A Geometry Problem for TJ/AOS/Blair Test Prep (Difficult). Target Time 60 - 120 seconds.

There are four cylindrical containers A ( r = 8, h = 16, B (r = 4, h = 8), C and D. Containers C and D are identical to containers B and A respectively. Container A is completely filled with a "nonvolatile" liquid; containers B, C and D are empty.  Content of container A is poured to completely fill containers B and C.   Half of the remaining fluid in container A is poured into cylinder D. What is the height of fluid in container D?

Note. The target time assumes that you will do it step by step using formula taught in your prealgebra class. However, it is possible to solve it without using pencil and paper. See if you can do it? 

Science Trivia- If you read the problem carefully, you must be wondering why the word nonvolatile is put in quotation marks. If you can't think of a good answer, you can ask me by emailing to learn@tripathi.com.

A Simple Algebra Problem for TJ/AOS/Blair Prep (Easy). Target Time 25-40 seconds.

X^2 = 16, Y^2 = 9 and XY = -12. What is the value of 12 (X + Y)^2 ? 

A Simple Algebra Problem for TJ/SOS/Blair Prep Problem (Easy). Target Time. 30-40 seconds.

If (8^100) = N (80^40), what is N? 

A Mixture/Proportion Problem for TJ test Prep/Blair Test Prep (Difficult). Target Time 40-60 seconds.

60 liters of salad dressing A is composed of 1 part olive oil and 4 part of blue cheese and 90 liters of salad dressing B is composed of 5 parts olive oil and 2 parts blue cheese. Mr Mixer took M liters of A and mixed it with N liters of B to to produce M+N liters of a salad dressing containing 2 parts olive oil and 3 parts blue cheese. What was the ratio of M:N?

A Deceptively Simple Calendar Problem (Easy) for TJ/AOS/Blair Test Prep. Target Time 30 seconds.

If three days before the day before yesterday was a Saturday, what day will it be 65 days after the day after tomorrow? Note. This question was originally posted on July 12, 2013. Everyone who attempted got this wrong. I am guilty of assuming that my students could not be wrong. I re-post this with the hope that you will think carefully and solve it correctly.

A Number Line Ratio Problem for TJ Prep/AOS Test Prep Problem (Difficult). Target Time: 40-80 seconds.

Points S, T, U, V, W are located in that order on a line. The arrangement of the points is described in the figure below. Use the information give in the figure to find:

1. TU : UV, and

2. UV:SW?

An Algebra Word Problem for TJ Test Prep (Medium). Target Time. 30-45 seconds.

One side of a scalene triangle is 2 more than twice the smallest side and it is 4 less than the longest side. If the perimeter of the triangle is 83, find the lengths of the three sides.

A Simple Algebra Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 30-45 seconds.

Ashok has certain quarters and dimes. The number of quarters is twice the number of dimes. If the number of quarters and dimes is exchanged, the amount of his money decreases by $4.50. Find the number of quarters and dimes in Ashok's possession?

A Geometry Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 30-35 seconds.

What is the area of a circle whose circumference is Q T Pi where Pi = 3.1415... Please use Pi in your answer.

An Algebra/Arithmetic Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 30-45 seconds.

Cashews cost $9/Kg and peanuts cost $5/Kg. To make a 300 Kg mixture of cashews and peanuts which will sell for $6.50/Kg, how many Kg of cashews and peanuts will be required? Assume there is no cost for mixing. Note. Although the specified target time is 30-45 seconds, it is possible to solve the problem in 20 seconds or less after you read the question; see if you can solve this question in 20 seconds after reading it!

Arithmetic problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 30-40 seconds.

In writing all the numbers from 400 to 600, how many times the number 5 is used?

Arithmetic Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 40-50 seconds.

Bob has some crackers. If he divides them in groups of 4, 3 are left over. If he divides them in groups of 7, 5 are left over.  How many crackers does bob have?

Note. Multiple answers are possible. Can you find all the answers below 200? Can you find a rule to find all the answers between any given range of positive integers?

A Difficult Geometry Problem for TJ Test Prep. Target Time. 20 seconds to 2 minutes.

ABC is an equilatera triangle. AP = AQ = BU = BT = CS = CR = 1/3 of AB. .

I. Ratio of the area of the hexagon PQRSTU to the area of triangle ABC?

2. Ratio of the area of the hexagon to the sum of the areas of the equilateral triangles APQ, BUT and CRS?

Note. If you use the techniques taught in geometry class, you may take 2 to 4 minutes per part, however, if you have developed appropriate, geometry "common sense" or "geometric maturity", you can solve each part in 20-30 seconds.  I invite you to solve this two-part problem to check on geometric maturity.

A Rate Problem for TJ/AOS/Blair Test Prep (Easy). Target Time. 30 seconds.

If 15 frogs catch 90 insects insects in 20 minutes, at the same rate, 60 frogs will take how many hours to catch 1200 insects?

A Speed-Distance Problem for TJ Prep & AOS/Blair Test Prep (Hard). Target Time. 40-45 seconds.

A beaver can swim 2 miles in 3 Hrs with a river current (downstream) ; the same beaver can swim 1 mile in 3 Hrs against the river current (upstream). What is the speed of the river current and how fast can the beaver swim in a calm lake (without current)?

A Rate-Work Problem for TJ Test Prep. Target Time. 30-40 seconds.

Sela and Neela are painter robots. Sela takes 48 Hrs to paint your house. If Sela and Neela (a trainee) work together, they can paint your house in 40 Hrs. Working alone, Neela will take how many Hrs to paint your house?

Note: Ark, thank you for pointing out the typo in the first version of of the problem. I appreciate all corrections.

A Counting Question (Medium) for TJ/AOS/Blair Test Prep. Target Time. 25-35 seconds.

An undergrad calculus class has 75 students. If each student shakes hand with every other student exactly one, how many handshakes will occur?

A Geometry Problem for TJ/AOS/Blair Test Prep (Difficult). Target Time. 30-45 seconds.

A rectangular tank 6 yard long, 4 yard wide and 15 yard depth has water filled to a depth of 4 yards. When a cylinder with a radius of 30" and a height of 12' was completely immersed in the tank, the water level in the tank will rise by how many inches?

An Arithmetic Problem for TJ/AOS and Blair Test Prep (Easy). Target Time 20 seconds.

How many rectangular sheets 1/18" must be stacked to reach a height of 16 yards?

A Volume Problem for TJ/AOS/ Blair Test Prep (Medium). Target Time 30-45 seconds.

A 14P' long, 18P yard wide and 6P' feet deep rectangular hole is to filled by bricks with dimensions a' x b" x c". What ids the number of bricks required?