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Number Series Quiz 5 (10 MCQs)

This set of multiple-choice questions evaluates numerical reasoning skills, focusing on identifying perfect squares, recognizing number patterns, and understanding sequences such as arithmetic sequences, alternating patterns, and the properties of odd numbers. It also tests the ability to analyze number series, including cubes of odd numbers, triangular number sequences, and proportional reasoning.

Quiz Instructions

Select an option to see the correct answer instantly.

1. What is in between 3 and 5?

Correct Answer: Correct answer is: (A) 4.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Very Easy

Concept notes: In a number series, the number that comes between two consecutive integers is the integer that is exactly one more than the first and one less than the second.

Common Mistakes: A common mistake is to choose a number that is not directly between the two given numbers, such as choosing 6 instead of 4.

Explanations: The number between 3 and 5 in a number series is 4 because it is the integer that is one more than 3 and one less than 5.

Option Analysis:

Option A: 4 is the correct answer as it is the integer directly between 3 and 5.
Option B: 6 is incorrect as it is not between 3 and 5; it is greater than 5.

2. Look at this series:12, 11, 13, 12, 14, 13, ..... What number should come next

Correct Answer: Correct answer is: (D) 15.

Exam Relevance: GRE, GMAT, SAT, ACT

Difficulty: Moderate

Concept notes: The series alternates between increasing by 1 and decreasing by 1.

Common Mistakes: A common mistake is to assume a consistent pattern without recognizing the alternating nature of the series.

Explanations: The series alternates between increasing by 1 and decreasing by 1. Starting with 12, the pattern is: 12 (start) 11 (decrease by 1) 13 (increase by 1) 12 (decrease by 1) 14 (increase by 1) 13 (decrease by 1) The next number should increase by 1, resulting in 15.

Option Analysis:

Option A: 10 is incorrect because it does not follow the alternating pattern of increasing and decreasing by 1.
Option B: 16 is incorrect because it does not follow the alternating pattern of increasing and decreasing by 1.
Option C: 13 is incorrect because it does not follow the alternating pattern of increasing and decreasing by 1.
Option D: 15 is correct because it follows the alternating pattern of increasing and decreasing by 1.

3. Find the number which will come in the place of the question mark in the given series 4, 6, 9, 14, 21,?.

Correct Answer: Correct answer is: (B) 32.

Exam Relevance: GRE, GMAT, CAT, Bank PO

Difficulty: Moderate

Concept notes: The series follows a pattern where each number is obtained by adding an increasing sequence of numbers to the previous number.

Common Mistakes: A common mistake is to assume a simple arithmetic or geometric progression without identifying the increasing sequence of additions.

Explanations: The series is: 4, 6, 9, 14, 21, ? - The difference between the first and second term is 2 (6 - 4 = 2). - The difference between the second and third term is 3 (9 - 6 = 3). - The difference between the third and fourth term is 5 (14 - 9 = 5). - The difference between the fourth and fifth term is 7 (21 - 14 = 7). The differences form a sequence: 2, 3, 5, 7. This sequence is increasing by 1, 2, 2, and the next number in the sequence would be 4 (since 7 + 4 = 11). Thus, the next term in the series is 21 + 11 = 32.

Option Analysis:

Option A: 28 is incorrect because it does not follow the pattern of increasing differences.
Option B: 32 is correct as it follows the pattern of increasing differences.
Option C: 34 is incorrect because it does not follow the pattern of increasing differences.
Option D: 40 is incorrect because it does not follow the pattern of increasing differences.

4. In the following questions, a set of similar terms is given in which one of the term is odd and does not fit in the given set. You have to choose the term which does NOT fit in the set.

Correct Answer: Correct answer is: (C) 644.

Exam Relevance: GRE, GMAT, SAT, ACT

Difficulty: Moderate

Concept notes: The question tests the ability to identify numbers that are perfect squares and to recognize the odd one out in a set of numbers.

Common Mistakes: A common mistake is to overlook the fact that the numbers should be perfect squares and instead focus on other numerical properties.

