Question

The sum of all integers between 200 and 300 which are divisible by both 5 and 3 is

• A. 854
• B. 1485
• C. 1548
• D. 1500

Answer 1

The correct option is B 1485

LCM(5, 3) = 15
Between 200 and 300, there are six numbers (210, 225, 240, 255, 270, 285) that are completely divisible by 15 and, hence are divisible by 5 and 3.
Thus, the progression is 210, 225, 240, 255, 270, 285.
Clearly, these numbers form an AP with a = 210, d = 225 – 210 = 15, n = 6.
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$\Rightarrow S_6=\frac{6}{2}[2\times 210+(6-1)\times 15]$
$\Rightarrow S_6=3[420+5\times 15]$
$\Rightarrow S_6=3(420+75)$
$\Rightarrow S_6=3\times 495$
$\Rightarrow S_6=1485$
Hence the correct answer option is (2)