Find the value of n if (n+1)! = 42 (n-1)!

Option a: 6. Solution: Let us solve the factorial equation step-by-step: (n+1)! = 42(n-1)! Expanding (n+1)! : (n+1) × n × (n-1)! = 42(n-1)! Since n ≥ 1 , we can divide both sides by (n-1)! : n(n+1) = 42 n2 + n - 42 = 0 (n+7)(n-6) = 0 Since n must be a positive integer, we discard n = -7 , leaving: n = 6 This matches Option A. Hence, Option A is the correct answer.

Find the value of n if $(n+1)! = 42 (n-1)!$

The correct answer is Option a: 6. Let us solve the factorial equation step-by-step: $$(n+1)! = 42(n-1)!$$ Expanding $(n+1)!$: $$(n+1) \\times n \\times (n-1)! = 42(n-1)!$$ Since $n \\ge 1$, we can divide both sides by $(n-1)!$: $$n(n+1) = 42$$ $$n^2 + n - 42 = 0$$ $$(n+7)(n-6) = 0$$ Since $n$ must be a positive integer, we discard $n = -7$, leaving: $$n = 6$$ This matches Option A. Hence, **Option A** is the correct answer.

Permutations and CombinationsMCQMTP Oct 21Question 1636 of 251

All Questions

Find the value of n if $\displaystyle (n+1)! = 42 (n-1)!$

Options

D-7

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Correct Answer

✅ Option a — 6

All Options:

Detailed Solution & Explanation

Let us solve the factorial equation step-by-step:

(n+1)! = 42(n-1)!

Expanding

\displaystyle (n+1)!

(n+1) \\times n \\times (n-1)! = 42(n-1)!

Since

\displaystyle n \\ge 1

, we can divide both sides by

\displaystyle (n-1)!

n(n+1) = 42

n^2 + n - 42 = 0

(n+7)(n-6) = 0

Since

\displaystyle n

must be a positive integer, we discard

\displaystyle n = -7

, leaving:

n = 6

This matches Option A.
Hence, **Option A** is the correct answer.

About This Chapter: Permutations and Combinations

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Factorials, Permutations, Combinations

This chapter deals with the fundamental principles of counting. It covers factorials, circular permutations, restricted permutations, combinations, and the differences between selecting items versus arranging them.

View Official ICAI Syllabus

Exam Strategy Tip

The most common mistake is confusing 'P' (Arrangement) with 'C' (Selection). If order matters (like opening a lock), use P. If order doesn't matter (like choosing a team), use C.

Related Comparison Tables

Permutations vs Combinations: The Quantitative Aptitude Guide

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Find the value of n if (n+1)!=42(n−1)!\displaystyle (n+1)! = 42 (n-1)!(n+1)!=42(n−1)!