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

video

Click on the Email ☝️ to Watch the Video Solution

Create a FREE account and get:

All Quant CAT complete Formulas and shortcuts PDF
35+ CAT previous papers with video solutions PDF
5000+ Topic-wise Previous year CAT Solved Questions for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Linear Equations Questions CAT Quadratic Equations Questions CAT Logarithms Questions CAT Number Systems Questions CAT Arithmetic Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Coins and Weights Questions CAT Truth Lie Concept Questions CAT Games and Tournamnents Questions CAT 2D & 3D LR Questions CAT Puzzles Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Grammar and Sentence Correction Questions CAT Reading Comprehension Questions CAT Odd One Out Questions CAT Para Jumbles Questions CAT Critical Reasoning Questions

Follow us on

Boost your Prep!

Download App