6TH edition Number properties Ch1 problem 5

[RussellK544]

The question states, if 6 is a divisor of r and r is a factor of s, is 6 a factor of s. The Answer says yes, but there is a problem. A number can be a divisor of another number and NOT be a factor. For example, 8/5. In this case 5 is a divisor of 8 but is not a factor of 8. This example is actually used on page 21 where it defines divisor. I feel that this question answer is wrong. It can not be determined.

[StaceyKoprince]

Welcome to the forums! Please take a look through the forum guidelines before posting.

A problem from one of our books goes in the MPrep non-CAT folder for that subject—so this one would go in the folder titled Manhattan Prep GMAT Non-CAT Math.

In addition, the guidelines ask that you post the full text of the problem about which you're asking. Having to look up the problem text every time would mean that we aren't able to answer as many questions / help as many students.

I'll give you a quick answer here. If you'd like to discuss further, please post in the other folder (including the full problem text).

Annoyingly, the word divisor has two definitions. When you are talking about actual division, such as 8 divided by 5 (the example given on page 21), then 5 is called the divisor (the number that is divided into the other number) and 8 is called the dividend (the number that is...being divided into?—hard to say that in a non-awkward way )

When you are talking about the concept of divisibility in general, however, not the mathematical operation of division, then divisor is synonymous with factor. (This is mentioned on page 17.)

When the wording is "this number is a divisor of that number," the problem is talking about divisibility—it's giving the general rule that the first number is a factor of the second one.

Contrast that with a problem that asks you something like, When 8 is divided by 5, how many times does the divisor go into the dividend? Now, we're talking about the mathematical operation of division, not the concept of divisibility.

The GMAT is much more likely to test the factor / divisibility concept than to specifically name a number as the divisor when talking about doing division.