Quantitative reasoning uses mathematical skills to solve problems involving numbers and data. Different from qualitative reasoning, which probes the “whats” and “whys” of an issue or problem, quantitative reasoning asks “How many?”
Explicate the Term

To define “quantitative reasoning,” focus on the definition of the two words. When you quantify something, you use math, measure or count. When you reason, you draw valid and reliable conclusions from facts. Thus, quantitative reasoning is the process of developing conclusions and clarifying meaning through numbers.
A Necessary Skill

Quantitative reasoning requires basic competence with adding, subtracting, dividing, multiplying and computing percentages and fractions  all the concepts included in a challenging word problem. For example, you will need quantitative reasoning skills to compute a 20percent tip on a dinner bill or how much food to buy for 100 people if your boss tells you to ensure that you provide onequarterpound of meat for each attendee.
References
 College Board.org: Quantitative Reasoning on the Redesigned SAT
 University of Wyoming: Quantitative Reasoning: An Overview
 Imperial County Office of Education: Qualitative and Quantitative Research
 Wellesley College: The Ability to Think Clearly and Critically About Quantitative Issues Is Imperative ...
 ETS; What Is Quantitative Reasoning? Defining the Construct for Assessment Purposes; Carol Anne Dwyer et al.