## 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

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## 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**