First slide

Types of real valued functions XI

Question

Let $E = [\frac{1}{3} + \frac{1}{50}] + [\frac{1}{3} + \frac{2}{50}] + \dots +$ up to 50 terms, then

Moderate

A

E is divisible by exactly 2 primes
B

E is prime
C

$E \geq 30$
D

$E \leq 35$

Solution

For, $1 \leq x \leq 33, \frac{1}{3} < \frac{1}{3} + \frac{x}{50} < 1$ therefore,
$[\frac{1}{3} + \frac{x}{50}] = 0 for 1 \leq x \leq 33$
For $34 \leq x \leq 50, 1 < \frac{1}{3} + \frac{x}{50} < \frac{4}{3}$
$\Rightarrow [\frac{1}{3} + \frac{x}{50}] = 1 for 34 \leq x \leq 50$
Thus E=17

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