Number System & Arithmetic Simplification — JNV Class 6 PYQs: quick revision, 15 bites

BODMAS: The Order That Decides Every Answer

Wrong order, wrong answer — every time.

In any simplification question, operations must be solved in a fixed order — otherwise the same expression gives different answers.

Takeaway. BODMAS is the single rule that makes simplification questions (like Q14, Q15) solvable in one consistent way.

The Division Algorithm: Dividend = Divisor × Quotient + Remainder

One formula unlocks every division question.

Used directly in Q17: divisor 51, quotient 16, remainder 27 → dividend = 51 × 16 + 27 = **843**.

Takeaway. If any three of the four values are known, the fourth can always be found using this one formula.

Forming Greatest & Smallest Numbers from Given Digits

Same digits, two very different numbers.

Takeaway. Greatest = descending order; Smallest = ascending order with 0 pushed to the second position.

Don't Let Zero Lead the Smallest Number

0 first = wrong answer, every time.

Takeaway. A 4-digit number must start with a non-zero digit — always shift 0 to the second place.

How Many Two-Digit Natural Numbers Are There?

90 — not 89, not 91.

Q13 answer: **(b) 90**. The +1 is essential — forgetting it gives the wrong option 89.

Takeaway. For 'from a to b inclusive', count = b − a + 1. Always add 1.

Digit-Sum Clues: When Subtracting 18 Forces Divisibility by 9

Digit sum 8? Then 9 is the answer.

If the sum of digits of a two-digit number is 8, the number is always of the form 10a + b with a + b = 8.

Takeaway. Digit-sum = 8 combined with subtracting 18 forces divisibility by 9 — a classic JNV reasoning pattern.

Largest 7-Digit vs Smallest 8-Digit Number

One apart — always.

Largest 7-digit = 99,99,999; smallest 8-digit = 1,00,00,000. Difference = **1** (Q19).

Takeaway. The largest n-digit number and the smallest (n+1)-digit number always differ by exactly 1.

Largest 5-Digit Minus Largest 4-Digit = 90,000

99999 − 9999 = 90000. Memorize it.

Takeaway. For 'largest k-digit minus largest (k−1)-digit', the answer is 9 followed by (k−1) zeros.

Solving Mixed-Operation Expressions Step by Step

Brackets first, then divide, then multiply.

Takeaway. Break long expressions into bracket-sized chunks; never skip a step.

Mixed Fractions Inside Brackets — Q18 Walkthrough

Convert, subtract, divide — in that order.

The JNV Q18 pattern tests exactly this sequence — mixed fractions must be converted before any operation.

Takeaway. Always convert mixed fractions to improper fractions before adding, subtracting, or dividing.

Don't Add Fractions Without a Common Denominator

Different bottoms? Find LCM first.

Takeaway. Fractions must share a denominator before you add or subtract numerators.

Greatest 5-Digit Minus Smallest 4-Digit

99999 − 1000 = 98999.

Takeaway. Smallest 4-digit is 1000 — not 9999. Read the question carefully.

Remember BODMAS with 'Big Elephants Destroy Mice And Snails'

Silly sentence, serious rule.

Takeaway. A memorable phrase locks the order into long-term memory for exam day.

Use Options to Eliminate — Don't Always Fully Solve

Options are clues, not just answers.

Takeaway. Elimination saves 30–40 seconds per question in a timed entrance exam.

Watch Out: 'Difference' Means Subtract, Not Add

One word changes the whole answer.

Takeaway. Misreading 'difference' as 'sum' is the single most common careless error in number-system questions.