A teacher gave a student the task of adding $N$ natural numbers starting from 1. After a while, the student reported his result as 700. The teacher replied that the result was wrong. The student realised he had added one number twice. Find the sum of the digits of the number which the student had added twice.

Answer (Detailed Solution Below)View answer ▾

Answer: Option C — 7

Detailed Solution

The correct sum is $\frac{N ( N + 1 )}{2}$ , and the repeated number $d = 700 - \frac{N ( N + 1 )}{2}$ must satisfy $1 \leq d \leq N$ .

$N = 36$ gives $666$ and $d = 34 \leq 36$ . ( $N = 37$ gives $703 > 700$ , and $N = 35$ gives $630$ with $d = 70 > 35$ .)

The number added twice is 34; its digit sum is $3 + 4 = 7$ .

✓ Check

666 + 34 = 700

⚠ Common trap

Taking

N = 37

and

703 - 700 = 3

treats the error as a missed number, not a repeated one.

Quick tip

$\frac{36 \cdot 37}{2} = 666, 700 - 666 = 34 \Rightarrow 3 + 4 = 7$

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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.

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