Difficulty: Hard

Average Score: 43%

25x23=25 x 20+25 x 3 = 500+75= 575

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

Rationale

It has 6 and 15 as factors.

The number 90 can be factored into its prime components, specifically 2, 3, and 5, which allows us to identify its factors, including both 6 and 15. Since 6 (2 x 3) and 15 (3 x 5) are products of these prime factors, they are indeed factors of 90.

A (It has 10 as a multiple.) YOUR ANSWER

While 10 is a multiple of 90 (since 90 divided by 10 equals 9), the statement does not accurately reflect the nature of 90 itself. Instead, the relevant concept here is that 90 has multiples such as 90, 180, and so forth, rather than 10 being a multiple of 90.

C (It has four distinct prime factors.) YOUR ANSWER

The number 90 has three distinct prime factors: 2, 3, and 5. This can be verified through its prime factorization (90 = 2 x 3 x 3 x 5), which clearly shows only three unique primes. Therefore, claiming it has four distinct prime factors is incorrect.

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

The number 90 is divisible by 9 since 90 divided by 9 equals 10. However, 90 is also divisible by 18, as 90 divided by 18 equals 5. Thus, this statement is false because it contradicts the fact that 90 is indeed divisible by both 9 and 18.

Conclusion

Among the provided choices, the statement that 90 has 6 and 15 as factors is true, as both can be derived from its prime factorization. The other options either misrepresent the characteristics of 90 or present incorrect mathematical relationships. Understanding the factors and multiples of a number is essential in number theory, reinforcing the importance of accurate factor analysis.

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