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

 It is currently 24 Jan 2019, 03:34

### 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
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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Key Strategies to Master GMAT SC

January 26, 2019

January 26, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
• ### Free GMAT Number Properties Webinar

January 27, 2019

January 27, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.

# What is the greatest value of the positive integer p such that 2^p is

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52460
What is the greatest value of the positive integer p such that 2^p is  [#permalink]

### Show Tags

01 Apr 2018, 09:36
00:00

Difficulty:

25% (medium)

Question Stats:

67% (01:05) correct 33% (01:32) wrong based on 61 sessions

### HideShow timer Statistics

What is the greatest value of the positive integer p such that 2^p is a factor of 80^50?

(A) 4
(B) 10
(C) 50
(D) 100
(E) 200

_________________
Manager
Joined: 05 Feb 2016
Posts: 144
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: What is the greatest value of the positive integer p such that 2^p is  [#permalink]

### Show Tags

01 Apr 2018, 09:43
Bunuel wrote:
What is the greatest value of the positive integer p such that 2^p is a factor of 80^50?

(A) 4
(B) 10
(C) 50
(D) 100
(E) 200

80^50=(2^200*5^50)

so greatest value is 200

option E
VP
Joined: 31 Oct 2013
Posts: 1030
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
What is the greatest value of the positive integer p such that 2^p is  [#permalink]

### Show Tags

Updated on: 12 Aug 2018, 02:38
Bunuel wrote:
What is the greatest value of the positive integer p such that 2^p is a factor of 80^50?

(A) 4
(B) 10
(C) 50
(D) 100
(E) 200

we are asked to find the greatest value of the positive integer p. In order to find out the greatest value of p as a exponent of base 2 we have to factorize 80^50.

$$(2*2*2*2*5)^{50}$$
=$${(2^4)^{50}*5^{50}$$
=$$(2^{200} )*5^{50}$$

so,$$2^{200}$$shows that the greatest value of p. The correct answer is E.

Originally posted by selim on 06 Apr 2018, 12:39.
Last edited by selim on 12 Aug 2018, 02:38, edited 4 times in total.
Senior SC Moderator
Joined: 22 May 2016
Posts: 2376
What is the greatest value of the positive integer p such that 2^p is  [#permalink]

### Show Tags

07 Apr 2018, 11:15
Bunuel wrote:
What is the greatest value of the positive integer p such that 2^p is a factor of 80^50?

(A) 4
(B) 10
(C) 50
(D) 100
(E) 200

$$(ab)^{n} = a^{n}b^{n}$$
$$(a^{m})^{n}=a^{(m*n)}$$

Find prime factors of 80, raise to 50th power
$$80 = (2*2*2*2*5) = (2^4*5)$$
$$(2^4*5)^{50}=$$
$$(2^4)^{50}*5^{50}=$$
$$2^{200}5^{50}$$

5 to any power ends in 5. NEVER divisible by 2. The other factor of $$(80)^{50}=2^{200}$$

$$(80)^{50}=$$
$$(2^{200}*5^{50})=(2^{p}*5^{50})$$
$$2^{p}=2^{200}$$
$$p=200$$

There are 200 powers of 2 in $$(80)^{50}$$

Answer E

selim , I think there is a small typo in your answer: $$5^{200}$$
_________________

Sometimes at night I would sleep open-eyed underneath a sky dripping with stars.
I was alive then.

—Albert Camus

What is the greatest value of the positive integer p such that 2^p is &nbs [#permalink] 07 Apr 2018, 11:15
Display posts from previous: Sort by

# What is the greatest value of the positive integer p such that 2^p is

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

 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®.