Question

Find x if \(\frac{1}{{5!}} + \frac{1}{{6!}} = \frac{x}{{7!}}\) ?
1. 100
2. 36
3. 49
4. 64

Answer 1

Correct Answer - Option 3 : 49

CONCEPT:

n! = n × (n - 1) × ...... × 1

CALCULATION:

Given: \(\frac{1}{{5!}} + \frac{1}{{6!}} = \frac{x}{{7!}}\)

As we know that, n! = n × (n - 1) × ...... × 1

⇒ \(\frac{1}{{5!}} + \frac{1}{{6\; \times \;5!}} = \frac{x}{{7 \;\times \;6 \;\times \;5!}}\)

⇒ \(\frac{1}{{5!}} \times \left( {1 + \frac{1}{{6}}} \right) = \frac{1}{{5!}} \times \frac{x}{{42}}\)

⇒ \(1 + \frac{1}{{6}} = \frac{x}{{42}}\)

⇒ x = 49

Hence, option C is the correct answer.