“Numerical Ability & Quantitative Comparison” portion of Part A (General Aptitude) of CSIR-UGC NET/JRF/Ph.D.

 Below is a compact but exam-oriented set of class notes for the “Numerical Ability & Quantitative Comparison” portion of Part A (General Aptitude) of CSIR-UGC NET/JRF/Ph.D. examinations. The outline follows the official Part A syllabus and question trends.

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1. Question Types Asked

Type	What you must do	Typical weight
Numerical computation	Evaluate an arithmetic/algebraic expression quickly	3–5 Qs
Numerical estimation	Approximate square-roots, percentages, ratios	2–3 Qs
Series completion	Identify pattern and fill the next term	1–2 Qs
Quantitative comparison	Decide which of two quantities is larger/equal/indeterminable	3–4 Qs
Data sufficiency	Judge whether given statements are adequate to answer a value	1–2 Qs
Ration–proportion, averages, mixtures	Solve everyday arithmetic setups	2–3 Qs
Time–work, speed–distance	Apply LCM approach or relative speed	1–2 Qs

(Distribution derived from the last 10 papers’ blueprint.)diwakareducationhub+1

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2. Core Techniques & Short-Cuts

1. Vedic splits for fast multiplication

   • $99^2 = (100-1)^2 = 10,000-200+1 = 9,801$

   • Unit-digit rule for a×b ending in 5: e.g., $65×35 = 6×3 | 25 = 2 | 25 = 2,275$.

2. “5-second” fraction ↔ percentage table
   1/3 = 33⅓%, 2/3 = 66⅔%, 1/8 = 12.5%, 3/8 = 37.5%, 5/8 = 62.5%, 7/8 = 87.5%.

3. Ratio blend for mixtures
   Final ratio = (difference of parts opposite the ingredient) ⇒
   Milk:water target 3:1 from pure milk & 50% mix → mix 1 : 1.

4. Successive percentage change
   Net % = $a + b + \dfrac{ab}{100}$.
   Example: 20% hike then 10% discount → $20 – 10 – 2 = 8$ rise.

5. Relative speed (trains)
   Crossing time = (sum or difference of lengths)/relative speed.
   Convert km h⁻¹ to m s⁻¹ by × 5/18.

6. “LCM triangle” for work
   Take LCM of individual days → allocate work units → add rates.

7. Quantitative comparison decision tree

   • If both quantities simplify to the same expression → equal.

   • If expressions differ in sign domain, test boundary values.

   • If indeterminate, mark “Cannot be determined”.

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3. Must-Remember Formulae

Theme	Formula
n-term AP sum	$S_n = n(a_1+a_n)/2$
n-term GP sum	$S_n = a(r^n-1)/(r-1)$
Simple interest	$SI = PRT/100$
Compound interest	$A = P\,(1+\tfrac{r}{n})^{nt}$
Permutations	$^{n}P_{r}= n!/(n-r)!$
Combinations	$^{n}C_{r}= n!/[(n-r)!r!]$
Mean–variance link	$\sigma^2 = E(X^2) - [E(X)]^2$

Keep these on a single flash-card for last-minute revision.

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4. Practice Drill (5 Sample Qs)

1. Numerical estimation
   Evaluate $\sqrt{2025}$ without calculator.

   • Trick: 45² = 2,025 ⇒ answer 45.

2. Quantitative comparison
   Quantity A: $\frac{51}{17}$, Quantity B: 3. Decision?

   • Both equal ⇒ mark “A = B”.

3. Series completion
   3, 7, 15, 31, __?

   • Pattern ×2 + 1 ⇒ next = 63.

4. Mixture problem
   How many L of water must be added to 20 L of 60% acid to obtain 40% acid?

   • Acid litres = 12. Need total 30 L ⇒ add 10 L water.

5. Relative speed
   Two trains 180 m & 120 m long cross opposite each other in 12 s at 45 km h⁻¹ & ? km h⁻¹. Find second speed.

   • Relative speed $= (180+120)/12 = 25 m s⁻¹ = 90 km h⁻¹$.

   • So second speed = 90 – 45 = 45 km h⁻¹.