GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 14:34 GMAT Club Daily Prep

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

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.  Does the integer g have a factor f such that 1 < f < g ?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Intern  B
Joined: 19 Jul 2016
Posts: 49
Does the integer g have a factor f such that 1 < f < g ?  [#permalink]

Show Tags

1
14 00:00

Difficulty:   45% (medium)

Question Stats: 54% (01:12) correct 46% (01:53) wrong based on 101 sessions

HideShow timer Statistics

Does the integer g have a factor f such that 1 < f < g ?

(1) g > 3!
(2) 11! + 11 >= g >= 11! + 2
Math Expert V
Joined: 02 Sep 2009
Posts: 58427
Re: Does the integer g have a factor f such that 1 < f < g ?  [#permalink]

Show Tags

1
Manager  B
Joined: 08 Nov 2015
Posts: 56
GMAT 1: 460 Q32 V22 Re: Does the integer g have a factor f such that 1 < f < g ?  [#permalink]

Show Tags

gupta87 wrote:
Does the integer g have a factor f such that 1 < f < g ?
1. g>3!
2. 11!+11>=g>=11!+2

ans is B but why?

This problem is essentially saying 11>=g>=2.i.e g is between 11 and 2 (inclusive).
g can take 2, 3, 4, 5, 6,7,8,9,10,11
There are integer for ex: 6 for which the above condition holds. Hence the answer is B.
Manager  B
Joined: 24 Nov 2017
Posts: 63
Location: India
GMAT 1: 720 Q51 V36 Re: Does the integer g have a factor f such that 1 < f < g ?  [#permalink]

Show Tags

4
gupta87 wrote:
Does the integer g have a factor f such that 1 < f < g ?
1. g>3!
2. 11!+11>=g>=11!+2

ans is B but why?

It is evident that statement 1 ALONE is not sufficient.

So, let us focus on statement 2 ALONE.
11!+11>=g>=11!+2

Essentially, what the statement says is that 'g' is an integer that lies between (11! + 2) and (11! + 11). 'g' takes 10 different values.
What we have to determine is whether all of the values of 'g' have at least 1 factor other than 1 and g.

11! is divisible by all positive integers from 2 to 11.

So, if g = (11! + 2), because 11! is divisible by 2 and 2 is divisible by 2, (11! + 2) will be divisible by 2. So, we can infer that there exists a factor f for g such that 1 < f < g. In this case f = 2.
We can extend the same argument for all numbers from (11! + 3) to (11! + 11).
So, we can conclude that there will exist at least one factor f, such that 1 < f < g if g lies between (11! + 2) and (11! + 11)
Statement 2 ALONE is sufficient.
Choice B
_________________
An IIM C Alumnus - Class of '94
GMAT Tutor at Wizako GMAT Classes & Online Courses
VP  P
Joined: 14 Feb 2017
Posts: 1214
Location: Australia
Concentration: Technology, Strategy
Schools: LBS '22
GMAT 1: 560 Q41 V26 GMAT 2: 550 Q43 V23 GMAT 3: 650 Q47 V33 GMAT 4: 650 Q44 V36 WE: Management Consulting (Consulting)
Does the integer g have a factor f such that 1 < f < g ?  [#permalink]

Show Tags

1
The question is really asking whether g is prime.

If g is prime then it will only have factors g and 1. If g is not prime then it will have factors besides g and 1.

Statement 1 is insufficient as there are multiple answers that could be prime/ non-prime.

Statement 2 is sufficient because
11!+11 and all the integers between up to 11!+2 all contain 11! which has all the factors of 11! i.e. 11x10x9x8...x3x2x1 such that adding any factor in range of 11! will only make the final number contain more factors of any given added number.

This plays out as follows:
If g=11!+11 then we can factor out 11, so g would be multiple of 11, thus not a prime;
If g=11!+10 then we can factor out 10, so g would be multiple of 10, thus not a prime;
If g=11!+9 then we can factor out 10, so g would be multiple of 9, thus not a prime;
If g=11!+8 then we can factor out 10, so g would be multiple of 8, thus not a prime;
If g=11!+7 then we can factor out 10, so g would be multiple of 7, thus not a prime;
If g=11!+6 then we can factor out 10, so g would be multiple of 6, thus not a prime;
If g=11!+5 then we can factor out 10, so g would be multiple of 5, thus not a prime;
If g=11!+4 then we can factor out 10, so g would be multiple of 4, thus not a prime;
If g=11!+3 then we can factor out 10, so g would be multiple of 3, thus not a prime;
If g=11!+2 then we can factor out 10, so g would be multiple of 2, thus not a prime;

Thus all numbers we can factor out contain a factor other than g and 1; thus g is not prime.

Excellent learnings from Brian, here: https://gmatclub.com/forum/if-x-is-an-i ... ml#p777801

Thus, statement 2 tells us g has more than g and 1 as its factors. Thus statement 2 is sufficient.
_________________
Goal: Q49, V41

+1 Kudos if I have helped you
SVP  P
Joined: 03 Jun 2019
Posts: 1746
Location: India
Does the integer g have a factor f such that 1 < f < g ?  [#permalink]

Show Tags

gupta87 wrote:
Does the integer g have a factor f such that 1 < f < g ?

(1) g > 3!
(2) 11! + 11 >= g >= 11! + 2

Does the integer g have a factor f such that 1 < f < g ?

(1) g > 3!
g>6
g= 7 NO
g=8 YES
NOT SUFFICIENT

(2) 11! + 11 >= g >= 11! + 2
If g= 11! + k where $$2 \leq k \leq 11$$
Then g will be divisible by k
SUFFICIENT

IMO B

Posted from my mobile device
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com Does the integer g have a factor f such that 1 < f < g ?   [#permalink] 18 Aug 2019, 19:07
Display posts from previous: Sort by

Does the integer g have a factor f such that 1 < f < g ?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  