Please enter the following details
Free Daily Targets & Mocks
Study Material & Formulas PDFs
1 on 1 Mentorship
Question 63
If n is a positive integer such that $$(\sqrt[7]{10})(\sqrt[7]{10})^{2}...(\sqrt[7]{10})^{n}>999$$, then the smallest value of n is
Correct Answer: 6
Solution
$$(\sqrt[7]{10})(\sqrt[7]{10})^{2}...(\sqrt[7]{10})^{n}>999$$
$$(\sqrt[7]{10})^{1+2+...+n}>999$$
$$10^{\frac{1+2+...+n}{7}}>999$$
For minimum value of n,
$$\frac{1+2+...+n}{7}=3$$
1 + 2 + ... + n = 21
We can see that if n = 6, 1 + 2 + 3 + ... + 6 = 21.
Video Solution
Create a FREE account and get:
- All Quant CAT complete Formulas and shortcuts PDF
- 38+ CAT previous year papers with video solutions PDF
- 5000+ Topic-wise Previous year CAT Solved Questions for Free
CAT Quant Questions | CAT Quantitative Ability
CAT Linear Equations QuestionsCAT Mensuration QuestionsCAT Time And Work QuestionsCAT Logarithms QuestionsCAT Percentages Questions
CAT DILR Questions | LRDI Questions For CAT
CAT Venn Diagrams QuestionsCAT Puzzles QuestionsCAT Games and Tournamnents QuestionsCAT Data Interpretation QuestionsCAT Truth Lie Concept Questions
