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Number Patterns Quiz 3 (9 MCQs)

This set of multiple-choice questions evaluates understanding of arithmetic sequences, Roman numeral conversion, prime numbers, divisibility rules, and number patterns. It tests skills in identifying patterns, performing arithmetic operations, and analyzing unit digits, square numbers, and triangular numbers.

Quiz Instructions

Select an option to see the correct answer instantly.

1. Which number remains same in mirror image?

Correct Answer: Correct answer is: (C) 8.

Exam Relevance: GRE, GMAT, IQ Tests

Difficulty: Easy

Concept notes: The question asks which number remains the same when viewed in a mirror. This concept is based on the symmetry of numbers when reflected.

Common Mistakes: A common mistake is to assume that numbers like 2 or 3 might look the same in a mirror, but they do not. The number 8 is the only digit that remains unchanged when reflected.

Explanations: The number 8 is symmetrical both vertically and horizontally. When viewed in a mirror, the shape of the number 8 remains the same. Other numbers like 2, 3, and 9 do not have this property.

Option Analysis:

Option A: The number 2 does not remain the same in a mirror image.
Option B: The number 3 does not remain the same in a mirror image.
Option C: The number 8 remains the same in a mirror image.
Option D: The number 9 does not remain the same in a mirror image.

2. What is the next square number after 289?

Correct Answer: Correct answer is: (A) 324.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: A square number is the result of multiplying an integer by itself. The next square number after 289 can be found by identifying the integer whose square is 289 and then finding the square of the next integer.

Common Mistakes: A common mistake is to assume that the next square number is simply the next number after 289, which is incorrect. It is important to identify the integer whose square is 289 and then find the square of the next integer.

Explanations: The square root of 289 is 17, because \(17 \times 17 = 289\). The next integer is 18. Therefore, the next square number is \(18 \times 18 = 324\).

Option Analysis:

Option A: 324 is the correct answer as it is the square of 18, which is the next integer after 17.
Option B: 320 is not a square number.
Option C: 310 is not a square number.
Option D: 300 is not a square number.

3. Select the number that does NOT belong in the following group: 71, 73, 77, 79

Correct Answer: Correct answer is: (D) 77.

Exam Relevance: SAT, GRE, GMAT, ACT

Difficulty: Moderate

Concept notes: The question tests the ability to identify prime numbers within a given set.

Common Mistakes: A common mistake is to assume that all odd numbers are prime, which is not true.

Explanations: The numbers 71, 73, and 79 are prime numbers, meaning they have no divisors other than 1 and themselves. The number 77, however, is not a prime number because it can be factored into 7 × 11. Therefore, 77 does not belong in the group of prime numbers.

Option Analysis:

Option A: 79 is a prime number.
Option B: 71 is a prime number.
Option C: 73 is a prime number.
Option D: 77 is not a prime number because it can be factored into 7 × 11.

Mnemonic: Prime numbers are "purely indivisible," except by 1 and themselves.

4. The square of a number having 9 at the units place ends in

Correct Answer: Correct answer is: (D) 1.

Exam Relevance: SAT, GRE, GMAT, ACT

Difficulty: Easy

Concept notes: When a number ends in 9, its square will always end in 1.

Common Mistakes: A common mistake is to think that the square of a number ending in 9 will also end in 9, but this is incorrect.

Explanations: To understand why the square of a number ending in 9 ends in 1, consider the following: - Let the number be represented as \(10a + 9\), where \(a\) is an integer. - The square of this number is \((10a + 9)^2\). - Expanding this, we get \(100a^2 + 180a + 81\). - The last digit of this expression is determined by the last digit of 81, which is 1. - Therefore, the square of any number ending in 9 will end in 1.

Option Analysis:

Option A: Incorrect, because the square of a number ending in 9 does not end in 9.
Option B: Incorrect, because the square of a number ending in 9 does not end in 3.
Option C: Incorrect, because the square of a number ending in 9 does not end in 81, but the last digit is 1.
Option D: Correct, because the square of a number ending in 9 ends in 1.

5. Look at this series: V, VIII, XI, XIV, ....., XX, ..... What number should fill the blank?

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

Exam Relevance: SAT, GRE, GMAT, ACT

Difficulty: Moderate

Concept notes: The series is an arithmetic sequence in Roman numerals where each term increases by 3.

Common Mistakes: A common mistake is to misinterpret the pattern or incorrectly convert between Roman numerals and Arabic numerals.

Explanations: The series starts with V (5), followed by VIII (8), XI (11), and XIV (14). Each term increases by 3. Therefore, the next term after XIV (14) is XVII (17).

