nguyendinhtuong wrote:

What percent of a group of numbers are integers greater than 70?

(1) Of the integers in the group, 5 percent are greater than 70.

(2) Of the non-integers in the group, 10 percent are greater than 70.

Source: GMAT Free

Explanation

The question here is pretty straightforward; to answer it, we are going to need to know a little more about this particular group of numbers. On to the statements, separately first.... although we do happen to glance at both statements and notice that one statement is about integers and one statement is about non-integers. On the GMAT, we cannot assume that an unspecified number is an integer, a positive or negative whole number, unless we are specifically told so. It could be a non-integer. But we can assume that numbers are real numbers; if you don't know what a real number is, you can forget about it or look it up, but you don't need to know it for the GMAT. So all of the numbers greater than 70 are integers or non-integers. The problem is that each statements tells us about one segment of the group and not the other. For example, Statement (1) tells us that 5% of integers are greater than 70. But, for all we know, 0% or 100% of the non-integers could be above 70, so I've no way of knowing the overall percentage. Statement (2) has the exact same problem, logically speaking. So we conclude that each of the statements is insufficient individually. We'll have to combine them. There is still a problem here: we don't know how many integers or non-integers there are. There could be 10 integers and 100 non-integers, or 10 integers and 1,000 non-integers, yielding different answers to the question. So the statements are insufficient even when combined.

The correct answer is (E).

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