Difficulty: Medium

Average Score: 67%

Which of the following statements is true about the number 90?

Rationale

It has 6 and 15 as factors.

The number 90 can be evenly divided by both 6 and 15, confirming that they are indeed factors of 90. This means that when 90 is divided by either of these numbers, the result is a whole number, demonstrating their integral relationship to 90.

A (It has 10 as a multiple) YOUR ANSWER

While 90 is indeed a multiple of 10 (as 90 can be expressed as 10 times 9), this statement is misleading because it implies that 10 is a factor of 90, which it is not. A factor must divide a number evenly, and 10 does not meet this criterion since 90 divided by 10 results in 9, not a whole number.

C (It has four distinct prime factors) YOUR ANSWER

The prime factorization of 90 is 2 × 3 × 3 × 5, which consists of three distinct prime factors (2, 3, and 5). Therefore, stating that it has four distinct prime factors is incorrect, as there are only three unique primes that multiply to give 90.

D (It is divisible by 9 but not by 18) YOUR ANSWER

Although 90 is divisible by 9 (90 divided by 9 equals 10), it is also divisible by 18 since 90 divided by 18 equals 5. This makes the statement false, as 90 meets the criteria for divisibility by both 9 and 18.

Conclusion

Among the provided options, only the statement that 90 has 6 and 15 as factors is accurate. This reveals a fundamental property of the number, highlighting its divisibility. The other choices either misinterpret the relationships between factors and multiples or incorrectly state the number of distinct prime factors, thereby verifying B as the only true statement regarding the number 90.

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