# GMAT Maths | Sequences Series Q16

#### GMAT Sample Questions | Arithmetic and Geometric Progressions

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?

1. 897
2. 164,850
3. 164,749
4. 149,700
5. 156,720

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#### Step 1 of solving this GMAT Progressions Question: 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.

#### Step 2 of solving this GMAT Progressions Question: Compute the sum

Sum of an Arithmetic Progression (AP) = $$left[\frac{\text{first term + last term}}{2}\right]n$, where 'n' is the number of terms in the sequence. We know the first term: 101 We know the last term: 998. The only unknown is the number of terms, n. In an A.P., the nth term an = a1 +$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 #### Choice B is the correct answer. #### GMAT Online CourseTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GMAT Live Online Classes Next Batch June 18, 2023 ##### Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 14B/1 Dr Thirumurthy Nagar 1st Street Nungambakkam Chennai 600 034. India Work @ Wizako ##### How to reach Wizako? Mobile:$91) 95000 48484
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