M28-32

Question

Which of the following is a factor of  18!+1 ?

A.  15 
B.  17 
C.  19 
D.  33 
E.  39

Bunuel · Accepted Answer

Official Solution:

Which of the following is a factor of  18!+1 ?

A.  15 
B.  17 
C.  19 
D.  33 
E.  39

18!  and  18!+1  are consecutive integers. Two consecutive integers are always co-prime, meaning that they don't share any common factors other than 1. For example, 20 and 21 are consecutive integers, and the only common factor they share is 1.
 
Since we can factor out each of the numbers 15, 17, 33 (3*11), and 39 (3*13) from  18! , these numbers are indeed factors of  18!  but cannot be factors of  18!+1 . Therefore, only 19 could be a factor of  18!+1 .

Answer: C

vijaisingh2001 · Answer

there is a pattern for the factorial

for even
2! +1= 3 
4! +1 = 25 so 5 (4+1) a factor
6! +1= 721 so 7 (6+1 ) is a factor

for odd
3! +1= 7 =(3*2 +1)

5! +1 = 121 = 11(5*2 +1) a factor

munishrattanpal · Answer

If P is a prime number , (p-1)!+1 is divisible by p

mbadude2017 · Answer

This is not true, the pattern actually breaks in the next two examples:
7!+1 = 5041, which is NOT divisible by (2*7+1)=15
8!+1 = 40321, which is NOT divisible by (8+1)=9

dcummins · Answer

Good Question.

Two consecutive integers never share any of the same factors except 1, so since 18! and (18!+1) are consecutive, 18!+1 will not share the factors of 18!

Just ask whether each answer choice is a factor of 18!
A. 15 - Yes, 3 and 5
B. 17 - Yes, 17
C. 19 - No, 19 is a prime not found in 18!
D. 33 - Yes, made up of 3 and 11
E. 39 - Yes, made up of 13 and 3

Jessie265 · Answer

Which of the following is a factor of 18!+1?

I use exclusion method to solve this case 
We have 18!=1*2*3...17*18.
So 18!+1 is indivisibled by number that 18 is divisibled by.
The answer is C

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

jafrinalo · Answer

Coprime

Bunuel · Answer

18! = 18*17*16*...*1, not 18 + 17 + 16 +  ... + 1. Hence, the above is not correct.

braddouglas10 · Answer

O great Bunuel, the man who could easily pull my wife, mother, and daughter, do you have any more similar problems?

Thanks!

Bunuel · Answer

Similar questions to practice: https://gmatclub.com/forum/if-q-40-1-wh ... 17582.html https://gmatclub.com/forum/if-x-30-23-w ... 81763.html https://gmatclub.com/forum/which-number ... 52407.html Hope it helps.

braddouglas10 · Answer

O great Bunuel, the man who could easily pull my wife, mother, and daughter, thank you!

M28-32

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