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

 It is currently 21 Feb 2019, 14:05

### 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

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
• ### 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

# What is the greatest prime factor of 49^19 - 7^35

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 12 Aug 2015
Posts: 2621
Schools: Boston U '20 (M)
GRE 1: Q169 V154
What is the greatest prime factor of 49^19 - 7^35  [#permalink]

### Show Tags

03 Jan 2017, 10:40
2
00:00

Difficulty:

35% (medium)

Question Stats:

66% (01:26) correct 34% (01:14) wrong based on 93 sessions

### HideShow timer Statistics

What is the greatest prime factor of $$49^{19}-7^{35}$$

A) 2
B) 3
C) 7
D) 13
E) 19

_________________
Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: What is the greatest prime factor of 49^19 - 7^35  [#permalink]

### Show Tags

03 Jan 2017, 12:07
2
stonecold wrote:
What is the greatest prime factor of $$49^{19}-7^{35}$$
A)2
B)3
C)7
D)13
E)19

$$(7^2)^{19} - 7^{35} = 7^{38} - 7^{35} = 7^{35}(7^3 - 1) = 7^{35}*342 = 7^{35}*2*3^2*19$$

Manager
Joined: 21 Jul 2018
Posts: 141
What is the greatest prime factor of 49^19−7^35  [#permalink]

### Show Tags

27 Jan 2019, 21:17
What is the greatest prime factor of 49^19−7^35

A) 2
B) 3
C) 7
D) 13
E) 19
_________________

______________________________
Press +1 Kudos if my post helped you a little and help me to ulcock the tests Wish you all success

I'd appreciate learning about the grammatical errors in my posts

Please let me know if I'm wrong somewhere

VP
Joined: 09 Mar 2018
Posts: 1001
Location: India
Re: What is the greatest prime factor of 49^19−7^35  [#permalink]

### Show Tags

27 Jan 2019, 21:32
1
Gmatprep550 wrote:
What is the greatest prime factor of 49^19−7^35

A)2
B)3
C)7
D)13
E)19

I am not able to understand solution for this, can any one help

Would like to share my thoughts on this

$$49^{19}−7^{35}$$

Always reduce the terms in their lowest factors, said that

$$7^{2* 19} - 7^{35}$$

$$7^{35} ( 7^3 - 1)$$

$$7^{35}$$, will always have 7 has a factor

$$7^3 - 1$$, can be reduced to 342, which can be written as $$2 * 3^2 * 19$$

So out of this bunch 2,3,7 and 19

E is the largest prime number
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Math Expert
Joined: 02 Sep 2009
Posts: 53063
Re: What is the greatest prime factor of 49^19 - 7^35  [#permalink]

### Show Tags

27 Jan 2019, 22:36
Gmatprep550 wrote:
What is the greatest prime factor of 49^19−7^35

A) 2
B) 3
C) 7
D) 13
E) 19

Merging topics.

Please do not re-post existing questions. Also, do not re-post questions from here: https://gmatclub.com/forum/stonecold-s- ... 17160.html Thank you.
_________________
SVP
Joined: 18 Aug 2017
Posts: 1923
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: What is the greatest prime factor of 49^19 - 7^35  [#permalink]

### Show Tags

28 Jan 2019, 01:15
stonecold wrote:
What is the greatest prime factor of $$49^{19}-7^{35}$$

A) 2
B) 3
C) 7
D) 13
E) 19

$$49^{19}-7^{35}$$

7^35( 7^3-1)
7^35* 342
342= 2*3^2*19^1

so greatest prime factor
7^35 * 2*3^2*19^1

IMO E 19
_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

Re: What is the greatest prime factor of 49^19 - 7^35   [#permalink] 28 Jan 2019, 01:15
Display posts from previous: Sort by