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**

Try it free!

Register in 2 easy steps and

Start learning in 5 minutes!

1. Number Systems | Types of Numbers | Chart

2. Number Properties | Rational & Irrational Numbers

3. GMAT Number Properties | Indices & Rule of Exponents

4. Number Systems | Surds & Conjugates

5. Number Properties | Tests of divisibility

6. Number Properties | How to check whether a number is prime?

7. Number Properties | How to prime factorize a number?

8. GMAT Number Theory | Prime factorization | Properties of squares & cubes

9. Number Properties | What is HCF? | How to find HCF?

10. Number Properties | What is LCM? | How to find LCM?

11. 3 important properties of LCM & HCF | LCM & HCF of fractions

12. Number Properties | When to use LCM and HCF?

13. Number Theory | How to find number of factors?

14. Number Theory | Number of ways to express as a product of 2 factors

15. Number Theory | Sum of all factors of a number

16. Number Theory | Product of all factors of a number

17. Number Theory | Remainders of sum & product

18. Number Theory | Remainder of dividing x^{n} by 'd'

19. Polynomials | Remainder when a monomial divides it

20. Number Theory | Highest power of a prime that divides factorial of 'n'

21. Number Theory | Highest power of a composite number that divides factorial of 'n'

22. Number Theory | Number of trailing zeroes in a number

23. Number Theory | Unit digit of higher powers of numbers

Copyrights © 2016 - 21 All Rights Reserved by Wizako.com - An Ascent Education Initiative.

Privacy Policy | Terms & Conditions

GMAT^{®} is a registered trademark of the Graduate Management Admission Council (GMAC). This website is not endorsed or approved by GMAC.

GRE^{®} is a registered trademarks of Educational Testing Service (ETS). This website is not endorsed or approved by ETS.

SAT^{®} is a registered trademark of the College Board, which was not involved in the production of, and does not endorse this product.

Wizako - GMAT, GRE, SAT Prep

An Ascent Education Initiative

48/1 Ramagiri Nagar

Velachery Taramani Link Road.,

Velachery, Chennai 600 042. India

**Phone:** (91) 44 4500 8484

**Mobile:** (91) 95000 48484

**WhatsApp:** WhatsApp Now

**Email:** learn@wizako.com

Leave A Message