GMAT Question of the Day – DS – Number Properties Puzzle 1

GMAT Question of the Day – Data Sufficiency – Number Properties

Set x contains only positive integers. What is the range of set x?

(1) The sum of the greatest number and the least number in set x is 10.

(2) The range of the squares of set x is 60

[spoiler]C.[/spoiler]

GMAT Question of the Day Solution:

Get organized with your GMAT Data Sufficiency. Write down what you are solving for: Range = Max -Min. This will help focus your work.

(1) For statement one you might want to make a chart with the positive integers that sum to 10. There are multiple options. Insufficient

(2) Write this out algebraically. Notice that you have the difference of squares. Always convert the difference of squares. Doing so will normally help in some way. Now factor that 60 to see what your possibilities are for the parentheses. 60/1, 15/4, 20/3 are not possible because the numbers generated in each parenthesis must either both be even or both be odd since subtraction and addition will not change the oddness or evenness of the resulting integer. 8 – 2 = 6 (even) 8 + 2 = 10 (even). Still you are left with two options 30/2 and 10/6. Insufficient

(1) + (2) Putting both statements together eliminates 30/2 so you only have 10/6. Max – Min = 6. Sufficient

Additional GMAT Statistics Example Questions!

Here’s a GMAT statistics challenge (median/range) which will teach you how to work with a whole bunch of unknowns. Also a good one to work on maximizing a value.

A set of 15 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?

Here’s a mini-statistics puzzle from the GMAT Official Guide. It has a very simple solution. Still, it’s surprising how often it comes up in tutoring sessions.

If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

Here’s a challenging statistics, max/min question which we review in just about every GMAT preparation. it’s a great one to master not only to understand how to organize a whole bunch of potential variables but to understand how to put context on a max/min scenario.

Seven pieces of rope have an average (arithmetic mean) length of 68 centimeters and a median length of 84 centimeters. If the length of the longest piece of rope is 14 centimeters more than 4 times the length of the shortest piece of rope, what is the maximum possible length, in centimeters, of the longest piece of rope?

Kind of a basic GMAT statistics question. Not the most challenging but it is still very important to be ready to interpret a chart/graph. What isn’t challenging in practice can quickly become a mess on test day.

The table above shows the distribution of test scores for a group of management trainees. Which score interval contains the median of the 73 scores?

Great one to wrap your head around statistics concepts and how they can be tested on the GMAT. It’s a problem solving question but having this square will also help you on DS statistics questions.

Last month 15 homes were sold in Town X. The average (arithmetic mean) sale price of the homes was $150,000 and the median sale price was $130,000. Which of the following statements must be true?

Middle difficulty DS statistics range question from GMAT question of the day

Good luck and happy studies!