When a certain positive number is divided by 342, the remainder is 47. If the same number is instead divided by 18, what remainder will be obtained?

Introduction / Context:
This question tests understanding of modular arithmetic and remainders. Instead of finding the original number directly, we use the given remainder with one divisor (342) to deduce the remainder with another divisor (18). Problems like this are very common in aptitude exams because they examine number sense and the ability to manipulate congruences without heavy calculation.

Given Data / Assumptions:

• Let the unknown number be N.
• When N is divided by 342, the remainder is 47.
• We need the remainder when the same N is divided by 18.
• All numbers involved are integers.

Concept / Approach:
From the remainder information, we can write N in the form N = 342k + 47, where k is a non negative integer. To find the remainder of N when divided by 18, we can reduce 342 and 47 modulo 18. Because 342 is a multiple of 18, its contribution to the remainder will vanish. Only the remainder of 47 modulo 18 will matter. This is a standard modular arithmetic technique that saves time in exams.

Step-by-Step Solution:
Express N using the division algorithm: N = 342k + 47 for some integer k.We want N mod 18, that is the remainder when N is divided by 18.First compute 342 mod 18. Since 18 * 19 = 342, 342 is exactly divisible by 18.Therefore, 342 mod 18 = 0.Now take N mod 18: N mod 18 = (342k + 47) mod 18.Split this as (342k mod 18) + (47 mod 18).Because 342k mod 18 = 0, we only need 47 mod 18.Compute 47 divided by 18: 18 * 2 = 36 and 47 - 36 = 11.So 47 mod 18 = 11.Hence N gives remainder 11 when divided by 18.

Verification / Alternative check:
Take one specific value, for example k = 1, so N = 342 + 47 = 389.Check with 342: 389 divided by 342 gives quotient 1 and remainder 47, which matches the given condition.Now divide 389 by 18: 18 * 21 = 378 and 389 - 378 = 11.The remainder is 11, which matches our computed answer.

Why Other Options Are Wrong:
15, 17, and 13 are incorrect because they do not match the simplified remainder 47 mod 18.Any remainder other than 11 would contradict the relation N = 342k + 47 when checked explicitly with small values of k.

Common Pitfalls:
A common mistake is to try to guess the original number N, which is unnecessary and time consuming.Another error is to use 342 and 18 directly without noticing that 342 is a multiple of 18, which greatly simplifies the calculation.Some learners forget that remainders repeat in cycles, so they do not take advantage of modular arithmetic to simplify expressions.

Final Answer:
The remainder when the number is divided by 18 is 11.