Lesson: Factorial Notation

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Which of the following is a multiple of 4!+6?
a)2!+3
b) 4!+12
c)5!+6
d)5!+30
e)8!+12

How do i tackle this problem Brent? Do i have to consider prime numbers?
gmat-admin's picture

Nice question!

If A and a multiple of B, then we can write A = kB for some integer k.

For example, we know that 24 is a multiple of 6, because we can write 24 = (4)(6)

4! + 6 = (4)(3)(2)(1) + 6

All MULTIPLES of 4! + 6 are in the form k(4! + 6), where k is an integers

k(4! + 6) = k[(4)(3)(2)(1) + 6]
= (k)(4)(3)(2)(1) + 6k

So, all multiples of 4! + 6 can be written in the form (k)(4)(3)(2)(1) + 6k

At this point, I SCAN the answer choices to see if any of them can be derived from the expression (k)(4)(3)(2)(1) + 6k

Notice that answer choice D, 5! + 30, can be derived if we let k = 5

That is, 5[4! + 6] = 5[(4)(3)(2)(1) + 6]
= (5)(4)(3)(2)(1) + 30
= 5! + 30

Answer: D

Did you work backwards and plugged in Answer Choice D?
gmat-admin's picture

Great question.
I have edited my response above to address that question.

Cheers.
Brent

Hey Brent,

Came across this question and found that you didn't cover the particular formula for circular arrangements in the module. Can you explain using the FCP?

"How many ways can six friends be arranged around a circular dinner table?"

Thanks
gmat-admin's picture

I'm not a big fan of questions involving people seated at a circular table. Those questions require some assumptions that are un-GMAT-like.

I've seen test-prep companies ask those question types, but I've never seen an official question with the same setup.

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