Option Analysis:

Option A: IX (9) is incorrect because it does not follow the pattern of increasing by 3.
Option B: XXIII (23) is incorrect because it is too large and does not follow the pattern of increasing by 3.
Option C: XV (15) is incorrect because it does not follow the pattern of increasing by 3.
Option D: XVII (17) is correct because it follows the pattern of increasing by 3 from XIV (14).

6. What is the next number in the series: 1, 3, 6, 10, .....?

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

Exam Relevance: SAT, GRE, GMAT, Competitive Math Exams

Difficulty: Moderate

Concept notes: The series given is a sequence of triangular numbers. Each number in the series is the sum of the first n natural numbers.

Common Mistakes: A common mistake is to assume the series follows a simple arithmetic or geometric progression, which it does not.

Explanations: The series is formed by the sum of the first n natural numbers: 1 = 1 3 = 1 + 2 6 = 1 + 2 + 3 10 = 1 + 2 + 3 + 4 The next number in the series is the sum of the first 5 natural numbers: 15 = 1 + 2 + 3 + 4 + 5

Option Analysis:

Option A: 21 is incorrect because it does not follow the pattern of triangular numbers.
Option B: 12 is incorrect because it does not follow the pattern of triangular numbers.
Option C: 15 is correct because it is the sum of the first 5 natural numbers.
Option D: 18 is incorrect because it does not follow the pattern of triangular numbers.

Mnemonic: Triangular numbers: Sum of first n natural numbers.

7. Number between 90 and 100 have both digits same.

Correct Answer: Correct answer is: (B) 99.

Exam Relevance: SAT, GRE, GMAT, Competitive Exams

Difficulty: Easy

Concept notes: The question asks for a number between 90 and 100 where both digits are the same.

Common Mistakes: A common mistake might be choosing a number that does not have both digits the same, such as 92 or 98.

Explanations: The number 99 is the only number between 90 and 100 where both digits are the same. The digits in 99 are both 9.

Option Analysis:

Option A: 92 does not have both digits the same.
Option B: 99 has both digits the same.
Option C: 98 does not have both digits the same.
Option D: 95 does not have both digits the same.

8. The square of a number having 5 at the units place ends in

Correct Answer: Correct answer is: (C) 5.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: The square of a number ending in 5 will always end in 5.

Common Mistakes: A common mistake is to think that the square of a number ending in 5 might end in 0, which is incorrect.

Explanations: When a number ends in 5, its square will always end in 5. For example, consider the number 5. The square of 5 is 25, which ends in 5. Similarly, the square of 15 is 225, which also ends in 5. This pattern holds true for any number ending in 5.

Option Analysis:

Option A: The square of a number ending in 5 does not end in 0.
Option B: The square of a number ending in 5 does not end in 2.
Option C: The square of a number ending in 5 always ends in 5.
Option D: The square of a number ending in 5 does not end in 1.

9. A number pattern is shown below. 100, 95, 110, 105, 120, ..... If this pattern continues, what number will come next?

Correct Answer: Correct answer is: (B) 115.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Moderate

Concept notes: The pattern alternates between subtracting 5 and adding 15.

Common Mistakes: A common mistake is to assume the pattern is consistently increasing or decreasing by a fixed amount.

Explanations: The sequence starts with 100. The next number is obtained by subtracting 5 (100 - 5 = 95). The following number is obtained by adding 15 (95 + 15 = 110). This pattern continues: subtract 5, then add 15. Therefore, the next number after 120 is obtained by subtracting 5 (120 - 5 = 115).

Option Analysis:

Option A: 100 is incorrect because it does not follow the established pattern of alternating between subtracting 5 and adding 15.
Option B: 115 is correct because it follows the pattern of subtracting 5 from the previous number, 120.
Option C: 120 is incorrect because it does not follow the pattern of subtracting 5 from the previous number, 120.
Option D: 130 is incorrect because it does not follow the pattern of subtracting 5 from the previous number, 120.

Mnemonic: Subtract 5, Add 15, Repeat

Frequently Asked Questions

What are number patterns?

Number patterns are sequences of numbers that follow a specific rule or set of rules. They can be arithmetic, geometric, or based on other mathematical operations.

How can I identify an alternating sequence?

An alternating sequence alternates between two different operations or values. For example, a sequence might alternate between adding and subtracting a fixed number.

What is the significance of divisibility in number patterns?

Divisibility helps in identifying patterns where numbers are multiples of a specific number. This can be useful in predicting the next number in a sequence or understanding the underlying rule.

How do square numbers fit into number patterns?

Square numbers are the result of multiplying a number by itself. They form a specific pattern where each number is the square of an integer, such as 1, 4, 9, 16, and so on.

What is the importance of prime numbers in number patterns?

Prime numbers are crucial in number patterns as they are only divisible by 1 and themselves. They can help in identifying unique sequences and understanding the distribution of numbers.

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