2. What is the probability of getting a vowel followed by an even number?
3. What is the probability of getting a multiple of 3 followed by an A or a D?
A Counting Problem for TJ/Blair?AOS Test Prep (Easy). Target Time. 20-25 seconds.
At a popular movie screening Mohan was waiting in a long line. His friend Mike got bored and began counting the line. Mike noticed that Mohan was 78th from the from the front but 87th from the back end of the line. How many person were in the line at that instant?
A Speed-Distance Algebra Problem for TJ/SSAT/Blair/HSPT Prep (Medium). Target Time 30-45 seconds.
Jack and Jill went on a hiking trip up a hill. The trail was 10 miles long. On their way back they were coming down hill so their speed was 25% faster than their speed on the way up. The entire trip took 6 hours including a one and a half hour long lunch break at the top of the hill. What was their speed on their way down the hill?
An Logic Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 40-45 seconds.
Clock A (with hour and minute hands) 120 whereas clock B shows 1050. The angle between the hour and the minutes hand in clock A is how many degrees more the angle between between the hour and the minute hand clock B.
A Geometry Problem for TJ/SSAT/HSPT/Blair Prep (Medium). Target Time. 25-60 seconds.
In the figure below triangles ABC and ADE are shown. What is the ratio of the areas of triangles DBP and CPE?
An Algebra Problem for TJ/AOS/Blair Prep (Medium). Target Time. 20-45 seconds.
Simplify the five algebraic expressions in the following figures.
A Geometry Problem for TJ/SSAT/AOS/Blair/HSPT Prep (Difficult). Target Time 30-45 seconds.
Circles I and II have radii 8 and 4 respectively. A sector of A degrees is shaded in circle I and a sector of B degrees is shaded in circle II (see the figure below). If the shaded area in circle I = 1/4th of the shaded area in circle II, what is A:B ?
Note: If you carefully read the question and think, you can solve it in 15-20- seconds after reading it.
An Algebra Problem for TJ/Blair/AOS Test Prep (Easy). Target Time. 25-40 seconds.
A large piece of sponge is balanced by a small brick and a 25 gram weight on a scale. If the brick's weight is 16 2/3% of the weight of the sponge, what is the weight of the sponge?
A Simple Arithmetic/Algebra Problem for TJ/Blair/AOS Prep (Medium). Target Time 15 seconds.
What is the value of 7^101 - 7^100 ?
A Set Notation Problems for TJ/Blair/AOS Test Prep (Medium). Target Time 30-45 seconds.
Overlapping and intersecting Sets, A, B and C are shown in the figure below. Please look at the relationships among the sets and answer the five questions.
An Algebra Problem for TJ/AOS/BlairTest Prep (Difficult). Target Time. 60-90 seconds.
1/A + 1/B = 6 and (A)(B) = 6. Find 1) A^2 + B^2 and 2) (A + B)^2.
Note. This is an Algebra question, please solve it using algebraic identities. The specified target time is sufficient for that approach.