GMAT Problem Solving

Question 1:

If the volume of a right circular cylinder is reduced by 60% by reducing the height of the cylinder by 10%, by what percent must the radius of the base be reduced?

Question 2:

How many ways can the eleven letters in the word MISSISSIPPI be arranged to create unique 11-letter codes if all the letters are used in each code?

Question 3:

If f(a) = a2, what is the value of (f(a + b) – f(a))/b?

Question 4:

A rectangular solid has dimensions of 3 x 5 x 7. What is the length of the longest segment whose endpoints are vertices of the solid?

Question 5:

Eight senators and six representatives have volunteered to work on a Congressional committee that will consist of two members from each body. How many unique committees can be created?

Question 6:

The volume of a cone is 1/3πr2h and the volume of a sphere is 4/3πr3, where r = radius and h = height. If a right circular cone whose radius is 4 is inscribed in a sphere with a radius of 5, what fraction of the sphere’s volume is the cone’s volume, approximately?

Question 7:

The circumference of a right circular cylinder is half its height. The radius of the cylinder is x. What is the volume of the cylinder in terms of x?

Question 8:


If AP = BP, and arc AP = 140, what is the measure of angle BPC?

Question 9:


If ABC is an equilateral triangle, B is equidistant from all points on the sector outside triangle ABC, and AC = 12, what is the area of the shaded region?

Question 10:


In an aquarium tank, the ratio of the number of clownfish to zebrafish is 7 to 56. If 6 more zebrafish were added to the tank, the new ratio would be 7 to 58. How many total clownfish and zebrafish will be in the tank after the zebrafish are added?