Explanations: To determine the odd one out, we need to check if each number is a perfect square. A perfect square is a number that can be expressed as the square of an integer. 1089 = 33^2 729 = 27^2 644 is not a perfect square. 529 = 23^2 Since 644 is not a perfect square, it does not fit the set of perfect squares. Therefore, the correct answer is 644.

Option Analysis:

Option A: 1089 is a perfect square (33^2).
Option B: 729 is a perfect square (27^2).
Option C: 644 is not a perfect square.
Option D: 529 is a perfect square (23^2).

Mnemonic: Perfect squares, check roots.

5. There is a certain relationship between the pair of numbers on either side of::Identify the relationship of given pair and find the missing term. 4:8::7:?

Correct Answer: Correct answer is: (B) 14.

Exam Relevance: GRE, GMAT, SAT, ACT

Difficulty: Easy

Concept notes: The relationship between the numbers in the pair 4:8 is that 8 is double 4. Therefore, the missing term should be double 7.

Common Mistakes: A common mistake would be to assume a different relationship, such as adding a constant or using a different mathematical operation.

Explanations: The relationship between the numbers in the pair 4:8 is that 8 is double 4. To find the missing term, we need to apply the same relationship to 7. Therefore, the missing term should be double 7, which is 14.

Option Analysis:

Option A: 18 is incorrect because it does not follow the relationship of doubling the first number.
Option B: 14 is correct because it is double 7, following the relationship established by 4:8.
Option C: 10 is incorrect because it does not follow the relationship of doubling the first number.
Option D: 49 is incorrect because it does not follow the relationship of doubling the first number.

Mnemonic: Double the first, find the second.

6. What are the next numbers in this sequence 1, 4, 9, ....., .....

Correct Answer: Correct answer is: (B) 16, 25.

Exam Relevance: GRE, GMAT, SAT, ACT

Difficulty: Easy

Concept notes: The sequence given is a series of perfect squares of consecutive integers.

Common Mistakes: A common mistake is to assume the sequence follows a linear pattern or another arithmetic progression.

Explanations: The sequence 1, 4, 9, ... is the sequence of squares of consecutive integers: \(1^2, 2^2, 3^2, \ldots\). The next two terms in the sequence are \(4^2 = 16\) and \(5^2 = 25\).

Option Analysis:

Option A: 15, 18 are not perfect squares.
Option B: 16, 25 are the squares of 4 and 5, respectively.
Option C: 16, 26 are not both perfect squares.
Option D: 12, 15 are not perfect squares.

Mnemonic: Square the next number.

7. What is the next square number after 256?

Correct Answer: Correct answer is: (C) 289.

Exam Relevance: SAT, GRE, GMAT, ACT

Difficulty: Moderate

Concept notes: A square number is the result of multiplying an integer by itself. The next square number after 256 is found by identifying the next integer after the square root of 256 and squaring it.

Common Mistakes: A common mistake is to assume that the next number in a sequence is simply the next integer, rather than the next square number.

Explanations: The square root of 256 is 16. The next integer is 17. Squaring 17 gives \(17^2 = 289\). Therefore, the next square number after 256 is 289.

Option Analysis:

Option A: 260 is not a square number.
Option B: 270 is not a square number.
Option C: 289 is the correct next square number after 256.
Option D: 280 is not a square number.

8. Find the missing number in the series: 125, 343,?, 1331, 2197.

Correct Answer: Correct answer is: (A) 729.

Exam Relevance: GRE, GMAT, CAT, SAT

Difficulty: Moderate

Concept notes: The series consists of cubes of consecutive odd numbers.

Common Mistakes: A common mistake is to assume the series follows a simple arithmetic or geometric progression without recognizing the pattern of cubes.

Explanations: The series is formed by the cubes of consecutive odd numbers: 125 = 5^3, 343 = 7^3, 729 = 9^3, 1331 = 11^3, 2197 = 13^3. Thus, the missing number is 729, which is 9^3.

