Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Quant Quizzes are back with a Bang and with lots of Prizes. The first Quiz will be on 8th Dec, 6PM PST (7:30AM IST). The Quiz will be Live for 12 hrs. Solution can be posted anytime between 6PM-6AM PST. Please click the link for all of the details.
Join IIMU Director to gain an understanding of DEM program, its curriculum & about the career prospects through a Q&A chat session. Dec 11th at 8 PM IST and 6:30 PST
For an integer n, the function f(n) is defined as the product of all
[#permalink]
Show Tags
30 Oct 2017, 22:14
2
00:00
A
B
C
D
E
Difficulty:
75% (hard)
Question Stats:
47% (01:34) correct 53% (01:36) wrong based on 134 sessions
HideShow timer Statistics
For an integer n, the function f(n) is defined as the product of all integers from 1 to n, where n is greater than 10. Which of the following is NOT a factor of f(n)+1?
I. 2 II. 3 III. 10
A. None B. II only C. I and II only D. I and III only E. I, II and III
Re: For an integer n, the function f(n) is defined as the product of all
[#permalink]
Show Tags
30 Oct 2017, 23:08
nkmungila wrote:
For an integer n, the function f(n) is defined as the product of all integers from 1 to n, where n is greater than 10. Which of the following is NOT a factor of f(n)+1?
I. 2 II. 3 III. 10
A. None B. II only C. I and II only D. I and III only E. I, II and III
f(n) = n!, where n > 10. So, f(n) is even, a multiple of 3 and a multiple of 10.
Therefore, f(n) + 1 is odd, 1 more than a multiple of 3 and 1 more than a multiple of 10, which means that f(n) + 1 is not divisible by 2, 3, or 10.
Re: For an integer n, the function f(n) is defined as the product of all
[#permalink]
Show Tags
30 Oct 2017, 23:10
2
Bunuel wrote:
nkmungila wrote:
For an integer n, the function f(n) is defined as the product of all integers from 1 to n, where n is greater than 10. Which of the following is NOT a factor of f(n)+1?
I. 2 II. 3 III. 10
A. None B. II only C. I and II only D. I and III only E. I, II and III
f(n) = n!, where n > 10. So, f(n) is even, a multiple of 3 and a multiple of 10.
Therefore, f(n) + 1 is odd, 1 more than a multiple of 3 and 1 more than a multiple of 10, which means that f(n) + 1 is not divisible by 2, 3, or 10.
Re: For the integer n, the function f(n) is defined as the product of all
[#permalink]
Show Tags
12 Sep 2018, 05:01
2
1
pushpitkc wrote:
For the integer n, the function f(n) is defined as the product of all integers from 1 to n, where n is greater than 10. Which of the following is NOT a factor of f(n) + 1?
I. 2 II. 3 III. 10
A. None B. II only C. I and II only D. I and III only E. I, II, and III
F(n)=1*2*3*...n where n>10 So f(n)=1*2*3*....*10*..*n Thus f(n) is product of all numbers till n and at least till 1 f(n) and f(n)+1 are co-prime, as they are consecutive terms.
Therefore f(n)+1 will not have any common factor that f(n) has.. So all numbers till 10 will NOT be factors
Re: For the integer n, the function f(n) is defined as the product of all
[#permalink]
Show Tags
12 Sep 2018, 09:27
urvashis09 wrote:
f(n) can be expressed as n! hence n! + 1 will be a prime integer and none of the integers smaller than n can be a factor of the same. Hence, E.
Although the second part that none of the integers smaller than n can be a factor of n!+1 is correct..
But that n!+1 will be prime integer may not be correct every time.. Example 3!+1=6+1=7 yes.. 4!+1=24+1=25....Not a prime 5!+1=120+1=121=11^2... Again not aprime integer..
So the point is that n!+1 will not be a multiple of any prime number <n
_________________
Re: For the integer n, the function f(n) is defined as the product of all
[#permalink]
Show Tags
14 Sep 2018, 17:40
pushpitkc wrote:
For the integer n, the function f(n) is defined as the product of all integers from 1 to n, where n is greater than 10. Which of the following is NOT a factor of f(n) + 1?
I. 2 II. 3 III. 10
A. None B. II only C. I and II only D. I and III only E. I, II, and III
Notice that f(n) = n!. Since two consecutive integers cannot share any of the same prime factors, f(n) and f(n) + 1 cannot share any of the same prime factors. Since f(n) is greater than 10!, and 10! has prime factors of 2, 3, 5, and 7, we see that 2, 3, and 2 x 5 = 10 cannot be primes of f(n) + 1.
Re: For an integer n, the function f(n) is defined as the product of all
[#permalink]
Show Tags
06 Feb 2019, 19:38
nkmungila wrote:
For an integer n, the function f(n) is defined as the product of all integers from 1 to n, where n is greater than 10. Which of the following is NOT a factor of f(n)+1?
I. 2 II. 3 III. 10
A. None B. II only C. I and II only D. I and III only E. I, II and III
We must remember that f(n) and f(n) + 1 WON’T SHARE ANY OF THE SAME PRIME FACTORS because they are consecutive integers.
So, since n is greater than 10, we see that f(n) will have prime factors of at least 2, 3, 5, and 7. Thus, 2, 3, and 10 won’t be factors of f(n) + 1.
Re: For an integer n, the function f(n) is defined as the product of all
[#permalink]
Show Tags
08 Sep 2019, 22:39
US09 wrote:
f(n) can be expressed as n! hence n! + 1 will be a prime integer and none of the integers smaller than n can be a factor of the same. Hence, E.
Is this a applicable rule for other problems or just "made up" for this problem? Because if I try it wih 4! => 4*3*2*1 = 24 + 1 will result in 25 which is not a prime integer.
_________________