Question

What is the average of all multiples of 10 from 2 to 198?

Choose one option
Official answer and solution
Official answer
B
From
Official GATE 2014 answer key

Solution

Identify the arithmetic sequence of multiples of 10 within the given range and compute its average.

  1. The integers in the specified range are between 22 and 198198.

  2. The multiples of 1010 in this range are:

    {10,20,30,…,190}.\{10, 20, 30, \dots, 190\}.
  3. This sequence forms an arithmetic progression where:

    • First term a=10a = 10
    • Last term l=190l = 190
    • Common difference d=10d = 10
    • Number of terms n=190−1010+1=19n = \frac{190 - 10}{10} + 1 = 19
  4. For any finite arithmetic progression, the average equals the average of the first and last terms:

    Average=a+l2=10+1902=2002=100.\text{Average} = \frac{a + l}{2} = \frac{10 + 190}{2} = \frac{200}{2} = 100.

This corresponds to option B.

Final answer

B

Common trap

Including 0 or 200, which are outside the range from 2 to 198.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2014 Computer Science and Information Technology (CS) Session 2
Question
4 of 65, printed as GA Q.4
Section
General Aptitude

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