Option Analysis:

Option A: 729 is the correct answer as it fits the pattern of cubes of consecutive odd numbers.
Option B: 1728 is incorrect as it is 12^3, which does not fit the pattern of consecutive odd numbers.
Option C: 1000 is incorrect as it is 10^3, which does not fit the pattern of consecutive odd numbers.
Option D: 512 is incorrect as it is 8^3, which does not fit the pattern of consecutive odd numbers.

Mnemonic: Odd cubes, next odd, cube it.

9. 3 6 10 ..... 21

Correct Answer: Correct answer is: (C) 15.

Exam Relevance: GRE, GMAT, SAT, ACT

Difficulty: Moderate

Concept notes: The sequence given is a number series where each term is the sum of the first n natural numbers. This is known as the triangular number sequence.

Common Mistakes: A common mistake is to assume a linear or arithmetic progression without identifying the pattern correctly.

Explanations: The sequence provided is 3, 6, 10, ..., 21. To identify the pattern, observe the differences between consecutive terms: - 6 - 3 = 3 - 10 - 6 = 4 The differences are increasing by 1 each time. This suggests the sequence is formed by the sum of the first n natural numbers. The nth term of the sequence can be calculated using the formula for the sum of the first n natural numbers: \( T_n = \frac{n(n+1)}{2} \). For the given sequence: - \( T_2 = \frac{2(2+1)}{2} = 3 \) - \( T_3 = \frac{3(3+1)}{2} = 6 \) - \( T_4 = \frac{4(4+1)}{2} = 10 \) To find the next term: - \( T_5 = \frac{5(5+1)}{2} = 15 \) Thus, the next term in the sequence is 15.

Option Analysis:

Option A: 20 is incorrect because it does not follow the pattern of the triangular number sequence.
Option B: 17 is incorrect because it does not follow the pattern of the triangular number sequence.
Option C: 15 is correct as it follows the pattern of the triangular number sequence.
Option D: 16 is incorrect because it does not follow the pattern of the triangular number sequence.

Mnemonic: Triangular numbers, sum of n, half n(n+1)

10. Number Series:5. 4. 6. 5. 7.?

Correct Answer: Correct answer is: (C) 6.

Exam Relevance: GRE, GMAT, CAT, SAT

Difficulty: Moderate

Concept notes: The number series follows a pattern where each number alternates between increasing by 1 and decreasing by 1.

Common Mistakes: A common mistake is to assume a consistent pattern of increase or decrease without recognizing the alternating nature.

Explanations: The series starts with 4, then increases by 2 to 6, decreases by 1 to 5, increases by 2 to 7, and following the pattern, the next number should decrease by 1 from 7, resulting in 6.

Option Analysis:

Option A: 2 is incorrect as it does not follow the alternating pattern of increase and decrease.
Option B: 4 is incorrect as it does not follow the alternating pattern of increase and decrease.
Option C: 6 is correct as it follows the alternating pattern of increase and decrease.
Option D: 8 is incorrect as it does not follow the alternating pattern of increase and decrease.
Option E: 10 is incorrect as it does not follow the alternating pattern of increase and decrease.

Frequently Asked Questions

What is a number series?

A number series is a sequence of numbers that follow a specific pattern or rule, often involving arithmetic operations, geometric progressions, or other numerical properties.

How can I identify the pattern in a number series?

To identify the pattern, look for consistent differences between consecutive numbers, check for multiplication or division relationships, and consider if the numbers are part of a known sequence like squares or cubes.

What skills are tested in number series questions?

Number series questions test skills in pattern recognition, logical reasoning, and the ability to apply mathematical operations to identify the next number in a sequence.

What is an alternating pattern in a number series?

An alternating pattern in a number series involves a sequence where the numbers alternate between two different rules or operations, such as adding and subtracting different values.

How do I approach a number series with increasing differences?

To approach a number series with increasing differences, calculate the differences between consecutive numbers and look for a pattern in these differences, which may involve arithmetic or geometric progression.

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