ISI2014-DCG-67

Question

Let $y=[\:\log_{10}3245.7\:]$ where $[ a ]$ denotes the greatest integer less than or equal to $a$. Then

• A. $y=0$
• B. $y=1$
• C. $y=2$
• D. $y=3$

Answer 1

Answer: $\mathbf D$

Explanation:

$\mathrm y = \log_{10}3245.7 \\= \log_{10}3.2457\times 10^3 \\= \log_{10}3.2457+\log10^3 \\= \underbrace{\log_{10}3.2457}_\text{less than 1} + \underbrace{3\log_{10}{10}}_\text{=3} \\= 3+ \text{ Some decimal values} = 3$

Since, the values for greatest integer function for $3.2 = 3$ or gif for $3.7 = 3$, i.e., it always gives the greatest integer value.

So, the answer comes out to be $3$

$\therefore \mathbf D$ is the correct option.