UGC-NET / SET · PAPER I · GENERAL PAPER ON TEACHING & RESEARCH APTITUDE

Unit V

Mathematical Reasoning & Aptitude

Reasoning with numbers, letters, and codes, and the everyday mathematical aptitude — fractions to averages — that NET Paper I regularly tests.

“A number series is never random — it is a rule waiting to be noticed.”

01

Types of Reasoning

TypeDescription
DeductiveMoves from general premises to a specific, certain conclusion (if premises are true, conclusion must be true)
InductiveMoves from specific observations to a general, probable conclusion
AnalogicalDraws a conclusion based on similarity between two situations
AbductiveInfers the most likely explanation from incomplete evidence
02

Number Series, Letter Series, Codes and Relationships

Number series

Identify the rule connecting consecutive terms — a constant difference (arithmetic), constant ratio (geometric), a difference-of-differences pattern, or a pattern like n² + n / n² − n.

Worked example

Series: 0, 2, 6, 12, 20, 30, …, ? — each term equals n² + n for n = 0,1,2,3,4,5. The next term (n = 6) is 6² + 6 = 42.

Letter series

Letters are usually mapped to their position in the alphabet (A = 1 … Z = 26) and the same arithmetic logic as number series is applied — e.g. a series that adds +1, +2, +3, +4… to successive letters.

Codes and relationships

Coding-decoding questions substitute letters/numbers for other letters/numbers using a hidden rule (shift by a fixed number of places, reversal, substitution) that the candidate must detect from a given example and then apply to a new word.

03

Mathematical Aptitude

TopicCore formula / idea
FractionsComparing, adding, and simplifying parts of a whole; converting to a common denominator
Time & DistanceSpeed = Distance ÷ Time; relative speed for meeting/overtaking problems
Ratio & Proportiona:b = c:d ⇒ a×d = b×c (cross-multiplication)
PercentagePercentage = (Part ÷ Whole) × 100
Profit & LossProfit % = (Profit ÷ Cost Price) × 100; Loss % similarly on Cost Price
Interest & DiscountSimple Interest = (P × R × T) ÷ 100; Discount = Marked Price − Selling Price
AveragesAverage = Sum of observations ÷ Number of observations
Exam tip

Most Paper I quantitative questions test the concept, not heavy calculation — look for the shortest arithmetic path (percentages as fractions, ratios in lowest terms) before solving.

Deductive Reasoning Number Series Coding-Decoding Ratio & Proportion

Notes prepared for UGC-NET/SET Paper I revision, structured to the UGC syllabus (Code No. 00) and cross-checked against standard reference material for accuracy. Rephrase and verify against the latest UGC notification before the exam.