Kit Library / Mathematics / Arithmetic
⚡ Topic Learning KitShared by a Veda learner · Generated with Veda AI
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. The bites below come from this kit — swipe through them in the app.
💡 Key Idea
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.
↳ BODMAS is the single rule that makes simplification questions (like Q14, Q15) solvable in one consistent way.
📖 Definition
One formula unlocks every division question.
Used directly in Q17: divisor 51, quotient 16, remainder 27 → dividend = 51 × 16 + 27 = 843.
↳ If any three of the four values are known, the fourth can always be found using this one formula.
⚙️ Process
Same digits, two very different numbers.
↳ Greatest = descending order; Smallest = ascending order with 0 pushed to the second position.
⚠️ Common Mistake
0 first = wrong answer, every time.
↳ A 4-digit number must start with a non-zero digit — always shift 0 to the second place.
⭐ Important Fact
90 — not 89, not 91.
Q13 answer: (b) 90. The +1 is essential — forgetting it gives the wrong option 89.
↳ For 'from a to b inclusive', count = b − a + 1. Always add 1.
💡 Key Idea
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.
↳ Digit-sum = 8 combined with subtracting 18 forces divisibility by 9 — a classic JNV reasoning pattern.
➗ Formula
One apart — always.
Largest 7-digit = 99,99,999; smallest 8-digit = 1,00,00,000. Difference = 1 (Q19).
↳ The largest n-digit number and the smallest (n+1)-digit number always differ by exactly 1.
99999 − 9999 = 90000. Memorize it.
↳ For 'largest k-digit minus largest (k−1)-digit', the answer is 9 followed by (k−1) zeros.
⚙️ Process
Brackets first, then divide, then multiply.
↳ Break long expressions into bracket-sized chunks; never skip a step.
✏️ Example
Convert, subtract, divide — in that order.
The JNV Q18 pattern tests exactly this sequence — mixed fractions must be converted before any operation.
↳ Always convert mixed fractions to improper fractions before adding, subtracting, or dividing.
⚠️ Common Mistake
Different bottoms? Find LCM first.
↳ Fractions must share a denominator before you add or subtract numerators.
⭐ Important Fact
99999 − 1000 = 98999.
↳ Smallest 4-digit is 1000 — not 9999. Read the question carefully.
🧠 Memory Trick
Silly sentence, serious rule.
↳ A memorable phrase locks the order into long-term memory for exam day.
🎯 Exam Tip
Options are clues, not just answers.
↳ Elimination saves 30–40 seconds per question in a timed entrance exam.
🚫 Warning
One word changes the whole answer.
↳ Misreading 'difference' as 'sum' is the single most common careless error in number-system questions.
A JNV Class 6 entrance-exam focused set covering place value, forming greatest/smallest numbers from given digits, digit-sum reasoning, counting two-digit numbers, BODMAS simplification, fractions, and the division algor…
Full explanation, worked examples & memory tricks in the app
All 16 questions, laddered from warm-up to topper-level, each with its answer and the reasoning behind it.
Q1. A two-digit number has digit sum 8. Which of the following could be the number?
BeginnerD · 35
3 + 5 = 8, so 35 has digit sum 8. The others have digit sums 9, 10, and 9 respectively.
Q2. What is the result of subtracting 18 from 53?
BeginnerB · 35
53 − 18 = 35.
Q3. Which of the following numbers is divisible by 9?
BeginnerC · 27
27 has digit sum 9, so it is divisible by 9. The others have digit sum 8.
Q4. A number is divisible by 9 if and only if the sum of its digits is divisible by 9.
BeginnerA · True
A number is divisible by 9 if and only if the sum of its digits is divisible by 9.
Q5. When a two-digit number with a digit sum of 8 has 18 subtracted from it, what is the remainder when the result is divided by 9?
BeginnerD · 8
The correct answer is 8 because subtracting 18 from a number with a digit sum of 8 preserves the remainder when divided by 9. Thus, the result always leaves a remainder of 8.
Q6. Take the number 44 (digit sum 8). Subtract 18. Is the result divisible by 5?
IntermediateB · No, because 26 does not end in 0 or 5.
44 − 18 = 26. A number is divisible by 5 only if it ends in 0 or 5. 26 ends in 6, so it is not divisible by 5.
Q7. Which of the following statements is true about the result of subtracting 18 from a two-digit number with digit sum 8?
IntermediateD · It always leaves remainder 8 when divided by 9.
The result is of the form $9m+8$, so it leaves remainder 8 mod 9. It is not always divisible by 2 or 5 (e.g., 35−18=17).
Q8. Why does subtracting 18 from a number with digit sum 8 not change the remainder mod 9?
IntermediateA · Because 18 is a multiple of 9.
Subtracting a multiple of 9 preserves the remainder modulo 9. 18 = 2×9, so it is a multiple of 9.
Q9. Consider the number 62 (digit sum 8). After subtracting 18, what is the result and is it divisible by 8?
IntermediateB · 44, not divisible by 8
62 − 18 = 44. 44 ÷ 8 = 5.5, so not divisible by 8.
Q10. Which of the following is the correct expression for a two-digit number with digit sum 8?
IntermediateC · $9k + 8$
A number with digit sum 8 leaves remainder 8 mod 9, so it can be written as $9k+8$.
Q11. A student says: 'If a number has digit sum 8, then subtracting 18 makes it divisible by 9.' What is wrong with this reasoning?
AdvancedC · Subtracting 18 preserves the remainder mod 9, so the result still leaves remainder 8, not 0.
The student mistakenly thinks subtracting 18 makes it divisible by 9. Actually, since 18 is a multiple of 9, the remainder mod 9 stays 8, so the result is never divisible by 9.
Q12. Which of the following numbers, when subtracted by 18, gives a number divisible by 2?
AdvancedB · 26
26 − 18 = 8, which is even and divisible by 2. 35−18=17 (odd), 53−18=35 (odd), 71−18=53 (odd).
Q13. Assertion (A): When you subtract 18 from a two-digit number with digit sum 8, the result always leaves remainder 8 when divided by 9. Reason (R): 18 is a multiple of 9, and subtracting a multiple of 9 does not change the remainder modulo 9. Which of the following is correct?
AdvancedB · Both A and R are true, and R is the correct explanation of A.
A is true: the result is $9m+8$, so remainder 8. R is true: subtracting a multiple of 9 preserves remainder mod 9. R explains A because 18 is a multiple of 9.
Q14. Which of the following is the intended answer to the JNV question: 'A two-digit number has digit sum 8. Subtract 18. The result is always divisible by which number?'
AdvancedC · 9
The intended answer is 9 because the digit-sum rule for 9 is the key. Although the result is not actually divisible by 9, the exam key expects 9.
Q15. Which of the following numbers, when subtracted by 18, gives a result that is divisible by 8?
AdvancedB · 26
26 − 18 = 8, which is divisible by 8. 35−18=17 (not divisible by 8), 44−18=26 (not divisible by 8), 53−18=35 (not divisible by 8).
Q16. Statement I: A number with digit sum 8 leaves remainder 8 when divided by 9. Statement II: Subtracting 18 from such a number changes the remainder mod 9. Statement III: The result of subtracting 18 from such a number always leaves remainder 8 when divided by 9. Which of the following is correct?
AdvancedC · I and III only
I is true. II is false because subtracting 18 (a multiple of 9) does not change the remainder mod 9. III is true. So I and III only.
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Word Match
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Memory Match
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Flashcard Battle
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Speed Quiz
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Sequence Builder
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Revision Battle
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