integer question

[Guest]

If n is a positive integer and a product of all integers form 1 to 10, inclusive, and it is a multiple of 990 as well, what is the value of n?

10, 11, 12, 13, or 14?

My answer: 11, but not sure because I do not understand what the underlined portion means

Thank you!

 

[Denis]

If n is a positive integer and a product of all integers form 1 to 10, inclusive, and it is a multiple of 990 as well, what is the value of n?
10, 11, 12, 13, or 14?
My answer: 11, but not sure because I do not understand what the underlined portion means

CHECK the wording of your problem...

(Webster's)Main Entry: multiple
Function: noun
1 a : the product of a quantity by an integer <35 is a multiple of 7>

10 to 14 are certainly not multiples of 990

Product of integers 1 to 10 = 3,628,800 ; whatever that means in your problem !

 

[Guest]

Sorry but I still don't get the answer. Can you please tell me the answer? Thank you so much for your help!

 

[stapel]

Can you please tell me the answer?

As the tutor explained, you need to check (verify) the wording of the question since, as currently stated, it doesn't make sense.

Eliz.

 

[TchrWill]

If n is a positive integer and a product of all integers form 1 to 10, inclusive, and it is a multiple of 990 as well, what is the value of n?

10, 11, 12, 13, or 14?

My answer: 11, but not sure because I do not understand what the underlined portion means

I could be wrong but I suspect your question is really what n times 10! is divisible by 990?

Of the numbers given, 11x10x9x8x7x6x5x4x3x2x1 = 39,916,800 which is divisible by 990 yielding 40,320.

 

[pka]

In factored form \(\displaystyle 990 = 2 \cdot 3^2 \cdot 5 \cdot 11\). Thus 990 has a factor of 11 and (10!) does not.
Therefore, 11(10!) is a multiple of 990.
So 11 is only one of the choices that works.

 

[Guest]

Thank you so much!

Thanks to all of you guys' help I already got to solve the problem. Thank you!