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

 It is currently 16 Feb 2019, 21:54

### 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 Algebra Webinar

February 17, 2019

February 17, 2019

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Free GMAT Strategy Webinar

February 16, 2019

February 16, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# If x = 2^74 - 2^70, what is the largest prime factor of x?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52902
If x = 2^74 - 2^70, what is the largest prime factor of x?  [#permalink]

### Show Tags

29 Aug 2018, 23:17
00:00

Difficulty:

15% (low)

Question Stats:

73% (00:46) correct 27% (00:55) wrong based on 117 sessions

### HideShow timer Statistics

If $$x = 2^{74} - 2^{70}$$, what is the largest prime factor of x?

A. 2
B. 3
C. 5
D. 7
E. 11

_________________
Intern
Joined: 28 Oct 2017
Posts: 32
Location: India
Schools: ISB '20 (WL), IIM (A)
GMAT 1: 640 Q47 V32
GMAT 2: 710 Q49 V38
Re: If x = 2^74 - 2^70, what is the largest prime factor of x?  [#permalink]

### Show Tags

29 Aug 2018, 23:32
2^74-2^70
= 2^70(2^4-1)
= 2^70 (16-1)
= 2^70*3*5

Hence, the largest prime factor is 5.

So, the correct answer is option (C).
Current Student
Joined: 19 Apr 2018
Posts: 5
Re: If x = 2^74 - 2^70, what is the largest prime factor of x?  [#permalink]

### Show Tags

30 Aug 2018, 00:13
x = 2^74 - 2^70
x = 2^70 ( 2^4 - 2^0)
x = 2^70 (16 - 1)
x = 2^70 * 15
x = 2^70 * 3^1 * 5^1
The largest prime factor is 5.
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 958
WE: Supply Chain Management (Energy and Utilities)
If x = 2^74 - 2^70, what is the largest prime factor of x?  [#permalink]

### Show Tags

30 Aug 2018, 00:47
Bunuel wrote:
If $$x = 2^{74} - 2^{70}$$, what is the largest prime factor of x?

A. 2
B. 3
C. 5
D. 7
E. 11

Given, $$x = 2^{74} - 2^{70}$$
Factor out the common term $$2^{70}$$,
$$x=2^{70}(2^4-1)=2^{70}*15$$
Prime factors are: 2,3,and 5
largest prime factor:5

Ans. (C)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

VP
Joined: 31 Oct 2013
Posts: 1116
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If x = 2^74 - 2^70, what is the largest prime factor of x?  [#permalink]

### Show Tags

30 Aug 2018, 05:41
Bunuel wrote:
If $$x = 2^{74} - 2^{70}$$, what is the largest prime factor of x?

A. 2
B. 3
C. 5
D. 7
E. 11

$$x = 2^{74} - 2^{70}$$

= $$2^{70}(2^4 - 1)$$

= $$2^{70} * 15$$

= $$2^{70} * 3*5$$

So, 5 is the greatest prime factor.

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4382
Location: India
GPA: 3.5
Re: If x = 2^74 - 2^70, what is the largest prime factor of x?  [#permalink]

### Show Tags

30 Aug 2018, 06:30
Bunuel wrote:
If $$x = 2^{74} - 2^{70}$$, what is the largest prime factor of x?

A. 2
B. 3
C. 5
D. 7
E. 11

$$x = 2^{74} - 2^{70}$$

Or, $$x = 2^{70}(2^4 - 1)$$

Or, $$x = 2^{70}(15)$$

Or, $$x = 2^{70}(3*5)$$, Thus the largest prime factor is 5, Answer must be (C)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2827
Re: If x = 2^74 - 2^70, what is the largest prime factor of x?  [#permalink]

### Show Tags

04 Sep 2018, 03:39
Bunuel wrote:
If $$x = 2^{74} - 2^{70}$$, what is the largest prime factor of x?

A. 2
B. 3
C. 5
D. 7
E. 11

We first factor 2^70 from both terms. Simplifying, we have:

2^70(2^4 - 1)

2^70 x 15

2^70 x 3 x 5

The largest prime factor is 5.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If x = 2^74 - 2^70, what is the largest prime factor of x?   [#permalink] 04 Sep 2018, 03:39
Display posts from previous: Sort by