# GMAT - **Sequences & Series**

You may get one or two questions from sequences and series in the quant section of the GMAT exam - in both variants viz., problem solving and data sufficiency. The concepts tested includes arithmetic progression and geometry progression. This topic may also feature questions that form a series that are neither AP nor GP. A collection of GMAT practice questions from arithmetic and multiplicative sequences is given below. Attempt these questions and check whether you have got the correct answer. If you could not crack the questions, go to the explanatory answer or the video explanations (wherever provided) to learn how to crack the question.

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

**Correct Answer**Choice (B).

The sum of all 3 digit numbers that leave a remainder of 2 when divided by 3 is**164,850**. Correct answer- Explanatory Answer
- Sum of AP
- Easy

How many 3 digit positive integers exist that when divided by 7 leave a remainder of 5?

- 128
- 142
- 143
- 141
- 129

**Correct Answer**Choice (E).

The number of 3 digit positive integers that leave a remainder of 5 when divided by 7 is**129**. Correct answer- Explanatory Answer
- AP - number of terms
- Easy

The average of 5 consecutive integers starting with m as the first integer is n. What is the average of 9 consecutive integers that start with (m + 2)?

- m + 4
- n + 6
- n + 3
- m + 5
- n + 4

**Correct Answer**Choice (E).

The average of 9 consecutive integers that start with (m + 2) is**(n + 4)**. Correct answer- Explanatory Answer
- Average of an A.P.
- Easy

The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 15 terms of the arithmetic progression?

- 300
- 120
- 150
- 170
- 270

**Correct Answer**Choice (C).

The sum of the first 15 terms is**150**. Correct answer- Explanatory Answer
- Sum of an A.P.
- Medium

If the ratio of the sum of the first 6 terms of a G.P. to the sum of the first 3 terms of the G.P. is 9, what is the common ratio of the G.P?

- 3
- 1/3
- 2
- 9
- 1/9

**Correct Answer**Choice (C).

The common ratio is**2**. Correct answer- Explanatory Answer
- Sum of G.P.
- Medium

Set A contains all the even numbers between 2 and 50

__inclusive__. Set B contains all the even numbers between 102 and 150__inclusive__. What is the difference between the sum of elements of set B and the sum of the elements of set A?- 2500
- 5050
- 11325
- 6275
- 2550

**Correct Answer**Choice (A).

The difference in the sum of the two sets is 2500. Correct answer- Explanatory Answer
- Sum of 2 A.P.
- Easy

Data Sufficiency : A set S contains the following elements: {7, 11, 15, 19, 23, x}. What is the value of x?

- The elements are in arithmetic progression.
- x is prime.

**Correct Answer**Choice (C).

The two statements together are sufficient. Correct answer- Explanatory Answer
- Data Sufficiency in AP
- Easy

In the first 1000 natural numbers, how many integers exist such that they leave a remainder 4 when divided by 7, and a remainder 9 when divided by 11?

- 11
- 14
- 12
- 13
- 10

**Correct Answer**Choice (D).

The number of integers up to the first 1000 natural numbers that satisfy both the conditions is 13. Correct answer- Explanatory Answer
- Elements common to 2 sequences
- Medium

Data Sufficiency : What is the 6

^{th}term of the Arithmetic sequence?- The sum of the 6
^{th}to the 12^{th}term of the sequence is 77. - The sum of the 2
^{nd}to the 10^{th}term of the sequence is 108.

**Correct Answer**Choice (B).

Statement 2 alone is sufficient; statement 1 is not. Correct answer- Explanatory Answer
- DS : Finding term of AP
- Medium

- The sum of the 6

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