The GMAT Sample Math question given below is from the topic Arithmetic Progressions. Concept: Sum of an arithmetic progression. Problems on Arithmetic Progressions are quite easy if one understands that the basic concept behind AP is just an extrapolation of simple multiplication tables.

Question 16: What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?

- 897
- 164,850
- 164,749
- 149,700
- 156,720

@ INR

Identify the series

The smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101.

The next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107.

The largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998.

It is evident that the numbers in the sequence will be a 3 digit positive integer of the form (3n + 2).

So, the given numbers are in an Arithmetic Progression with 101 as the first term, 998 as the last term, and 3 as the common difference of the sequence.

Compute the sum

Sum of an Arithmetic Progression (AP) = \\left[\frac{\text{first term + last term}}{2}\right]n), where 'n' is the number of terms in the sequence.

We know the first term: 101

We know the last term: 998.

The only unknown is the number of terms, n.

In an A.P., the nth term a_{n} = a_{1} + (n - 1) * d

In this question, 998 = 101 + (n - 1) * 3

Or 897 = (n - 1) * 3

(n - 1) = 299 or n = 300.

Sum of the AP is \\left[\frac{101 + 998}{2}\right] * 300) = **164,850**

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