30%~35% of the employees in a certain company have cell phones. Do at

Dear AustinKL,

I'm happy to respond.

There are a few problems with this question. First of all, having a tilde symbol, ~, between two percents is mathematically meaningless. I don't know whether this is how the problem appeared in its source, or this is how the student miscopied the problem.

Also, I get what the author is trying to express, about ranges of percents, but this is NOT how the GMAT would present this information. I imagine the GMAT would say something along the lines of:
A% of the employees ..., where 30 ≤ A ≤ 35.
The prompt and both statements would have to be rewritten. The general grammar in this question is not good: "employees in the Company with their houses"---presumably this means "employees in the company who own their own houses." This usage mistake is typical of someone who is still in the process of learning English. This question does not give evidence that the author had a thorough command of the English language.

How would we solve this? Let's say that the total number of employees is 10,000, so that we can use parts of a percent if needed. We know that number of employees with cell phones is a number somewhere from 3000 to 3500.
BTW, this scenario is 100% unrealistic!! In what company in the modern post-industrial world would only 30-35% of employees own cell phones? That's totally ridiculous! Obviously, the company is not in the third world, because so many employees own their own houses! All the scenarios in official GMAT problems are realistic, even if the company names are fictional.

Statement #1: We know the number of employees that own their own house is somewhere from 7000 to 7500.
We it could be that the 7000 that own there own house includes 100% of the cell phone owners. That produces a "yes" answer to the prompt question.
Or it could be that there is absolutely no overlap between the 7000 that own houses and the 3000 that own cells, so zero percent of the cell phone owners own a house. This produces a "no" answer to the prompt question.
Two different configurations, two different answers to the prompt. This statement, alone and by itself, is not sufficient.

Statement #2: Interesting.
We know that "40%~45% of the employees in the Company with their houses have cell phones."
Notice that there are two things we don't know:
(a) how many employees own their own houses.
(b) how many (or what percent) of employees who don't own their own houses have cell phones?
We will construct a few scenarios.

Scenario #1: 1000 employees own their own house.
Therefore, between 400 and 450 of these own cell phones. That means most of the 3000 people with cell phone do not own a house. This produces a "no" answer to the prompt.

Scenario #2: 8000 employees own their own house.
40% of 8000 = 3200, so the number of home-owners with cell phones would be this or more.
That's clearly most of a the 3000-3500 who own cell phones, so almost all of them, way over 50% own cell phones. This produces a "yes" to the prompt question.

Two scenarios, two different answers. This statement, alone and by itself, is not sufficient.

Combined statements
First, let's take the low values--only 7000 home owners, and 40% of them own cell phones. (0.40)(7000) = 2800. There are 2800 cell phone owners who own houses. That's definitely already more than half of anything from 3000 to 3500, so "yes," more than half the cell phone owners own a house. If we increase either the number of home owners from 7000 to 7500, or increase the percent among them from 40% to 45%, that will produce even more cell phone owners who own houses. All possible values are well over half the number of cell phone owners.
This statement, alone and by itself, is sufficient.

This produces an answer of (C).

Does all this make sense?
Mike