Sequence and SeriesMCQMTP Dec 22 Series IIQuestion 1806 of 213
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Sum lying from $100\displaystyle to $300 which is divisible by 4\displaystyle 4 and 5\displaystyle 5 is

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — 2200

All Options:

  • A2000
  • B2100
  • C2200
  • D2300

Detailed Solution & Explanation

A number divisible by both 4\displaystyle 4 and 5\displaystyle 5 must be divisible by their L.C.M., which is $20\displaystyle .<br>The numbers divisible by &#36;20 lying from $100\displaystyle to &#36;300 inclusive are:
100,120,140,…,300100, 120, 140, \dots, 300
Here:
First term a=100\displaystyle a = 100
Common difference d=20\displaystyle d = 20
Last term l=300\displaystyle l = 300.

Using the last term formula:
l=a+(n−1)dl = a + (n-1)d
300=100+(n−1)20300 = 100 + (n-1)20
200=(n−1)20  ⟹  n−1=10  ⟹  n=11200 = (n-1)20 \implies n-1 = 10 \implies n = 11

The sum is:
S11=112[a+l]=112[100+300]=112[400]=2200S_{11} = 112\displaystyle \frac{11}{2} [a + l] = 112\displaystyle \frac{11}{2} [100 + 300] = 112\displaystyle \frac{11}{2} [400] = 2200
Hence, **Option C** is the correct answer.

About This Chapter: Sequence and Series

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Arithmetic & Geometric Progressions

This chapter covers Arithmetic Progressions (AP) and Geometric Progressions (GP). Students learn how to find the nth term, sum of n terms, arithmetic/geometric means, and sum to infinity of a GP.

View Official ICAI Syllabus

Exam Strategy Tip

For complex 'sum of series' questions, a great hack is to substitute n = 1 and n = 2 into the question and the options to see which one matches, completely bypassing the formula.

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