Ease Into Prep with a DAT^® Question of the Day

The correct answer is A.

This problem requires approximation in order to make it manageable in the allotted time, and what's more it invites it by giving possible answers that are approximations. They are not even tightly clustered, but separated out quite comfortably. So at the very least we can approximate .00598 as .006 to make our division easier. We can probably approximate 479.93 as 480 as well, but we won't, because this makes our calculation of error more complicated.

First of all, let's multiply top and bottom of the fraction by 1000, making . If we approximate 5.98 with 6.00, we are adding 0.02 to it, which is less than 1% of the original value: our degree of error stays less than 1%. , and so a 1% degree of error comes to . This means we know , which is good enough to say that of the given choices it's closest to 80,000.

It's probably overkill to calculate the quantity of error explicitly in this problem when you are under time constraints, but you should certainly try to note with every approximation you make either its percent error (in the case of multiplying) or its absolute error (in the case of adding) and make sure the spacing of the possible answers allows such approximation. If 79,900 had been one of the possible answers for this problem we would have had to make more modest approximations.