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

 It is currently 22 Feb 2019, 07:28

### 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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# f(x)=(4x+1)(4x–3) for all positive integers x. Which of the following

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53069
f(x)=(4x+1)(4x–3) for all positive integers x. Which of the following  [#permalink]

### Show Tags

21 Dec 2017, 19:25
00:00

Difficulty:

65% (hard)

Question Stats:

51% (01:51) correct 49% (01:58) wrong based on 162 sessions

### HideShow timer Statistics

$$f(x)=(4x+1)(4x–3)$$ for all positive integers x. Which of the following cannot be a factor of f(x)?

I. 7
II. 16
III. 25

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

_________________
examPAL Representative
Joined: 07 Dec 2017
Posts: 890
f(x)=(4x+1)(4x–3) for all positive integers x. Which of the following  [#permalink]

### Show Tags

22 Dec 2017, 06:25
As it can often be hard to understand the rules underlying divisibility, we'll try a few numbers to see the pattern.
This is an Alternative approach.

Starting with x = 1, we get
5*1. Not divisible by 7,16 or 25.
9*5. Not divisible by 7,16 or 25.
13*9. Not divisible by 7,16 or 25.
17*13. Not divisible by 7,16 or 25.
21*17. Divisbile by 7!
25*21. Divisbile by 25!
So all we need to know is if f(x) can be divisible by 16.
Trying a few more options, we have
29*25
33*29
37*33
We've already tried quite a few numbers without finding one that is divisible by 16 so we should feel comfortable marking (B).
In fact, since neither of our numbers will ever be divisible by 4 (as they are 4x+1 and 4x-3), their product cannot be divisible by 16.
_________________
Retired Moderator
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
f(x)=(4x+1)(4x–3) for all positive integers x. Which of the following  [#permalink]

### Show Tags

22 Dec 2017, 10:38
1
Bunuel wrote:
$$f(x)=(4x+1)(4x–3)$$ for all positive integers x. Which of the following cannot be a factor of f(x)?

I. 7
II. 16
III. 25

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II, and III

Working through numbers has already been explained so here's an alternate approach

$$4x+1$$ & $$4x-3$$ are ODD as $$x$$ is an integer. Product of Odd numbers will not be divisible by Even number. So $$16$$ cannot be a factor of $$f(x)$$

So options A & D are out. Now I is present in options C & E, if we can eliminate I then the answer will be B.

if $$7$$ is a factor of $$f(x)$$, then either $$4x+1$$ or $$4x-3$$ has to be a multiple of $$7$$

so if, $$4x-1=7k => x=\frac{7k+1}{4}$$, where $$x$$ has to be an integer. clearly if $$k=1$$ then $$x=2$$, an integer

or $$4x-3=7k=> x=\frac{7k+3}{4}$$, if $$k=3$$ then $$x=6$$, an integer. So we can conclude $$7$$ can be a factor of $$f(x)$$

So we have eliminated Option A, C, D & E

---------------------------------------------------------

just to test $$25$$ as a factor of $$f(x)$$:

Now if $$4x+1=25 => x=6$$ an integer so $$25$$ can be a factor of $$4x+1$$. Similarly if $$4x-3=25=>x=7$$. hence $$25$$ can also be a factor of $$4x-3$$. so we know $$25$$ can be a factor of $$f(x)$$
Intern
Joined: 23 Nov 2016
Posts: 19
Re: f(x)=(4x+1)(4x–3) for all positive integers x. Which of the following  [#permalink]

### Show Tags

10 Oct 2018, 17:23
4X+1 is odd
4X-3 is odd

f(x)=odd*odd=odd

so 16 can not be a factor
Re: f(x)=(4x+1)(4x–3) for all positive integers x. Which of the following   [#permalink] 10 Oct 2018, 17:23
Display posts from previous: Sort by

# f(x)=(4x+1)(4x–3) for all positive integers x. Which of the following

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.