NIMCET 2009
If all the digits 6 in the numbers from 1 to 100 are replaced by 9, by how much does the algebraic sum of these numbers change?
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Answer: Option A —
Detailed Solution
A 6 in the units place becomes 9, raising the number by 3. Units-place 6s: 6, 16, …, 96, ten of them: .
A 6 in the tens place becomes 9, raising the number by 30. Tens-place 6s: 60 to 69, ten of them: .
Total change .
✓ Check
alone adds , so it is correctly counted once in each step.⚠ Common trap
Counting only the digits (twenty 6s, each worth 3) gives 60 and ignores place value: a tens-place 6 is worth 30.Quick tip
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Number System — Preparation
This question tests your understanding of Number System, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
The number system is the foundation of quantitative aptitude. It covers the different types of numbers (natural numbers, whole numbers, integers, rational and irrational numbers, primes and composites) and the rules that govern them. Exam questions test divisibility rules, unit digits of large powers, remainders, factors and multiples, HCF and LCM, and the number of trailing zeros in a factorial. Most of these questions can be solved in under a minute once you know the pattern. Unit digits repeat in cycles of four, and divisibility by 11 depends on the difference between the sums of alternate digits. Number properties also appear inside questions on simplification, averages and series, so strong basics here save time across the whole quant section. Practise the questions below to build speed with divisibility, remainders, unit digits and HCF-LCM. Every question has a step-by-step solution and, where possible, a shortcut method.