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GMAT - Sequences & Series

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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.

  1. 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
    • Correct AnswerChoice (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
  2. How many 3 digit positive integers exist that when divided by 7 leave a remainder of 5?

    1. 128
    2. 142
    3. 143
    4. 141
    5. 129
    • Correct AnswerChoice (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
  3. 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)?

    1. m + 4
    2. n + 6
    3. n + 3
    4. m + 5
    5. n + 4
    • Correct AnswerChoice (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
  4. 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?

    1. 300
    2. 120
    3. 150
    4. 170
    5. 270
    • Correct AnswerChoice (C).
      The sum of the first 15 terms is 150.
      Correct answer
    • Explanatory Answer
    • Sum of an A.P.
    • Medium
  5. 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?

    1. 3
    2. 1/3
    3. 2
    4. 9
    5. 1/9
    • Correct AnswerChoice (C).
      The common ratio is 2.
      Correct answer
    • Explanatory Answer
    • Sum of G.P.
    • Medium
  6. 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?

    1. 2500
    2. 5050
    3. 11325
    4. 6275
    5. 2550
    • Correct AnswerChoice (A).
      The difference in the sum of the two sets is 2500.
      Correct answer
    • Explanatory Answer
    • Sum of 2 A.P.
    • Easy
  7. Data Sufficiency : A set S contains the following elements: {7, 11, 15, 19, 23, x}. What is the value of x?

    1. The elements are in arithmetic progression.
    2. x is prime.
    • Correct AnswerChoice (C).
      The two statements together are sufficient.
      Correct answer
    • Explanatory Answer
    • Data Sufficiency in AP
    • Easy
  8. 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?

    1. 11
    2. 14
    3. 12
    4. 13
    5. 10
    • Correct AnswerChoice (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
  9. Data Sufficiency : What is the 6th term of the Arithmetic sequence?

    1. The sum of the 6th to the 12th term of the sequence is 77.
    2. The sum of the 2nd to the 10th term of the sequence is 108.
    • Correct AnswerChoice (B).
      Statement 2 alone is sufficient; statement 1 is not.
      Correct answer
    • Explanatory Answer
    • DS : Finding term of AP
    • Medium
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