Number Properties

Number Properties – Verified PYQ Authority Guide

Number Properties is organised as a topic-level PYQ authority page. It brings together the strongest verified question clusters, exam/year coverage and concept-level practice so students can revise the topic without jumping through unrelated notes. Every factual learning cue below is drawn from the existing verified, published and approved English PYQ corpus or from its Knowledge Graph relationships; the hub does not invent unsupported technical claims.

PYQ evidence snapshot

52 verified PYQs are currently mapped to this Topic hub. The represented years include 2025. Exam coverage currently includes RRB NTPC Under Graduate Level. Subject context includes Quantitative Aptitude. These values come from live mappings and can expand automatically when new verified PYQs are added.

Most useful verified PYQs to solve first

Start with the actual questions rather than memorising a generic note. The links below are ranked from the mapped corpus using repeat history and editorial quality, while the complete explanation stays on the individual question page.

1. Find the greatest number that will divide 186, 321 and 402 so as to leave the same remainder in each case.
   RRB NTPC Under Graduate Level · 2025 · Remainder
   Use the standard Remainder method and simplify; the result matches 27.
2. Which of the following numbers are not divisible by 68? ( i ) 17350 ( ii ) 23800 ( iii ) 28560 ( iv )
   RRB NTPC Under Graduate Level · 2025 · Divisibility
   Use the standard Divisibility method and simplify; the result matches ( i ) and ( iv ).
3. A five-digit number 7549A is divisible by 4 and 3. If it is divided by 12, what will be the remainder?
   RRB NTPC Under Graduate Level · 2025 · Divisibility
   Use the standard Divisibility method and simplify; the result matches 0.
4. The 7-digit number 12A916B is divisible by 24. What is the maximum value of (A + B)?
   RRB NTPC Under Graduate Level · 2025 · Divisibility
   Use the standard Divisibility method and simplify; the result matches 17.
5. The HCF of two numbers is 8, and their LCM is 240. If the sum of the two numbers is 88, what are the numbers?
   RRB NTPC Under Graduate Level · 2025 · LCM
   Use the standard LCM method and simplify; the result matches 40 and 48.
6. If the 8-digit number 79243p25 is divisible by 11, then the minimum value of p is:
   RRB NTPC Under Graduate Level · 2025 · Divisibility
   Use the standard Divisibility method and simplify; the result matches 7.
7. Which single digit should replace the blank in the number 1_36 so that the number is divisible by 9?
   RRB NTPC Under Graduate Level · 2025 · Divisibility
   Use the standard Divisibility method and simplify; the result matches 8.
8. A positive integer N divides 228, leaving a remainder of 18. What is the greatest two-digit value of N?
   RRB NTPC Under Graduate Level · 2025 · Remainder
   Use the standard Remainder method and simplify; the result matches 70.

Formula & key-relationship bank from verified solutions

• For repeating events, next common occurrence = LCM of the intervals
• sin²θ + cos²θ = 1; tanθ = sinθ/cosθ; cotθ = 1/tanθ

Use these as revision triggers and open the linked PYQ before applying a formula numerically; variable definitions and assumptions belong to the exact solved question.

Core ideas repeatedly reinforced by the solved corpus

• Use the standard Remainder method and simplify; the result matches 27.
• Use the standard Divisibility method and simplify; the result matches ( i ) and ( iv ).
• Use the standard Divisibility method and simplify; the result matches 0.
• Use the standard Divisibility method and simplify; the result matches 17.
• Use the standard LCM method and simplify; the result matches 40 and 48.

Exam tips already validated in SRO solutions

• Identify the Remainder relationship before calculation and keep units/bases consistent.
• Identify the Divisibility relationship before calculation and keep units/bases consistent.
• Identify the LCM relationship before calculation and keep units/bases consistent.

Common mistakes to avoid

• Using a shortcut without checking its conditions or using the wrong base/unit.

Topic and concept coverage

Mapped topic labels include Number Properties. The concept trail includes Divisibility, Remainder, LCM. Use these labels as a revision map: move from the broad area to the narrow concept, solve a verified PYQ, inspect the detailed reasoning, and then attempt another question from the same cluster.

Knowledge Graph navigation

Continue with Number System, HCF, LCM and Divisibility, Quantitative Aptitude, Divisibility, Remainder, LCM. These are canonical SRO entity links based on the Knowledge Graph and shared question mappings, not keyword-stuffed tag pages.

How to revise this authority page efficiently

1. Solve before reading: answer a mapped PYQ first.
2. Read the exact explanation: verify the correct principle, formula, distractor logic and common mistake on that question page.
3. Move one level in the graph: use the closest concept/sub-topic/topic link rather than opening unrelated content.
4. Reattempt: solve another verified PYQ from this hub and check whether the same error repeats.

Quality scope: this page is automatically maintained from SRO’s verified mapped corpus. It enriches one canonical authority URL instead of generating multiple near-duplicate pages for keyword variants. Manual authority articles are never overwritten by the automated engine.