# The DAT at a Glance

## Quantitative Reasoning

The Quantitative Reasoning section tests your proficiency in mathematics and assesses your problem solving skills. The questions you encounter on this section range from simple arithmetic to more advanced trigonometric problems.

To succeed on Quantitative Reasoning, you need to understand basic mathematical concepts and show proficiency in algebra, geometry, word problems, and trigonometry. On the test, you'll have 45 minutes to answer 40 questions—any of which could draw from these topics.

## Try a sample question for DAT Quantitative Reasoning:

Which of the following variables cannot be equal to 0 if *(v + w)(x - y - z)(x + y + z)z* = 3?

A. v

B. w

C. x

D. y

E. z

## Answer & Explanation:

**The answer is E.**

When the product of a group of numbers is nonzero, none of the numbers can be 0. This is because if even just one number is 0, the product is zero. For example, 7 × 10 × 12 × 0 × 4 × 35 = 0, because the fourth factor is a 0. Here, *(v + w)(x - y - z)(x + y + z)z* = 3, so *(v + w)(x - y - z)(x + y + z)z* does not equal 0. So each factor of this product must be nonzero. That is:

*v + w* does not equal 0

*x - y - z* does not equal 0

*x + y + z* does not equal 0

*z* does not equal 0

The last inequality tells us that *z* can never equal 0. Choice E is correct.

None of the other answer choices must be nonzero. If *v* = 0, *w* = -3, *x* = 0, *y* = 0, and *z* = 1, then *(v + w)(x - y - z)(x + y + z)z* = (-3)(-1)(1)(1) = 3, and choices A, C, and D are seen to be incorrect, because *v*, *x*, and *y* can each be 0. If *v* = -3, *w* = 0, *x* = 0, *y* = 0, and *z* = 1, then *(v + w)(x - y - z)(x + y + z)z* = 3 and choice B is seen to be incorrect, because *w* can be 0.

Only *z* cannot equal 0, and again, choice E is correct.